Quantum Mechanical Clock and Classical Relativistic Clock
Hitoshi Kitada
2004-07-08T23:59:59.000Z
A cyclic nature of quantum mechanical clock is discussed as ``quantization of time." Quantum mechanical clock is seen to be equivalent to the relativistic classical clock.
Thermodynamic integration from classical to quantum mechanics
Habershon, Scott [Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS (United Kingdom); Manolopoulos, David E. [Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ (United Kingdom)
2011-12-14T23:59:59.000Z
We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.
"Einstein's Dream" - Quantum Mechanics as Theory of Classical Random Fields
Andrei Khrennikov
2012-04-22T23:59:59.000Z
This is an introductory chapter of the book in progress on quantum foundations and incompleteness of quantum mechanics. Quantum mechanics is represented as statistical mechanics of classical fields.
The equivalence principle in classical mechanics and quantum mechanics
Philip D. Mannheim
2000-04-03T23:59:59.000Z
We discuss our understanding of the equivalence principle in both classical mechanics and quantum mechanics. We show that not only does the equivalence principle hold for the trajectories of quantum particles in a background gravitational field, but also that it is only because of this that the equivalence principle is even to be expected to hold for classical particles at all.
Quantum Mechanics and Discrete Time from "Timeless" Classical Dynamics
H. -T. Elze
2003-07-03T23:59:59.000Z
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless'' reparametrization invariant model of a relativistic particle with two compactified extradimensions. In this example, discrete physical time is constructed based on quasi-local observables. - Generally, employing the path-integral formulation of classical mechanics developed by Gozzi et al., we show that these deterministic classical systems can be naturally described as unitary quantum mechanical models. The emergent quantum Hamiltonian is derived from the underlying classical one. It is closely related to the Liouville operator. We demonstrate in several examples the necessity of regularization, in order to arrive at quantum models with bounded spectrum and stable groundstate.
Classical and quantum-mechanical phase space distributions
Thomas Kiesel
2013-06-21T23:59:59.000Z
We examine the notion of nonclassicality in terms of quasiprobability distributions. In particular, we do not only ask if a specific quasiprobability can be interpreted as a classical probability density, but require that characteristic features of classical electrodynamics are resembled. We show that the only quasiprobabilities which correctly describe the superposition principle of classical electromagnetic fields are the $s$-parameterized quasiprobabilities. Furthermore, the Glauber-Sudarshan P function is the only quantum-mechanical quasiprobability which is transformed at a classical attenuator in the same way as a classical probability distribution. This result strengthens the definition of nonclassicality in terms of the P function, in contrast to possible definitions in terms of other quasiprobabilities.
Bell's Experiment in Quantum Mechanics and Classical Physics
Tom Rother
2013-08-21T23:59:59.000Z
Both the quantum mechanical and classical Bells experiment are within the focus of this paper. The fact that one measures different probabilities in both experiments is traced back to the superposition of two orthogonal but nonentangled substates in the quantum mechanical case. This superposition results in an interference term that can be splitted into two additional states representing a sink and a source of probabilities in the classical event space related to Bells experiment. As a consequence, a statistical operator can be related to the quantum mechanical Bells experiment that contains already negative quasi probabilities, as usually known from quantum optics in conjunction with the Glauber-Sudarshan equation. It is proven that the existence of such negative quasi probabilities are neither a sufficient nor a necessary condition for entanglement. The equivalence of using an interaction picture in a fixed basis or of employing a change of basis to describe Bells experiment is demonstrated afterwards. The discussion at the end of this paper regarding the application of the complementarity principle to the quantum mechanical Bells experiment is supported by very recent double slit experiments performed with polarization entangled photons.
Twisting all the way: From classical mechanics to quantum fields
Aschieri, Paolo [Centro Studi e Ricerche 'Enrico Fermi' Compendio Viminale, 00184 Rome (Italy); Dipartimento di Scienze e Tecnologie Avanzate, Universita del Piemonte Orientale, and INFN, Sezione di Torino Via Bellini 25/G 15100 Alessandria (Italy); Lizzi, Fedele; Vitale, Patrizia [Dipartimento di Scienze Fisiche, Universita di Napoli Federico II and INFN, Sezione di Napoli Monte S. Angelo, Via Cintia, 80126 Naples (Italy)
2008-01-15T23:59:59.000Z
We discuss the effects that a noncommutative geometry induced by a Drinfeld twist has on physical theories. We systematically deform all products and symmetries of the theory. We discuss noncommutative classical mechanics, in particular its deformed Poisson bracket and hence time evolution and symmetries. The twisting is then extended to classical fields, and then to the main interest of this work: quantum fields. This leads to a geometric formulation of quantization on noncommutative space-time, i.e., we establish a noncommutative correspondence principle from *-Poisson brackets to * commutators. In particular commutation relations among creation and annihilation operators are deduced.
A classical, elementary approach to the foundations of Quantum Mechanics
Rodriguez, David
2011-01-01T23:59:59.000Z
Perhaps Quantum Mechanics can be seen just as the simplest mathematical formalism where angular momentum (the magnitude of each of its three orthogonal projections) is by construction quantized: all possible values are taken from a discrete set. Indeed: (i) This idea finds support in very reasonable, completely classical physical arguments, if we place ourselves in the framework of Stochastic Electrodynamics (SED): there, all sustained periodic movement must satisfy a power balance that restricts the value of the average angular momentum, on each of its projections. (ii) It gives a natural explanation of the concept of "photon", as a constraint on the observable spectrum of energy-momentum exchanges between metastable physical states, in particular its discreteness. QM would be, in this picture, a semi-static theory, transparent to all the (micro)-dynamics taking place between apparently "discrete" events (transitions in the state of the system). For instance, (the magnitude of the projections of) quantum ang...
Lee, Sang-Bong
1993-09-01T23:59:59.000Z
Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaotic nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover`s and Kubo-Fox-Keizer`s approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty.
CO2 Adsorption in Fe2(dobdc): A Classical Force Field Parameterized from Quantum Mechanical
Paris-Sud XI, Université de
CO2 Adsorption in Fe2(dobdc): A Classical Force Field Parameterized from Quantum Mechanical : 10.1021/jp500313j #12;Abstract Carbon dioxide adsorption isotherms have been computed for the Metal derived from quantum mechanical calculations has been used to model adsorption isotherms within a MOF
On a Link between Classical Phenomenological Laws of Gases and Quantum Mechanics
Yarman, Tolga; Korfali, Onder
2008-01-01T23:59:59.000Z
In this paper we find a connection between the macroscopic classical laws of gases and the quantum mechanical description of molecules, composing an ideal gas. In such a gas, the motion of each individual molecule can be considered independently on all other molecules, and thus the macroscopic parameters of ideal gas, like pressure P and temperature T, can be introduced as a result of simple averaging over all individual motions of molecules. It is shown that for an ideal gas enclosed in a macroscopic cubic box of volume V, the constant, in the classical law of adiabatic expansion, i.e.PV^5/3=const, can be derived, based on quantum mechanics. Physical implications of the result we disclose are discussed. In any case, our finding proves, seemingly for the first time, a macroscopic manifestation of a quantum mechanical behavior, and this in relation to classical thermodynamics.
On a Link between Classical Phenomenological Laws of Gases and Quantum Mechanics
Tolga Yarman; Alexander Kholmetskii; Onder Korfali
2008-05-29T23:59:59.000Z
In this paper we find a connection between the macroscopic classical laws of gases and the quantum mechanical description of molecules, composing an ideal gas. In such a gas, the motion of each individual molecule can be considered independently on all other molecules, and thus the macroscopic parameters of ideal gas, like pressure P and temperature T, can be introduced as a result of simple averaging over all individual motions of molecules. It is shown that for an ideal gas enclosed in a macroscopic cubic box of volume V, the constant, in the classical law of adiabatic expansion, i.e.PV^5/3=const, can be derived, based on quantum mechanics. Physical implications of the result we disclose are discussed. In any case, our finding proves, seemingly for the first time, a macroscopic manifestation of a quantum mechanical behavior, and this in relation to classical thermodynamics.
Goddard III, William A.
crossing in reactions still lags far behind. Theoretical approaches to extracting the underlying chemicalCorrelation Analysis of Chemical Bonds (CACB) II: Quantum Mechanical Operators for Classical of the statistical covariance of the previous operator. Here the bonds correlation relates to bond exchange processes
Classical limits of quantum mechanics on a non-commutative configuration space
Benatti, Fabio [Department of Physics, University of Trieste and INFN, Sezione di Trieste, Strada Costiera 11, I-34051 Trieste (Italy)] [Department of Physics, University of Trieste and INFN, Sezione di Trieste, Strada Costiera 11, I-34051 Trieste (Italy); Gouba, Laure [The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I-34151 Trieste (Italy)] [The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I-34151 Trieste (Italy)
2013-06-15T23:59:59.000Z
We consider a model of non-commutative quantum mechanics given by two harmonic oscillators over a non-commutative two dimensional configuration space. We study possible ways of removing the non-commutativity based on the classical limit context known as anti-Wick quantization. We show that removal of non-commutativity from the configuration space and from the canonical operators is not commuting operation.
Le Roy, Robert J.
February 1998 Comparisons of classical and quantum Monte Carlo simulation of SF6 Ar n and SF6 Ne n clusters are used to examine whether certain novel types of behavior seen in classical simulations of SF6 Ar n and SF6 Kr n persist when quantum effects are taken into account. For mixed clusters formed
Matteo Villani
2009-07-28T23:59:59.000Z
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not contemplated by this function. Within this scheme, quantum mechanics, classical field theory and a quantum theory for scalar fields are discussed. As a by-product of the probabilistic scheme for classical field theory, the equations of the De Donder-Weyl theory for multi-dimensional variational problems are recovered.
Thermodynamics and equilibrium structure of Ne38 cluster: Quantum mechanics versus classical
Mandelshtam, Vladimir A.
. For example, although the heat capacity Cv T around the "solid-liquid" transition temperature T 10 K MC simulations are implemented in the parallel tempering framework. The classical heat capacity Cv do not play an essential role in the thermodynamics of Ne38, the quantum heat capacity
Quantum particles from classical statistics
C. Wetterich
2010-02-11T23:59:59.000Z
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs, however, between quantum and classical particles. We describe position, motion and correlations of a quantum particle in terms of observables in a classical statistical ensemble. On the other side, we also construct explicitly the quantum formalism with wave function and Hamiltonian for classical particles. For a suitable time evolution of the classical probabilities and a suitable choice of observables all features of a quantum particle in a potential can be derived from classical statistics, including interference and tunneling. Besides conceptual advances, the treatment of classical and quantum particles in a common formalism could lead to interesting cross-fertilization between classical statistics and quantum physics.
Arik, Metin; Kholmetskii, Alexander L
2009-01-01T23:59:59.000Z
Previously, we established a connection between the macroscopic classical laws of gases and the quantum mechanical description of molecules of an ideal gas (T. Yarman et al. arXiv:0805.4494). In such a gas, the motion of each molecule can be considered independently on all other molecules, and thus the macroscopic parameters of the ideal gas, like pressure P and temperature T, can be introduced as a result of simple averaging over all individual motions of the molecules. It was shown that for an ideal gas enclosed in a macroscopic cubic box of volume V, the constant, arising along with the classical law of adiabatic expansion, i.e. PV5/3=constant, can be explicitly derived based on quantum mechanics, so that the constant comes to be proportional to h^2/m; here h is the Planck Constant, and m is the relativistic mass of the molecule the gas is made of. In this article we show that the same holds for a photon gas, although the related setup is quite different than the previous ideal gas setup. At any rate, we c...
Fulvio Sbisa
2014-10-23T23:59:59.000Z
The aim of these notes is to provide a self-contained review of why it is generically a problem when a solution of a theory possesses ghost fields among the perturbation modes. We define what a ghost field is and we show that its presence is associated to a classical instability whenever the ghost field interacts with standard fields. We then show that the instability is more severe at quantum level, and that perturbative ghosts can exist only in low energy effective theories. However, if we don't consider very ad-hoc choices, compatibility with observational constraints implies that low energy effective ghosts can exist only at the price of giving up Lorentz-invariance or locality above the cut-off, in which case the cut-off has to be much lower that the energy scales we currently probe in particle colliders. We also comment on the possible role of extra degrees of freedom which break Lorentz-invariance spontaneously.
Exact Classical Correspondence in Quantum Cosmology
Moncy V. John
2014-05-30T23:59:59.000Z
We find a Friedmann model with appropriate matter/energy density such that the solution of the Wheeler-DeWitt equation exactly corresponds to the classical evolution. The well-known problems in quantum cosmology disappear in the resulting coasting evolution. The exact quantum-classical correspondence is demonstrated with the help of the de Broglie-Bohm and modified de Broglie-Bohm approaches to quantum mechanics. It is reassuring that such a solution leads to a robust model for the universe, which agrees well with cosmological expansion indicated by SNe Ia data.
The Classical and Quantum Mechanics of a Particle on a Knot
V. V. Sreedhar
2015-01-06T23:59:59.000Z
A free particle is constrained to move on a knot obtained by winding around a putative torus. The classical equations of motion for this system are solved in a closed form. The exact energy eigenspectrum, in the thin torus limit, is obtained by mapping the time-independent Schrodinger equation to the Mathieu equation. In the general case, the eigenvalue problem is described by the Hill equation. Finite-thickness corrections are incorporated perturbatively by truncating the Hill equation. Comparisons and contrasts between this problem and the well-studied problem of a particle on a circle (planar rigid rotor) are performed throughout.
Classical Resonances and Quantum Scarring
Christopher Manderfeld
2003-01-22T23:59:59.000Z
We study the correspondence between phase-space localization of quantum (quasi-)energy eigenstates and classical correlation decay, given by Ruelle-Pollicott resonances of the Frobenius-Perron operator. It will be shown that scarred (quasi-)energy eigenstates are correlated: Pairs of eigenstates strongly overlap in phase space (scar in same phase-space regions) if the difference of their eigenenergies is close to the phase of a leading classical resonance. Phase-space localization of quantum states will be measured by $L^2$ norms of their Husimi functions.
Relation of classical non-equilibrium dynamics and quantum annealing
Hidetosni Nishimori
2015-03-07T23:59:59.000Z
Non-equilibrium dynamics of the Ising model is a classical stochastic process whereas quantum mechanics has no stochastic elements in the classical sense. Nevertheless, it has been known that there exists a close formal relationship between these two processes. We reformulate this relationship and use it to compare the efficiency of simulated annealing that uses classical stochastic processes and quantum annealing to solve combinatorial optimization problems. It is shown that classical dynamics can be efficiently simulated by quantum-mechanical processes whereas the converse is not necessarily true. This may imply that quantum annealing may be regarded as a more powerful tool than simulated annealing for optimization problems.
Exploring Classically Chaotic Potentials with a Matter Wave Quantum Probe
Gattobigio, G. L. [Laboratoire de Collisions Agregats Reactivite, CNRS UMR 5589, IRSAMC, Universite de Toulouse (UPS), 118 Route de Narbonne, 31062 Toulouse CEDEX 4 (France); Laboratoire Kastler Brossel, Ecole Normale Superieure, 24 rue Lhomond, 75005 Paris (France); Couvert, A. [Laboratoire Kastler Brossel, Ecole Normale Superieure, 24 rue Lhomond, 75005 Paris (France); Georgeot, B. [Laboratoire de Physique Theorique (IRSAMC), Universite de Toulouse (UPS), 31062 Toulouse (France); CNRS, LPT UMR5152 (IRSAMC), 31062 Toulouse (France); Guery-Odelin, D. [Laboratoire de Collisions Agregats Reactivite, CNRS UMR 5589, IRSAMC, Universite de Toulouse (UPS), 118 Route de Narbonne, 31062 Toulouse CEDEX 4 (France)
2011-12-16T23:59:59.000Z
We study an experimental setup in which a quantum probe, provided by a quasimonomode guided atom laser, interacts with a static localized attractive potential whose characteristic parameters are tunable. In this system, classical mechanics predicts a transition from regular to chaotic behavior as a result of the coupling between the different degrees of freedom. Our experimental results display a clear signature of this transition. On the basis of extensive numerical simulations, we discuss the quantum versus classical physics predictions in this context. This system opens new possibilities for investigating quantum scattering, provides a new testing ground for classical and quantum chaos, and enables us to revisit the quantum-classical correspondence.
Quantum mechanical Carnot engine
Bender, C M; Meister, B K
2000-01-01T23:59:59.000Z
A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum-mechanical particle confined to a potential well. The efficiency of this engine is shown to equal the Carnot efficiency because quantum dynamics is reversible. The quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes that are close analogues of the corresponding classical processes.
Quantum mechanical Carnot engine
C. M. Bender; D. C. Brody; B. K. Meister
2000-07-03T23:59:59.000Z
A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum-mechanical particle confined to a potential well. The efficiency of this engine is shown to equal the Carnot efficiency because quantum dynamics is reversible. The quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes that are close analogues of the corresponding classical processes.
Quantum fields with classical perturbations
Derezi?ski, Jan, E-mail: Jan.Derezinski@fuw.edu.pl [Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Hoza 74, 00-682 Warszawa (Poland)
2014-07-15T23:59:59.000Z
The main purpose of these notes is a review of various models of Quantum Field Theory (QFT) involving quadratic Lagrangians. We discuss scalar and vector bosons, spin 1/2 fermions, both neutral and charged. Beside free theories, we study their interactions with classical perturbations, called, depending on the context, an external linear source, mass-like term, current or electromagnetic potential. The notes may serve as a first introduction to QFT.
X. Q. Huang
2006-04-04T23:59:59.000Z
We study the energy conversion laws of the macroscopic harmonic $LC $ oscillator, the electromagnetic wave (photon) and the hydrogen atom. As our analysis indicates that the energies of these apparently different systems obey exactly the same energy conversion law. Based on our results and the wave-particle duality of electron, we find that the atom in fact is a natural microscopic $LC$ oscillator. In the framework of classical electromagnetic field theory we analytically obtain, for the hydrogen atom, the quantized electron orbit radius. Without the adaptation of any other fundamental principles of quantum mechanics, we present a reasonable explanation of the polarization of photon, the Zeeman effect, Selection rules and Pauli exclusion principle. Particularly, it is found that a pairing Pauli electron can move closely and steadily in a DNA-like double helical electron orbit. Our results also reveal an essential connection between electron spin and the intrinsic helical movement of electron and indicate that the spin itself is the effect of quantum confinement. In addition, a possible physical mechanism of superconductivity and the deeper physical understandings of the electron mass, zero point energy, and the hardness property of electron are also provided. Finally, we show analytically that the Dirac's quantization of magnetic monopole is merely a special handed electron at absolute zero-temperature, which strongly suggests that any efforts to seek for the magneticmonopole in real space will be entirely in vain. Furthermore, it appears that the electron's spin and the magnetic monopole are actually two different concepts for one possible physical phenomenon.
Xi Kong; Mingjun Shi; Fazhan Shi; Pengfei Wang; Pu Huang; Qi Zhang; Chenyong Ju; Changkui Duan; Sixia Yu; Jiangfeng Du
2012-10-03T23:59:59.000Z
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for by some realistic models with hidden variables. There are, however, two powerful theorems against the hidden-variable theories showing that certain quantum features cannot be reproduced based on two rationale premises of locality, Bell's theorem, and noncontextuality, due to Bell, Kochen and Specker (BKS). Noncontextuality is independent of nonlocality, and the contextuality manifests itself even in a single object. Here we report an experimental verification of quantum contextuality by a single spin-1 electron system at room temperature. Such a three-level system is indivisible and then we close the compatibility loophole which exists in the experiments performed on bipartite systems. Our results confirm the quantum contextuality to be the intrinsic property of single particles.
Visualizing quantum mechanics in phase space
Heiko Bauke; Noya Ruth Itzhak
2011-01-11T23:59:59.000Z
We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner function formalism resembles the mathematical language of classical mechanics of non-interacting particles. Thus, it allows a more direct comparison between classical and quantum dynamical features.
Sudden transition between classical and quantum decoherence
L. Mazzola; J. Piilo; S. Maniscalco
2010-04-25T23:59:59.000Z
We study the dynamics of quantum and classical correlations in the presence of nondissipative decoherence. We discover a class of initial states for which the quantum correlations, quantified by the quantum discord, are not destroyed by decoherence for times t \\bar{t}, on the other hand, classical correlations do not change in time and only quantum correlations are lost due to the interaction with the environment. Therefore, at the transition time \\bar{t} the open system dynamics exhibits a sudden transition from classical to quantum decoherence regime.
Smets, Quentin; Verreck, Devin; Vandervorst, Wilfried; Groeseneken, Guido; Heyns, Marc M. [Imec, Kapeldreef 75, 3001 Heverlee (Belgium); KULeuven, 3001 Leuven (Belgium); Verhulst, Anne S.; Rooyackers, Rita; Merckling, Clément; Simoen, Eddy; Collaert, Nadine; Thean, Voon Y. [Imec, Kapeldreef 75, 3001 Heverlee (Belgium); Van De Put, Maarten; Sorée, Bart [Imec, Kapeldreef 75, 3001 Heverlee (Belgium); Universiteit Antwerpen, 2020 Antwerpen (Belgium)
2014-05-14T23:59:59.000Z
Promising predictions are made for III-V tunnel-field-effect transistor (FET), but there is still uncertainty on the parameters used in the band-to-band tunneling models. Therefore, two simulators are calibrated in this paper; the first one uses a semi-classical tunneling model based on Kane's formalism, and the second one is a quantum mechanical simulator implemented with an envelope function formalism. The calibration is done for In{sub 0.53}Ga{sub 0.47}As using several p+/intrinsic/n+ diodes with different intrinsic region thicknesses. The dopant profile is determined by SIMS and capacitance-voltage measurements. Error bars are used based on statistical and systematic uncertainties in the measurement techniques. The obtained parameters are in close agreement with theoretically predicted values and validate the semi-classical and quantum mechanical models. Finally, the models are applied to predict the input characteristics of In{sub 0.53}Ga{sub 0.47}As n- and p-lineTFET, with the n-lineTFET showing competitive performance compared to MOSFET.
Wigner spacing distribution in classical mechanics
Jamal Sakhr
2014-07-09T23:59:59.000Z
The Wigner spacing distribution has a long and illustrious history in nuclear physics and in the quantum mechanics of classically chaotic systems. In this paper, a long-overlooked connection between the Wigner distribution and classical chaos in two-degree-of-freedom (2D) conservative systems is introduced. In the specific context of fully chaotic 2D systems, the hypothesis that typical pseudotrajectories of a canonical Poincar\\'{e} map have a Wignerian nearest-neighbor spacing distribution (NNSD), is put forward and tested. Employing the 2D circular stadium billiard as a generic test case, the NNSD of a typical pseudotrajectory of the Birkhoff map is shown to be in excellent agreement with the Wigner distribution. The relevance of the higher-order Wigner surmises from random matrix theory are also illustrated.
Classicalization of Quantum Fluctuation in Inflationary Universe
H. Kubotani; T. Uesugi; M. Morikawa; A. Sugamoto
1997-01-20T23:59:59.000Z
We discuss the classicalization of a quantum state induced by an environment in the inflationary stage of the universe. The classicalization is necessary for the homogeneous ground sate to become classical non-homogeneous one accompanied with the statistical fluctuation, which is a plausible candidate for the seeds of structure formation. Using simple models, we show that i) the two classicalization criteria, the classical correlation and quantum decoherence, are simultaneously satisfied by the environment and that ii) the power spectrum of the resultant statistical fluctuation depends upon the detail of the classicalization process. Especially, the result ii) means that, taking account of the classicalization process, the inflationary scenario does not necessarily predict the unique spectrum which is usually believed.
Geometric Phase and Classical-Quantum Correspondence
Indubala I. Satija; Radha Balakrishnan
2004-03-05T23:59:59.000Z
We study the geometric phase factors underlying the classical and the corresponding quantum dynamics of a driven nonlinear oscillator exhibiting chaotic dynamics. For the classical problem, we compute the geometric phase factors associated with the phase space trajectories using Frenet-Serret formulation. For the corresponding quantum problem, the geometric phase associated with the time evolution of the wave function is computed. Our studies suggest that the classical geometric phase may be related to the the difference in the quantum geometric phases between two neighboring eigenstates.
Classical and Quantum Chaos in Atom Optics
Farhan Saif
2006-04-10T23:59:59.000Z
The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits dynamical localization and quantum recurrences.
Quantum Cryptography Approaching the Classical Limit
Weedbrook, Christian
We consider the security of continuous-variable quantum cryptography as we approach the classical limit, i.e., when the unknown preparation noise at the sender’s station becomes significantly noisy or thermal (even by as ...
Classical and quantum control in nanosystems
Rudner, Mark S. (Mark Spencer)
2008-01-01T23:59:59.000Z
The central claim of this thesis is that nanoscale devices offer a platform to study and demonstrate new forms of control over both quantum and classical degrees of freedom in solid-state systems. To support this claim, I ...
Quantum feedback control and classical control theory
Doherty, Andrew C. [Department of Physics, University of Auckland, Private Bag 92019, Auckland, (New Zealand)] [Department of Physics, University of Auckland, Private Bag 92019, Auckland, (New Zealand); Habib, Salman [Theoretical Division, T-8, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)] [Theoretical Division, T-8, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Jacobs, Kurt [Theoretical Division, T-8, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)] [Theoretical Division, T-8, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Mabuchi, Hideo [Norman Bridge Laboratory of Physics 12-33, California Institute of Technology, Pasadena, California 91125 (United States)] [Norman Bridge Laboratory of Physics 12-33, California Institute of Technology, Pasadena, California 91125 (United States); Tan, Sze M. [Department of Physics, University of Auckland, Private Bag 92019, Auckland, (New Zealand)] [Department of Physics, University of Auckland, Private Bag 92019, Auckland, (New Zealand)
2000-07-01T23:59:59.000Z
We introduce and discuss the problem of quantum feedback control in the context of established formulations of classical control theory, examining conceptual analogies and essential differences. We describe the application of state-observer-based control laws, familiar in classical control theory, to quantum systems and apply our methods to the particular case of switching the state of a particle in a double-well potential. (c) 2000 The American Physical Society.
Statistical mechanics of Yang-Mills classical mechanics
Bannur, Vishnu M. [Department of Physics, University of Calicut, Kerala-673 635 (India)
2005-08-01T23:59:59.000Z
Statistical mechanics (SM) of Yang-Mills classical mechanics is studied by using a toy model that resembles chaotic quartic oscillators. This nonlinear system attains the thermodynamic equilibrium not by collisions, which is generally assumed in SM, but by chaotic dynamics. This is a new mechanism of thermalization that may be relevent to the quark-gluon plasma (QGP) formation in relativistic heavy-ion collisions because the interactions governing QGP involve quantum chromodynamics (QCD), which is a Yang-Mills theory [SU(3)]. The thermalization time is estimated from the Lyapunov exponent. The Lyapunov exponent is evaluated using the recently developed monodromy matrix method. We also discuss the physical meaning of thermalization and SM in this system of few degrees in terms of chromo-electric and chromomagnetic fields. One of the consequence of thermalization, such as equipartition of energy and dynamical temperature, is also numerically verified.
Trading classical and quantum computational resources
Sergey Bravyi; Graeme Smith; John Smolin
2015-06-03T23:59:59.000Z
We propose examples of a hybrid quantum-classical simulation where a classical computer assisted by a small quantum processor can efficiently simulate a larger quantum system. First we consider sparse quantum circuits such that each qubit participates in O(1) two-qubit gates. It is shown that any sparse circuit on n+k qubits can be simulated by sparse circuits on n qubits and a classical processing that takes time $2^{O(k)} poly(n)$. Secondly, we study Pauli-based computation (PBC) where allowed operations are non-destructive eigenvalue measurements of n-qubit Pauli operators. The computation begins by initializing each qubit in the so-called magic state. This model is known to be equivalent to the universal quantum computer. We show that any PBC on n+k qubits can be simulated by PBCs on n qubits and a classical processing that takes time $2^{O(k)} poly(n)$. Finally, we propose a purely classical algorithm that can simulate a PBC on n qubits in a time $2^{c n} poly(n)$ where $c\\approx 0.94$. This improves upon the brute-force simulation method which takes time $2^n poly(n)$. Our algorithm exploits the fact that n-fold tensor products of magic states admit a low-rank decomposition into n-qubit stabilizer states.
Mirror-induced decoherence in hybrid quantum-classical theory
Aniello Lampo; Lorenzo Fratino; Hans-Thomas Elze
2014-10-16T23:59:59.000Z
We re-analyse the optomechanical interferometer experiment proposed by Marshall, Simon, Penrose and Bouwmeester with the help of a recently developed quantum-classical hybrid theory. This leads to an alternative evaluation of the mirror induced decoherence. Surprisingly, we find that it behaves essentially in the same way for suitable initial conditions and experimentally relevant parameters, no matter whether the mirror is considered a classical or quantum mechanical object. We discuss the parameter ranges where this result holds and possible implications for a test of spontaneous collapse models, for which this experiment has been designed.
Distinguishing quantum and classical transport through nanostructures
Neill Lambert; Clive Emary; Yueh-Nan Chen; Franco Nori
2010-08-23T23:59:59.000Z
We consider the question of how to distinguish quantum from classical transport through nanostructures. To address this issue we have derived two inequalities for temporal correlations in nonequilibrium transport in nanostructures weakly coupled to leads. The first inequality concerns local charge measurements and is of general validity; the second concerns the current flow through the device and is relevant for double quantum dots. Violation of either of these inequalities indicates that physics beyond that of a classical Markovian model is occurring in the nanostructure.
Classical Control of Large-Scale Quantum Computers
Simon J. Devitt
2014-05-20T23:59:59.000Z
The accelerated development of quantum technology has reached a pivotal point. Early in 2014, several results were published demonstrating that several experimental technologies are now accurate enough to satisfy the requirements of fault-tolerant, error corrected quantum computation. While there are many technological and experimental issues that still need to be solved, the ability of experimental systems to now have error rates low enough to satisfy the fault-tolerant threshold for several error correction models is a tremendous milestone. Consequently, it is now a good time for the computer science and classical engineering community to examine the {\\em classical} problems associated with compiling quantum algorithms and implementing them on future quantum hardware. In this paper, we will review the basic operational rules of a topological quantum computing architecture and outline one of the most important classical problems that need to be solved; the decoding of error correction data for a large-scale quantum computer. We will endeavour to present these problems independently from the underlying physics as much of this work can be effectively solved by non-experts in quantum information or quantum mechanics.
Homological Error Correction: Classical and Quantum Codes
H. Bombin; M. A. Martin-Delgado
2006-05-10T23:59:59.000Z
We prove several theorems characterizing the existence of homological error correction codes both classically and quantumly. Not every classical code is homological, but we find a family of classical homological codes saturating the Hamming bound. In the quantum case, we show that for non-orientable surfaces it is impossible to construct homological codes based on qudits of dimension $D>2$, while for orientable surfaces with boundaries it is possible to construct them for arbitrary dimension $D$. We give a method to obtain planar homological codes based on the construction of quantum codes on compact surfaces without boundaries. We show how the original Shor's 9-qubit code can be visualized as a homological quantum code. We study the problem of constructing quantum codes with optimal encoding rate. In the particular case of toric codes we construct an optimal family and give an explicit proof of its optimality. For homological quantum codes on surfaces of arbitrary genus we also construct a family of codes asymptotically attaining the maximum possible encoding rate. We provide the tools of homology group theory for graphs embedded on surfaces in a self-contained manner.
Classical Theorems in Noncommutative Quantum Field Theory
M. Chaichian; M. Mnatsakanova; A. Tureanu; Yu. Vernov
2006-12-12T23:59:59.000Z
Classical results of the axiomatic quantum field theory - Reeh and Schlieder's theorems, irreducibility of the set of field operators and generalized Haag's theorem are proven in SO(1,1) invariant quantum field theory, of which an important example is noncommutative quantum field theory. In SO(1,3) invariant theory new consequences of generalized Haag's theorem are obtained. It has been proven that the equality of four-point Wightman functions in two theories leads to the equality of elastic scattering amplitudes and thus the total cross-sections in these theories.
Kreis, Karsten; Donadio, Davide; Kremer, Kurt; Potestio, Raffaello
2015-01-01T23:59:59.000Z
In computer simulations, quantum delocalization of atomic nuclei can be modeled making use of the Path Integral (PI) formulation of quantum statistical mechanics. This approach, however, comes with a large computational cost. By restricting the PI modeling to a small region of space, this cost can be significantly reduced. In the present work we derive a Hamiltonian formulation for a bottom-up, theoretically solid simulation protocol that allows molecules to change their resolution from quantum-mechanical to classical and vice versa on the fly, while freely diffusing across the system. This approach renders possible simulations of quantum systems at constant chemical potential. The validity of the proposed scheme is demonstrated by means of simulations of low temperature parahydrogen. Potential future applications include simulations of biomolecules, membranes, and interfaces.
Kowalevski top in quantum mechanics
Matsuyama, A., E-mail: spamatu@ipc.shizuoka.ac.jp
2013-09-15T23:59:59.000Z
The quantum mechanical Kowalevski top is studied by the direct diagonalization of the Hamiltonian. The spectra show different behaviors depending on the region divided by the bifurcation sets of the classical invariant tori. Some of these spectra are nearly degenerate due to the multiplicity of the invariant tori. The Kowalevski top has several symmetries and symmetry quantum numbers can be assigned to the eigenstates. We have also carried out the semiclassical quantization of the Kowalevski top by the EBK formulation. It is found that the semiclassical spectra are close to the exact values, thus the eigenstates can be also labeled by the integer quantum numbers. The symmetries of the system are shown to have close relations with the semiclassical quantum numbers and the near-degeneracy of the spectra. -- Highlights: •Quantum spectra of the Kowalevski top are calculated. •Semiclassical quantization is carried out by the EBK formulation. •Quantum states are labeled by the semiclassical integer quantum numbers. •Multiplicity of the classical torus makes the spectra nearly degenerate. •Symmetries, quantum numbers and near-degenerate spectra are closely related.
On Quantum and Classical BCH Codes
Salah A. Aly; Andreas Klappenecker; Pradeep Kiran Sarvepalli
2006-04-14T23:59:59.000Z
Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes; this correspondence studies the properties of such codes. It is shown that a BCH code of length n can contain its dual code only if its designed distance d=O(sqrt(n)), and the converse is proved in the case of narrow-sense codes. Furthermore, the dimension of narrow-sense BCH codes with small design distance is completely determined, and - consequently - the bounds on their minimum distance are improved. These results make it possible to determine the parameters of quantum BCH codes in terms of their design parameters.
Is Fresnel Optics Quantum Mechanics in Phase Space?
O. Crasser; H. Mack; W. P. Schleich
2004-02-17T23:59:59.000Z
We formulate and argue in favor of the following conjecture: There exists an intimate connection between Wigner's quantum mechanical phase space distribution function and classical Fresnel optics.
Topological mechanisms as classical spinor fields
Vincenzo Vitelli; Nitin Upadhyaya; Bryan Gin-ge Chen
2014-07-11T23:59:59.000Z
A mechanism is a zero-energy motion of a mechanical structure that does not stretch or compress any of its components. Here, we focus on a special class of mechanisms that we dub topological because they are insensitive to smooth changes in material parameters. Topological mechanisms do not arise from local under-coordination, but they can be localized to solitons in the underlying structure. In this letter, we exploit supersymmetry to develop a real-space formalism whereby a topological mechanism can be described as a classical spinor whose real components are the soliton-induced displacement and stress fields. Our analytical approach goes beyond topological band theory by addressing the non-linearity and inhomogeneity of the underlying structure key to the very definition of a mechanism. We apply this general method to an activated mechanism, inspired by the organic molecule polyacetylene, that can propagate down an assembly line without deploying the whole structure.
Computational costs of data definition at the quantum - classical interface
Chris Fields
2010-05-26T23:59:59.000Z
Model-independent semantic requirements for user specification and interpretation of data before and after quantum computations are characterized. Classical computational costs of assigning classical data values to quantum registers and to run-time parameters passed across a classical-to-quantum application programming interface are derived. It is shown that the classical computational costs of data definition equal or exceed the classical computational cost of solving the problem of interest for all applications of quantum computing except computations defined over the integers and the simulation of linear systems with linear boundary conditions.
How Quantum is the Classical World?
Schmid, Gary Bruno
2011-01-01T23:59:59.000Z
It has been experimentally confirmed that quantum physical phenomena can violate the Information Bell Inequalities. A violation of the one or the other of these Information Bell Inequalites is equivalent to a violation of local realism meaning that either objectivity or locality, or both, do not hold for the phenomena under investigation. We propose (1) an experimental design for carrying out classical measurements in the absence of ontological complementarity; (2) a rational way to extract epistemologically complementary (pseudocomplementary) data from it; (3) a statistical approach which can reject stochastic and/or suspected violations of local realism in measurements of such data.
Displacement Echoes: Classical Decay and Quantum Freeze
Cyril Petitjean; Diego V. Bevilaqua; Eric J. Heller; Philippe Jacquod
2007-04-23T23:59:59.000Z
Motivated by neutron scattering experiments, we investigate the decay of the fidelity with which a wave packet is reconstructed by a perfect time-reversal operation performed after a phase space displacement. In the semiclassical limit, we show that the decay rate is generically given by the Lyapunov exponent of the classical dynamics. For small displacements, we additionally show that, following a short-time Lyapunov decay, the decay freezes well above the ergodic value because of quantum effects. Our analytical results are corroborated by numerical simulations.
Displacement Echoes: Classical Decay and Quantum Freeze
Petitjean, Cyril [Departement de Physique Theorique, Universite de Geneve, CH-1211 Geneva 4 (Switzerland); Bevilaqua, Diego V. [Department of Physics, Harvard University, Cambridge, Massachusetts 02138 (United States); Heller, Eric J. [Department of Physics, Harvard University, Cambridge, Massachusetts 02138 (United States); Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138 (United States); Jacquod, Philippe [Physics Department, University of Arizona, Tucson, Arizona 85721 (United States)
2007-04-20T23:59:59.000Z
Motivated by neutron scattering experiments, we investigate the decay of the fidelity with which a wave packet is reconstructed by a perfect time-reversal operation performed after a phase-space displacement. In the semiclassical limit, we show that the decay rate is generically given by the Lyapunov exponent of the classical dynamics. For small displacements, we additionally show that, following a short-time Lyapunov decay, the decay freezes well above the ergodic value because of quantum effects. Our analytical results are corroborated by numerical simulations.
Adding quantum effects to the semi-classical molecular dynamics simulations
Yang, Siyang
2011-01-01T23:59:59.000Z
Simulating the molecular dynamics (MD) using classical or semi-classical trajectories provides important details for the understanding of many chemical reactions, protein folding, drug design, and solvation effects. MD simulations using trajectories have achieved great successes in the computer simulations of various systems, but it is difficult to incorporate quantum effects in a robust way. Therefore, improving quantum wavepacket dynamics and incorporating nonadiabatic transitions and quantum effects into classical and semi-classical molecular dynamics is critical as well as challenging. In this paper, we present a MD scheme in which a new set of equations of motion (EOM) are proposed to effectively propagate nuclear trajectories while conserving quantum mechanical energy which is critical for describing quantum effects like tunneling. The new quantum EOM is tested on a one-state one-dimensional and a two-state two-dimensional model nonadiabatic systems. The global quantum force experienced by each trajecto...
Lessons from Classical Gravity about the Quantum Structure of Spacetime
Padmanabhan, T
2010-01-01T23:59:59.000Z
I present the theoretical evidence which suggests that gravity is an emergent phenomenon like gas dynamics or elasticity with the gravitational field equations having the same status as, say, the equations of fluid dynamics/elasticity. This paradigm views a wide class of gravitational theories - including Einstein's theory - as describing the thermodynamic limit of the statistical mechanics of "atoms of spacetime". The evidence for this paradigm is hidden in several classical features of the gravitational theories and depends on just one quantum mechanical input, viz. the existence of Davies-Unruh temperature of horizons. I discuss several conceptual ingredients of this approach.
Lessons from Classical Gravity about the Quantum Structure of Spacetime
T. Padmanabhan
2011-01-22T23:59:59.000Z
I present the theoretical evidence which suggests that gravity is an emergent phenomenon like gas dynamics or elasticity with the gravitational field equations having the same status as, say, the equations of fluid dynamics/elasticity. This paradigm views a wide class of gravitational theories - including Einstein's theory - as describing the thermodynamic limit of the statistical mechanics of "atoms of spacetime". The evidence for this paradigm is hidden in several classical features of the gravitational theories and depends on just one quantum mechanical input, viz. the existence of Davies-Unruh temperature of horizons. I discuss several conceptual ingredients of this approach.
Decoherence Control in Open Quantum System via Classical Feedback
Narayan Ganesan; Tzyh Jong Tarn
2006-11-29T23:59:59.000Z
In this work we propose a novel strategy using techniques from systems theory to completely eliminate decoherence and also provide conditions under which it can be done so. A novel construction employing an auxiliary system, the bait, which is instrumental to decoupling the system from the environment is presented. Our approach to decoherence control in contrast to other approaches in the literature involves the bilinear input affine model of quantum control system which lends itself to various techniques from classical control theory, but with non-trivial modifications to the quantum regime. The elegance of this approach yields interesting results on open loop decouplability and Decoherence Free Subspaces(DFS). Additionally, the feedback control of decoherence may be related to disturbance decoupling for classical input affine systems, which entails careful application of the methods by avoiding all the quantum mechanical pitfalls. In the process of calculating a suitable feedback the system has to be restructured due to its tensorial nature of interaction with the environment, which is unique to quantum systems. The results are qualitatively different and superior to the ones obtained via master equations. Finally, a methodology to synthesize feedback parameters itself is given, that technology permitting, could be implemented for practical 2-qubit systems to perform decoherence free Quantum Computing.
Quantum to Classical Transition in a Single-Ion Laser
François Dubin; Carlos Russo; Helena G. Barros; Andreas Stute; Christoph Becher; Piet O. Schmidt; Rainer Blatt
2010-02-18T23:59:59.000Z
Stimulated emission of photons from a large number of atoms into the mode of a strong light field is the principle mechanism for lasing in "classical" lasers. The onset of lasing is marked by a threshold which can be characterised by a sharp increase in photon flux as a function of external pumping strength. The same is not necessarily true for the fundamental building block of a laser: a single trapped atom interacting with a single optical radiation mode. It has been shown that such a "quantum" laser can exhibit thresholdless lasing in the regime of strong coupling between atom and radiation field. However, although theoretically predicted, a threshold at the single-atom level could not be experimentally observed so far. Here, we demonstrate and characterise a single-atom laser with and without threshold behaviour by changing the strength of atom-light field coupling. We observe the establishment of a laser threshold through the accumulation of photons in the optical mode even for a mean photon number substantially lower than for the classical case. Furthermore, self-quenching occurs for very strong external pumping and constitutes an intrinsic limitation of single-atom lasers. Moreover, we find that the statistical properties of the emitted light can be adjusted for weak external pumping, from the quantum to the classical domain. Our observations mark an important step towards fundamental understanding of laser operation in the few-atom limit including systems based on semiconductor quantum dots or molecules.
Quantum and classical coin-flipping protocols based on bit ...
2015-04-22T23:59:59.000Z
Apr 22, 2015 ... Concerning security analysis, we use the classical point games to prove that .... The first few proposals for quantum information processing,.
Generic Quantum Ratchet Accelerator with Full Classical Chaos
Jiangbin Gong; Paul Brumer
2006-09-05T23:59:59.000Z
A simple model of quantum ratchet transport that can generate unbounded linear acceleration of the quantum ratchet current is proposed, with the underlying classical dynamics fully chaotic. The results demonstrate that generic acceleration of quantum ratchet transport can occur with any type of classical phase space structure. The quantum ratchet transport with full classical chaos is also shown to be very robust to noise due to the large linear acceleration afforded by the quantum dynamics. One possible experiment allowing observation of these predictions is suggested.
Probable Inference and Quantum Mechanics
Grandy, W. T. Jr. [Department of Physics and Astronomy, University of Wyoming, Laramie, WY 82070 (United States)
2009-12-08T23:59:59.000Z
In its current very successful interpretation the quantum theory is fundamentally statistical in nature. Although commonly viewed as a probability amplitude whose (complex) square is a probability, the wavefunction or state vector continues to defy consensus as to its exact meaning, primarily because it is not a physical observable. Rather than approach this problem directly, it is suggested that it is first necessary to clarify the precise role of probability theory in quantum mechanics, either as applied to, or as an intrinsic part of the quantum theory. When all is said and done the unsurprising conclusion is that quantum mechanics does not constitute a logic and probability unto itself, but adheres to the long-established rules of classical probability theory while providing a means within itself for calculating the relevant probabilities. In addition, the wavefunction is seen to be a description of the quantum state assigned by an observer based on definite information, such that the same state must be assigned by any other observer based on the same information, in much the same way that probabilities are assigned.
Black holes: interfacing the classical and the quantum
B. P. Kosyakov
2007-07-18T23:59:59.000Z
The central idea advocated in this paper is that {forming the black hole horizon is attended with transition from the classical regime of evolution to the quantum one}. We justify the following criterion for discriminating between the classical and the quantum: {spontaneous creations and annihilations of particle-antiparticle pairs are impossible in the classical world but possible in the quantum world}. We show that it is sufficient to {change the overall sign of the spacetime signature in the classical picture of field propagation for it to be treated as its associated quantum picture}. To describe a self-gravitating object at the last stage of its classical evolution, we propose to use the Foldy--Wouthuysen representation of the Dirac equation in curved spacetimes, and the Gozzi classical path integral. In both approaches, maintaining the dynamics in the classical regime is controlled by supersymmetry.
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D. [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)] [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)
2013-10-15T23:59:59.000Z
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q? 1. The main characteristic of this field theory consists on the fact that besides the usual ?(x(vector sign),t), a new field ?(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field ?(x(vector sign),t), which is defined by means of an additional equation, becomes ?{sup *}(x(vector sign),t) only when q? 1. The solutions for the fields ?(x(vector sign),t) and ?(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Entanglement dynamics in a quantum-classical hybrid of two q-bits and one oscillator
L. Fratino; A. Lampo; H. -T. Elze
2014-08-05T23:59:59.000Z
We investigate new features, especially of entanglement dynamics, which arise in a quantum-classical hybrid. As a model, we study the coupling between two quantum mechanical two-level systems, i.e. two q-bits, and a classical harmonic oscillator. Their interaction is described by a hybrid coupling, in accordance with a recently developed quantum-classical hybrid theory. We discuss various situations in which entanglement of the q-bits does (not) evolve. Furthermore, we point out an experimental application in a hybrid cooling scheme and indicate topics for future study.
Quantum Calabi-Yau and Classical Crystals
Andrei Okounkov; Nikolai Reshetikhin; Cumrun Vafa
2003-11-11T23:59:59.000Z
We propose a new duality involving topological strings in the limit of large string coupling constant. The dual is described in terms of a classical statistical mechanical model of crystal melting, where the temperature is inverse of the string coupling constant. The crystal is a discretization of the toric base of the Calabi-Yau with lattice length $g_s$. As a strong evidence for this duality we recover the topological vertex in terms of the statistical mechanical probability distribution for crystal melting. We also propose a more general duality involving the dimer problem on periodic lattices and topological A-model string on arbitrary local toric threefolds. The $(p,q)$ 5-brane web, dual to Calabi-Yau, gets identified with the transition regions of rigid dimer configurations.
Classical and quantum pumping in closed systems Doron Cohen*
Cohen, Doron
Classical and quantum pumping in closed systems Doron Cohen* Department of Physics, Ben 17 December 2004 by M. Heiblum Available online 6 January 2005 Abstract Pumping of charge (Q for classical dissipative pumping, classical adiabatic pumping, and in particular we make an explicit
Cosmological fluctuations: Comparing Quantum and Classical Statistical and Stringy Effects
de Alwis, S P
2015-01-01T23:59:59.000Z
The theory of cosmological fluctuations assumes that the pre-inflationary state of the universe was the quantum vacuum of a scalar field(s) coupled to gravity. The observed cosmic microwave background fluctuations are then interpreted as quantum fluctuations. Here we consider alternate interpretations of the classic calculations of scalar and tensor power spectra by replacing the quantum vacuum with a classical statistical distribution, and suggest a way of distinguishing the quantum from the classical alternatives. The possibility that the latter is governed by a fundamental length scale as in string theory is also explored.
Statistical Mechanics and Quantum Cosmology
B. L. Hu
1995-11-29T23:59:59.000Z
Statistical mechanical concepts and processes such as decoherence, correlation, and dissipation can prove to be of basic importance to understanding some fundamental issues of quantum cosmology and theoretical physics such as the choice of initial states, quantum to classical transition and the emergence of time. Here we summarize our effort in 1) constructing a unified theoretical framework using techniques in interacting quantum field theory such as influence functional and coarse-grained effective action to discuss the interplay of noise, fluctuation, dissipation and decoherence; and 2) illustrating how these concepts when applied to quantum cosmology can alter the conventional views on some basic issues. Two questions we address are 1) the validity of minisuperspace truncation, which is usually assumed without proof in most discussions, and 2) the relevance of specific initial conditions, which is the prevailing view of the past decade. We also mention how some current ideas in chaotic dynamics, dissipative collective dynamics and complexity can alter our view of the quantum nature of the universe.
Accounting for Classical Hardware in the Control of Quantum Devices
Ian N. Hincks; Christopher Granade; Troy W. Borneman; D. G. Cory
2014-09-29T23:59:59.000Z
High fidelity coherent control of quantum systems is critical to building quantum devices and quantum computers. We provide a general optimal control framework for designing control sequences that account for hardware control distortions while maintaining robustness to environmental noise. We demonstrate the utility of our algorithm by presenting examples of robust quantum gates optimized in the presence of nonlinear distortions. We show that nonlinear classical controllers do not necessarily incur additional computational cost to pulse optimization, enabling more powerful quantum devices.
Testing foundations of quantum mechanics with photons
Peter Shadbolt; Jonathan C. F. Matthews; Anthony Laing; Jeremy L. O'Brien
2015-01-15T23:59:59.000Z
The foundational ideas of quantum mechanics continue to give rise to counterintuitive theories and physical effects that are in conflict with a classical description of Nature. Experiments with light at the single photon level have historically been at the forefront of tests of fundamental quantum theory and new developments in photonics engineering continue to enable new experiments. Here we review recent photonic experiments to test two foundational themes in quantum mechanics: wave-particle duality, central to recent complementarity and delayed-choice experiments; and Bell nonlocality where recent theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different photonics experiments.
Quantum size effects in classical hadrodynamics
Nix, J.R.
1994-03-01T23:59:59.000Z
The author discusses future directions in the development of classical hydrodynamics for extended nucleons, corresponding to nucleons of finite size interacting with massive meson fields. This new theory provides a natural covariant microscopic approach to relativistic nucleus-nucleus collisions that includes automatically spacetime nonlocality and retardation, nonequilibrium phenomena, interactions among all nucleons, and particle production. The present version of the theory includes only the neutral scalar ({sigma}) and neutral vector ({omega}) meson fields. In the future, additional isovector pseudoscalar ({pi}{sup +}, {pi}{sup {minus}}, {pi}{sup 0}), isovector vector ({rho}{sup +}, {rho}{sup {minus}}, {rho}{sup 0}), and neutral pseudoscalar ({eta}) meson fields should be incorporated. Quantum size effects should be included in the equations of motion by use of the spreading function of Moniz and Sharp, which generates an effective nucleon mass density smeared out over a Compton wavelength. However, unlike the situation in electrodynamics, the Compton wavelength of the nucleon is small compared to its radius, so that effects due to the intrinsic size of the nucleon dominate.
Quantum Error Correcting Subsystem Codes From Two Classical Linear Codes
Dave Bacon; Andrea Casaccino
2006-10-17T23:59:59.000Z
The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most general method for encoding quantum information is to encode it into a subsystem, there exists a novel form of quantum error correction beyond the traditional quantum error correcting subspace codes. These new quantum error correcting subsystem codes differ from subspace codes in that their quantum correcting routines can be considerably simpler than related subspace codes. Here we present a class of quantum error correcting subsystem codes constructed from two classical linear codes. These codes are the subsystem versions of the quantum error correcting subspace codes which are generalizations of Shor's original quantum error correcting subspace codes. For every Shor-type code, the codes we present give a considerable savings in the number of stabilizer measurements needed in their error recovery routines.
Quantum Mechanical Coherence, Resonance, and Mind
Henry P. Stapp
1995-04-04T23:59:59.000Z
Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a role in nature that is causally interactive and effective, rather than purely epiphenomenal, as required by classical mechanics. The mathematical basis of this suggestion is described here, and it is then shown how, by giving mind this efficacious role in natural process, the classical character of our perceptions of the quantum universe can be seen to be a consequence of evolutionary pressures for the survival of the species.
Quantum Leap Quantum Mechanics' Killer App
Bigelow, Stephen
Quantum Leap Quantum Mechanics' Killer App Q&A with Craig Hawker Director of the Materials Research. Q&A with Craig Hawker LEAP The Materials Research Laboratory is the only Wes
Quantum ballistic evolution in quantum mechanics: Application to quantum computers
Benioff, P. [Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States)] [Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States)
1996-08-01T23:59:59.000Z
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single-step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators {ital T} is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e., motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem which gives necessary and sufficient conditions that {ital T} must satisfy so that there exists a Hamiltonian description of quantum ballistic evolution for the process, namely, that {ital T} is a partial isometry and is orthogonality preserving and stable on some basis. Simple examples of quantum ballistic evolution for quantum Turing machines with one and with more than one type of elementary step are discussed. It is seen that for nondeterministic machines the basis set can be quite complex with much entanglement present. It is also proven that, given a step operator {ital T} for an arbitrary {ital deterministic} quantum Turing machine, it is decidable if {ital T} is stable and orthogonality preserving, and if quantum ballistic evolution is possible. The proof fails if {ital T} is a step operator for a {ital nondeterministic} machine. It is an open question if such a decision procedure exists for nondeterministic machines. This problem does not occur in classical mechanics. Also the definition of quantum Turing machines used here is compared with that used by other authors. {copyright} {ital 1996 The American Physical Society.}
Quantum information becomes classical when distributed to many users
G. Chiribella; G. M. D'Ariano
2007-01-31T23:59:59.000Z
Any physical transformation that equally distributes quantum information over a large number M of users can be approximated by a classical broadcasting of measurement outcomes. The accuracy of the approximation is at least of the order 1/M. In particular, quantum cloning of pure and mixed states can be approximated via quantum state estimation. As an example, for optimal qubit cloning with 10 output copies, a single user has error probability p > 0.45 in distinguishing classical from quantum output--a value close to the error probability of the random guess.
(Quantum Molecular Dynamics Method) (Classical Molecular Dynamics Method)
Maruyama, Shigeo
1-1 (Quantum Molecular Dynamics Method) (Classical Molecular Dynamics Method) 2) Verlet(Verlet's leap frog) (17)(18) ( ) i i ii m t t t t t t F vv + -= + 22 (17
Geometric Critical Exponents in Classical and Quantum Phase Transitions
Prashant Kumar; Tapobrata Sarkar
2014-11-02T23:59:59.000Z
We define geometric critical exponents for systems that undergo continuous second order classical and quantum phase transitions. These relate scalar quantities on the information theoretic parameter manifolds of such systems, near criticality. We calculate these exponents by approximating the metric and thereby solving geodesic equations analytically, near curvature singularities of two dimensional parameter manifolds. The critical exponents are seen to be the same for both classical and quantum systems that we consider, and we provide evidence about the possible universality of our results.
Quantization of classical integrable systems. Part I: quasi-integrable quantum systems
M. Marino; N. N. Nekhoroshev
2010-01-26T23:59:59.000Z
We propose in this work a concept of integrability for quantum systems, which corresponds to the concept of noncommutative integrability for systems in classical mechanics. We determine a condition for quantum operators which can be a suitable replacement for the condition of functional independence for functions on the classical phase space. This condition is based on the properties of the main parts of the operators with respect to the momenta. We are led in this way to the definition of what we call a "quasi-integrable quantum system". This concept will be further developed in a series of following papers.
Impossibility of secure cloud quantum computing for classical client
Tomoyuki Morimae; Takeshi Koshiba
2014-07-07T23:59:59.000Z
The first generation quantum computer will be implemented in the cloud style, since only few groups will be able to access such an expensive and high-maintenance machine. How the privacy of the client can be protected in such a cloud quantum computing? It was theoretically shown [A. Broadbent, J. F. Fitzsimons, and E. Kashefi, Proceedings of the 50th Annual IEEE Symposium on Foundation of Computer Science, 517 (2009)], and experimentally demonstrated [S. Barz, E. Kashefi, A. Broadbent, J. F. Fitzsimons, A. Zeilinger, and P. Walther, Science {\\bf335}, 303 (2012)] that a client who can generate randomly-rotated single qubit states can delegate her quantum computing to a remote quantum server without leaking any privacy. The generation of a single qubit state is not too much burden for the client, and therefore we can say that "almost classical client" can enjoy the secure cloud quantum computing. However, isn't is possible to realize a secure cloud quantum computing for a client who is completely free from any quantum technology? Here we show that perfectly-secure cloud quantum computing is impossible for a completely classical client unless classical computing can simulate quantum computing, or a breakthrough is brought in classical cryptography.
Universal Single-Server Blind Quantum Computation for Classical Client
Hai-Ru Xu; Bang-Hai Wang
2014-11-12T23:59:59.000Z
Blind quantum computation allows a client without enough quantum technologies to delegate her quantum computation to quantum server, while keeping her input, output and algorithm secure. In this paper, we propose a universal single-server and classical-client blind quantum computation protocol based on entanglement swapping technology. In our protocol, the client interface with only one server and the only ability of the client requires is to get particles from trusted center and forward them to the server. Moreover, the protocol can be modified to make client completely classical by improving the ability of the trusted center. Numbers of blind quantum computation protocols have been presented in recent years, including single-, double- and triple-server protocols. In the single-server protocol, client needs to prepare single qubits. Though client can be classical in the double-server protocol, the two servers, who share Bell state from trusted center, are not allowed to communicate with each other. Recently, the triple-server protocol solves the noncommunication problem. Three servers, however, make the implementation of the computation sophisticated and unrealistic. Since it is impossible for blind quantum computation with only classical client and single server, blind quantum computation may work in the "Cloud + E-commerce" style in the future. Our protocol might become a key ingredient for real-life application in the first generation of quantum computations.
The Möbius Symmetry of Quantum Mechanics
Alon E. Faraggi; Marco Matone
2015-02-16T23:59:59.000Z
The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under $D$--dimensional M\\"obius transformations with respect to the Euclidean or Minkowski metrics. The invariance under global M\\"obius transformations implies that spatial space is compact. Furthermore, it implies energy quantisation and undefinability of quantum trajectories without assuming any prior interpretation of the wave function. The approach may be viewed as conventional quantum mechanics with the caveat that spatial space is compact, as dictated by the M\\"obius symmetry, with the classical limit corresponding to the decompactification limit. Correspondingly, there exists a finite length scale in the formalism and consequently an intrinsic regularisation scheme. Evidence for the compactness of space may exist in the cosmic microwave background radiation.
Communication tasks with infinite quantum-classical separation
Christopher Perry; Rahul Jain; Jonathan Oppenheim
2015-03-03T23:59:59.000Z
Quantum resources can be more powerful than classical resources - a quantum computer can solve certain problems exponentially faster than a classical computer, and computing a function of two people's inputs can be done with exponentially less communication with quantum messages than with classical ones. Here we consider a task between two players, Alice and Bob where quantum resources are infinitely more powerful than classical ones. Alice is given a string of length n, and Bob's task is to exclude certain combinations of bits that Alice might have. If Alice must send classical messages, then she must reveal nearly n bits of information to Bob, but if she is allowed to send quantum bits, the amount of information she must reveal goes to zero with increasing n. Next, we consider a version of the task where the parties can only send classical messages but may have access to entanglement. When assisted by entanglement, Alice only needs to send a constant number of bits, while without entanglement, the number of bits Alice must send grows linearly with n. The task is related to the PBR theorem which arises in the context of the foundations of quantum theory.
Non-relativistic classical mechanics for spinning particles
G. Salesi
2005-07-11T23:59:59.000Z
We study the classical dynamics of non-relativistic particles endowed with spin. Non-vanishing Zitterbewegung terms appear in the equation of motion also in the small momentum limit. We derive a generalized work-energy theorem which suggests classical interpretations for tunnel effect and quantum potential.
Classical and Quantum Equations of Motion for a BTZ Black String in AdS Space
Eric Greenwood; Evan Halstead; Peng Hao
2010-01-24T23:59:59.000Z
We investigate gravitational collapse of a $(3+1)$-dimensional BTZ black string in AdS space in the context of both classical and quantum mechanics. This is done by first deriving the conserved mass per unit length of the cylindrically symmetric domain wall, which is taken as the classical Hamiltonian of the black string. In the quantum mechanical context, we take primary interest in the behavior of the collapse near the horizon and near the origin (classical singularity) from the point of view of an infalling observer. In the absence of radiation, quantum effects near the horizon do not change the classical conclusions for an infalling observer, meaning that the horizon is not an obstacle for him/her. The most interesting quantum mechanical effect comes in when investigating near the origin. First, quantum effects are able to remove the classical singularity at the origin, since the wave function is non-singular at the origin. Second, the Schr\\"odinger equation describing the behavior near the origin displays non-local effects, which depend on the energy density of the domain wall. This is manifest in that derivatives of the wavefunction at one point are related to the value of the wavefunction at some other distant point.
Nonlinear friction in quantum mechanics
Roumen Tsekov
2013-03-10T23:59:59.000Z
The effect of nonlinear friction forces in quantum mechanics is studied via dissipative Madelung hydrodynamics. A new thermo-quantum diffusion equation is derived, which is solved for the particular case of quantum Brownian motion with a cubic friction. It is extended also by a chemical reaction term to describe quantum reaction-diffusion systems with nonlinear friction as well.
A coupled-trajectory quantum-classical approach to decoherence in non-adiabatic processes
Min, Seung Kyu; Gross, E K U
2015-01-01T23:59:59.000Z
We present a novel quantum-classical approach to non-adiabatic dynamics, deduced from the coupled electronic and nuclear equations in the framework of the exact factorization of the electron-nuclear wave function. The method is based on the quasi-classical interpretation of the nuclear wave function, whose phase is related to the classical momentum and whose density is represented in terms of classical trajectories. In this approximation, electronic decoherence is naturally induced as effect of the coupling to the nuclei and correctly reproduces the expected quantum behaviour. Moreover, the splitting of the nuclear wave packet is captured as consequence of the correct approximation of the time-dependent potential of the theory. This new approach offers a clear improvement over Ehrenfest-like dynamics. The theoretical derivation presented in the Letter is supported by numerical results that are compared to quantum mechanical calculations.
Quantum entropy dynamics for chaotic systems beyond the classical limit
Arnaldo Gammal; Arjendu K. Pattanayak
2007-02-15T23:59:59.000Z
The entropy production rate for an open quantum system with a classically chaotic limit has been previously argued to be independent of $\\hbar$ and $D$, the parameter denoting coupling to the environment, and to be equal to the sum of generalized Lyapunov exponents, with these results applying in the near-classical regime. We present results for a specific system going well beyond earlier work, considering how these dynamics are altered for the Duffing problem by changing $\\hbar,D$ and show that the entropy dynamics have a transition from classical to quantum behavior that scales, at least for a finite time, as a function of $\\hbar^2/D$.
Information States in Control Theory: From Classical to Quantum
Matthew James
2014-06-20T23:59:59.000Z
This paper is concerned with the concept of {\\em information state} and its use in optimal feedback control of classical and quantum systems. The use of information states for measurement feedback problems is summarized. Generalization to fully quantum coherent feedback control problems is considered.
A quantum algorithm for Viterbi decoding of classical convolutional codes
Jon R. Grice; David A. Meyer
2014-05-29T23:59:59.000Z
We present a quantum Viterbi algorithm with better than classical performance under certain conditions (for decoding convolutional codes, for instance; large constraint length $Q$ and short decode frames $N$). The algorithm exploits the fact that the decoding trellis is similar to the butterfly diagram of the fast Fourier transform, with its corresponding fast quantum algorithm.
Time Gravity and Quantum Mechanics
W. G. Unruh
1993-12-17T23:59:59.000Z
Time plays different roles in quantum mechanics and gravity. These roles are examined and the problems that the conflict in the roles presents for quantum gravity are briefly summarised.
Quantum Mind from a Classical Field Theory of the Brain
Paola Zizzi
2011-04-13T23:59:59.000Z
We suggest that, with regard to a theory of quantum mind, brain processes can be described by a classical, dissipative, non-abelian gauge theory. In fact, such a theory has a hidden quantum nature due to its non-abelian character, which is revealed through dissipation, when the theory reduces to a quantum vacuum, where temperatures are of the order of absolute zero, and coherence of quantum states is preserved. We consider in particular the case of pure SU(2) gauge theory with a special anzatz for the gauge field, which breaks Lorentz invariance. In the ansatz, a contraction mapping plays the role of dissipation. In the limit of maximal dissipation, which corresponds to the attractive fixed point of the contraction mapping, the gauge fields reduce, up to constant factors, to the Pauli quantum gates for one-qubit states. Then tubuline-qubits can be processed in the quantum vacuum of the classical field theory of the brain, where decoherence is avoided due to the extremely low temperature. Finally, we interpret the classical SU(2) dissipative gauge theory as the quantum metalanguage (relative to the quantum logic of qubits), which holds the non-algorithmic aspect of the mind.
Tampering detection system using quantum-mechanical systems
Humble, Travis S. (Knoxville, TN); Bennink, Ryan S. (Knoxville, TN); Grice, Warren P. (Oak Ridge, TN)
2011-12-13T23:59:59.000Z
The use of quantum-mechanically entangled photons for monitoring the integrity of a physical border or a communication link is described. The no-cloning principle of quantum information science is used as protection against an intruder's ability to spoof a sensor receiver using a `classical` intercept-resend attack. Correlated measurement outcomes from polarization-entangled photons are used to protect against quantum intercept-resend attacks, i.e., attacks using quantum teleportation.
The Unfinished Search for Wave-Particle and Classical-Quantum Harmony
Partha Ghose
2015-02-11T23:59:59.000Z
The main purpose of this paper is to review the progress that has taken place so far in the search for a single unifying principle that harmonizes (i) the wave and particle natures of matter and radiation, both at the quantum and the classical levels, on the one hand and (ii) the classical and quantum theories of matter and radiation on the other hand. The famous paradoxes of quantum theory, the mysterious nature of measurements in quantum theory and the principal no-go theorems for hidden variables are first briefly reviewed. The Koopman-von Neumann Hilbert space theory based on complex wave functions underlying particle trajectories in classical phase space, is an important step forward in that direction. It provides a clear and beautiful harmony of classical waves and particles. Sudarshan has given an alternative but equivalent formulation that shows that classical mechanics can be regarded as a quantum theory with essentially hidden non-commuting variables. An extension of KvNS theory to classical electrodynamics provides a sound Hilbert space foundation to it and satisfactorily accounts for entanglement and Bell-CHSH-like violations already observed in classical polarization optics. An important new insight that has been obtained through these developments is that entanglement and Bell-like inequality violations are neither unique signatures of quantumness nor of non-locality---they are rather signatures of non-separability. Finally, Sudarshan's proposed solution to the measurement problem using KvNS theory for the measuring apparatus is sketched to show to what extent wave and particles can be harmonized in quantum theory.
Classical and Quantum Dynamics of Free Electromagnetic Laser Pulses
Goto, S; Walton, T J
2015-01-01T23:59:59.000Z
We discuss the use of a class of exact finite energy solutions to the vacuum source free Maxwell equations as models for multi- and single cycle laser pulses in classical interaction with relativistic charged point particles. These solutions are classified in terms of their chiral content and their influence on particular charge configurations in space. The results of such classical interactions motivate a particular quantum description of a freely propagating laser pulse in terms of an effective quantum Hamiltonian. The classical chiral states that evolve according to the classical vacuum Maxwell equations are now replaced by quantized bi-qutrit elements satisfying the Schrodinger equation. This description may offer a means to control and manipulate qu-trit states encoded into such laser pulses.
Anthropomorphic Quantum Darwinism as an explanation for Classicality
Thomas Durt
2009-06-15T23:59:59.000Z
According to the so-called ``Quantum Darwinist'' approach, the emergence of ``classical islands'' from a quantum background is assumed to obey a (selection) principle of maximal information. We illustrate this idea by considering the coupling of two particles that interact through a position-dependent potential. This approach sheds a new light on the emergence of classical logics and of our classical preconceptions about the world. The distinction between internal and external world, the Cartesian prejudice according to which the whole can be reduced to the sum of its parts and the appearance of preferred representation bases such as the position is seen here as the result of a very long evolution and would correspond to the most useful way of extracting stable and useful information from the quantum correlations.
Quantum plasma effects in the classical regime
G. Brodin; M. Marklund; G. Manfredi
2008-02-01T23:59:59.000Z
For quantum effects to be significant in plasmas it is often assumed that the temperature over density ratio must be small. In this paper we challenge this assumption by considering the contribution to the dynamics from the electron spin properties. As a starting point we consider a multicomponent plasma model, where electrons with spin up and spin down are regarded as different fluids. By studying the propagation of Alfv\\'{e}n wave solitons we demonstrate that quantum effects can survive in a relatively high-temperature plasma. The consequences of our results are discussed.
Quantum Gaussian Channels with Additive Correlated Classical Noise
Giovanna Ruggeri; Stefano Mancini
2006-09-04T23:59:59.000Z
We provide a model to study memory effects in quantum Gaussian channels with additive classical noise over an arbitrary number of uses. The correlation among different uses is introduced by contiguous two-mode interactions. Numerical results for few modes are presented. They confirm the possibility to enhance the classical information rate with the aid of entangled inputs, and show a likely asymptotic behavior that should lead to the full capacity of the channel.
From Quantum Mechanics to Thermodynamics?
Steinhoff, Heinz-Jürgen
From Quantum Mechanics to Thermodynamics? Dresden, 22.11.2004 Jochen Gemmer Universit¨at Osnabr to thermodynamical behavior · Quantum approach to thermodynamical behavior · The route to equilibrium · Summary of thermodynamical behavior entirely on the basis of Hamilton models and Schr¨odinger-type quantum dynamics. · define
The Boltzmann Equation in Classical and Quantum Field Theory
Sangyong Jeon
2005-07-18T23:59:59.000Z
Improving upon the previous treatment by Mueller and Son, we derive the Boltzmann equation that results from a classical scalar field theory. This is obtained by starting from the corresponding quantum field theory and taking the classical limit with particular emphasis on the path integral and perturbation theory. A previously overlooked Van-Vleck determinant is shown to control the tadpole type of self-energy that can still appear in the classical perturbation theory. Further comments on the validity of the approximations and possible applications are also given.
Hydrogen atom as a quantum-classical hybrid system
Fei Zhan; Biao Wu
2013-02-15T23:59:59.000Z
Hydrogen atom is studied as a quantum-classical hybrid system, where the proton is treated as a classical object while the electron is regarded as a quantum object. We use a well known mean-field approach to describe this hybrid hydrogen atom; the resulting dynamics for the electron and the proton is compared to their full quantum dynamics. The electron dynamics in the hybrid description is found to be only marginally different from its full quantum counterpart. The situation is very different for the proton: in the hybrid description, the proton behaves like a free particle; in the fully quantum description, the wave packet center of the proton orbits around the center of mass. Furthermore, we find that the failure to describe the proton dynamics properly can be regarded as a manifestation of the fact that there is no conservation of momentum in the mean-field hybrid approach. We expect that such a failure is a common feature for all existing approaches for quantum-classical hybrid systems of Born-Oppenheimer type.
Physics 430, Classical Mechanics Exam 2,2010 Nov 09
Gary, Dale E.
E,*-dt7rno + gr=49' y(Q,-('f [# si^[,",+)+ o-ces&uP)J -1- 6 N"'l6 #12;Physics430,ClassicalMechanics Exam2Physics 430, Classical Mechanics Exam 2,2010 Nov 09 - l Name 5o I wt t 6h Instructions:No books,notes,or "cheatsheet"allowed. You may usea calculator,but no otherelectronicdevicesduring the exam. Pleasetum your cell
Upper quantum Lyapunov Exponent and Anosov relations for quantum systems driven by a classical flow
O. Sapin; H. R. Jauslin; S. Weigert
2005-10-27T23:59:59.000Z
We generalize the definition of quantum Anosov properties and the related Lyapunov exponents to the case of quantum systems driven by a classical flow, i.e. skew-product systems. We show that the skew Anosov properties can be interpreted as regular Anosov properties in an enlarged Hilbert space, in the framework of a generalized Floquet theory. This extension allows us to describe the hyperbolicity properties of almost-periodic quantum parametric oscillators and we show that their upper Lyapunov exponents are positive and equal to the Lyapunov exponent of the corresponding classical parametric oscillators. As second example, we show that the configurational quantum cat system satisfies quantum Anosov properties.
Quantum Mechanical Pressure Frank Rioux
Rioux, Frank
by the kinetic theory of gases for an individual gas molecule. #12; Planck's constant. Using de Broglie's equation in the classical expression for kinetic energy converts provides, as we see now, a quantum interpretation for gas pressure. #12;To show this we will consider
The minimum distance of classical and quantum turbo-codes
Abbara, Mamdouh
2011-01-01T23:59:59.000Z
We present a theory of quantum stabilizer turbo-encoders with unbounded minimum distance. This theory is presented under a framework common to both classical and quantum turbo-encoding theory. The main conditions to have an unbounded minimum distance are that the inner seed encoder has to be recursive, and either systematic or with a totally recursive truncated decoder. This last condition has been introduced in order to obtain a theory viable in the quantum stabilizer case, since it was known that in this case the inner seed encoder could not be recursive and systematic in the same time.
The minimum distance of classical and quantum turbo-codes
Mamdouh Abbara; Jean-Pierre Tillich
2011-09-01T23:59:59.000Z
We present a theory of quantum stabilizer turbo-encoders with unbounded minimum distance. This theory is presented under a framework common to both classical and quantum turbo-encoding theory. The main conditions to have an unbounded minimum distance are that the inner seed encoder has to be recursive, and either systematic or with a totally recursive truncated decoder. This last condition has been introduced in order to obtain a theory viable in the quantum stabilizer case, since it was known that in this case the inner seed encoder could not be recursive and systematic in the same time.
Inverting quantum decoherence by classical feedback from the environment
Francesco Buscemi; Giulio Chiribella; Giacomo Mauro D'Ariano
2005-08-23T23:59:59.000Z
We show that for qubits and qutrits it is always possible to perfectly recover quantum coherence by performing a measurement only on the environment, whereas for dimension d>3 there are situations where recovery is impossible, even with complete access to the environment. For qubits, the minimal amount of classical information to be extracted from the environment equals the entropy exchange.
Non-monotonic quantum to classical transition in multiparticle interference
Young-Sik Ra; Malte C. Tichy; Hyang-Tag Lim; Osung Kwon; Florian Mintert; Andreas Buchleitner; Yoon-Ho Kim
2011-09-08T23:59:59.000Z
We experimentally demonstrate the non-monotonic dependence of genuine many-particle interference signals on the particles' mutual distinguishability. Our theoretical analysis shows that such non-monotonicity is a generic feature of the quantum to classical transition in multiparticle correlation functions of more than two particles.
Quantum Mechanics of a Rotating Billiard
Nandan Jha; Sudhir R. Jain
2014-06-12T23:59:59.000Z
Integrability of a square billiard is spontaneously broken as it rotates about one of its corners. The system becomes quasi-integrable where the invariant tori are broken with respect to a certain parameter, $\\lambda = 2E/\\omega^{2}$ where E is the energy of the particle inside the billiard and $\\omega$ is the angular frequency of rotation of billiard. We study the system classically and quantum mechanically in view of obtaining a correspondence in the two descriptions. Classical phase space in Poincar\\'{e} surface of section shows transition from regular to chaotic motion as the parameter $\\lambda$ is decreased. In the Quantum counterpart, the spectral statistics shows a transition from Poisson to Wigner distribution as the system turns chaotic with decrease in $\\lambda$. The wavefunction statistics however show breakdown of time-reversal symmetry as $\\lambda$ decreases.
Distinguishing Quantum and Classical Many-Body Systems
Dvir Kafri; Jacob Taylor
2015-04-06T23:59:59.000Z
Controllable systems relying on quantum behavior to simulate distinctly quantum models so far rely on increasingly challenging classical computing to verify their results. We develop a general protocol for confirming that an arbitrary many-body system, such as a quantum simulator, can entangle distant objects. The protocol verifies that distant qubits interacting separately with the system can become mutually entangled, and therefore serves as a local test that excitations of the system can create non-local quantum correlations. We derive an inequality analogous to Bell's inequality which can only be violated through entanglement between distant sites of the many-body system. Although our protocol is applicable to general many-body systems, it requires finding system-dependent local operations to violate the inequality. A specific example in quantum magnetism is presented.
Does Quantum Mechanics Save Free Will?
Laszlo E. Szabo
1995-06-28T23:59:59.000Z
According to the widely accepted opinion, classical (statistical) physics does not support objective indeterminism, since the statistical laws of classical physics allow a deterministic hidden background, while --- as Arthur Fine writes polemizing with Gr\\"unbaum --- "{\\sl the antilibertarian position finds little room to breathe in a statistical world if we take laws of the quantum theory as exemplars of the statistical laws in such a world. So, it appears that, contrary to what Gr\\"unbaum claims, the libertarians' 'could have done otherwise' does indeed find support from indeterminism if we take the indeterministic laws to be of the sort found in the quantum theory.}" In this paper I will show that, quite the contrary, quantum mechanics does not save free will. For instance, the EPR experiments are compatible with a deterministic world. They admit a deterministic local hidden parameter description if the deterministic model is 'allowed' to describe not only the measurement outcomes, but also the outcomes of the 'decisions' whether this or that measurement will be performed. So, the derivation of the freedom of the will from quantum mechanics is a tautology: from the assumption that the world is indeterministic it is derived that the world cannot be deterministic.
Phase space quantum mechanics - Direct
Nasiri, S.; Sobouti, Y.; Taati, F. [Institute for Advanced Studies in Basic Sciences, Zanjan, 45195-1159 (Iran, Islamic Republic of) and Department of Physics, Zanjan University, Zanjan (Iran); Institute for Advanced Studies in Basic Sciences, Zanjan, 45195-1159 (Iran, Islamic Republic of); Institute for Advanced Studies in Basic Sciences, Zanjan, 45195-1159 (Iran, Islamic Republic of) and Department of Physics, University of Kurdistan, D-78457 Sanadaj (Iran)
2006-09-15T23:59:59.000Z
Conventional approach to quantum mechanics in phase space (q,p), is to take the operator based quantum mechanics of Schroedinger, or an equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of noncommuting observables. Further conceptual and practical merits of the formalism are demonstrated throughout the text.
Combined Quantum Mechanical and Molecular Mechanics Studies of...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Mechanical and Molecular Mechanics Studies of the Electron-Transfer Reactions Involving Carbon Tetrachloride in Combined Quantum Mechanical and Molecular Mechanics Studies of the...
Quantum vs. Classical Read-once Branching Programs
Martin Sauerhoff
2005-09-23T23:59:59.000Z
The paper presents the first nontrivial upper and lower bounds for (non-oblivious) quantum read-once branching programs. It is shown that the computational power of quantum and classical read-once branching programs is incomparable in the following sense: (i) A simple, explicit boolean function on 2n input bits is presented that is computable by error-free quantum read-once branching programs of size O(n^3), while each classical randomized read-once branching program and each quantum OBDD for this function with bounded two-sided error requires size 2^{\\Omega(n)}. (ii) Quantum branching programs reading each input variable exactly once are shown to require size 2^{\\Omega(n)} for computing the set-disjointness function DISJ_n from communication complexity theory with two-sided error bounded by a constant smaller than 1/2-2\\sqrt{3}/7. This function is trivially computable even by deterministic OBDDs of linear size. The technically most involved part is the proof of the lower bound in (ii). For this, a new model of quantum multi-partition communication protocols is introduced and a suitable extension of the information cost technique of Jain, Radhakrishnan, and Sen (2003) to this model is presented.
Classical universes of the no-boundary quantum state
Hartle, James B. [Department of Physics, University of California, Santa Barbara, CA 93106-9530 (United States); Hawking, S. W. [DAMTP, CMS, Wilberforce Road, CB3 0WA Cambridge (United Kingdom); Hertog, Thomas [Laboratoire APC, 10 rue A. Domon et L. Duquet, 75205 Paris (France) and International Solvay Institutes, Boulevard du Triomphe, ULB, C.P. 231, 1050 Brussels (Belgium)
2008-06-15T23:59:59.000Z
We analyze the origin of the quasiclassical realm from the no-boundary proposal for the Universe's quantum state in a class of minisuperspace models. The models assume homogeneous, isotropic, closed spacetime geometries, a single scalar field moving in a quadratic potential, and a fundamental cosmological constant. The allowed classical histories and their probabilities are calculated to leading semiclassical order. For the most realistic range of parameters analyzed, we find that a minimum amount of scalar field is required, if there is any at all, in order for the Universe to behave classically at late times. If the classical late time histories are extended back, they may be singular or bounce at a finite radius. The ensemble of classical histories is time symmetric although individual histories are generally not. The no-boundary proposal selects inflationary histories, but the measure on the classical solutions it provides is heavily biased towards small amounts of inflation. However, the probability for a large number of e-foldings is enhanced by the volume factor needed to obtain the probability for what we observe in our past light cone, given our present age. Our results emphasize that it is the quantum state of the Universe that determines whether or not it exhibits a quasiclassical realm and what histories are possible or probable within that realm.
Team Decision Problems with Classical and Quantum Signals
Adam Brandenburger; Pierfrancesco La Mura
2015-01-22T23:59:59.000Z
We study team decision problems where communication is not possible, but coordination among team members can be realized via signals in a shared environment. We consider a variety of decision problems that differ in what team members know about one another's actions and knowledge. For each type of decision problem, we investigate how different assumptions on the available signals affect team performance. Specifically, we consider the cases of perfectly correlated, i.i.d., and exchangeable classical signals, as well as the case of quantum signals. We find that, whereas in perfect-recall trees (Kuhn [1950], [1953]) no type of signal improves performance, in imperfect-recall trees quantum signals may bring an improvement. Isbell [1957] proved that in non-Kuhn trees, classical i.i.d. signals may improve performance. We show that further improvement may be possible by use of classical exchangeable or quantum signals. We include an example of the effect of quantum signals in the context of high-frequency trading.
Quantum Mechanics of Neutrino Oscillations
C. Giunti; C. W. Kim
2000-11-06T23:59:59.000Z
We present a simple but general treatment of neutrino oscillations in the framework of quantum mechanics using plane waves and intuitive wave packet principles when necessary. We attempt to clarify some confusing statements that have recently appeared in the literature.
Classical and Quantum Oscillators of Sextic and Octic Anharmonicities
Anirban Pathak; Swapan Mandal
2002-06-03T23:59:59.000Z
Classical oscillators of sextic and octic anharmonicities are solved analytically up to the linear power of \\lambda (Anharmonic Constant) by using Taylor series method. These solutions exhibit the presence of secular terms which are summed up for all orders. The frequency shifts of the oscillators for small anharmonic constants are obtained. It is found that the calculated shifts agree nicely with the available results to-date. The solutions for classical anharmonic oscillators are used to obtain the solutions corresponding to quantum anharmonic oscillators by imposing fundamental commutation relations between position and momentum operators.
A Super-Additivity Inequality for Channel Capacity of Classical-Quantum Channels
Rahul Jain
2009-02-20T23:59:59.000Z
We show a super-additivity inequality for the channel capacity of classical-quantum (c - q) channels.
Classical kinetic energy, quantum fluctuation terms and kinetic-energy functionals
I. P. Hamilton; Ricardo A. Mosna; L. Delle Site
2007-04-08T23:59:59.000Z
We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum momentum. This leads to an interesting analogy with Nelson's stochastic approach to quantum mechanics, which we use to conceptually clarify the physical nature of part of the kinetic-energy functional in terms of statistical fluctuations and in direct correspondence with Fisher Information Theory. We show that the N-electron purely quantum kinetic energy can be written as the sum of the (one-electron) Weizsacker term and an (N-1)-electron kinetic correlation term. We further show that the Weizsacker term results from local fluctuations while the kinetic correlation term results from the nonlocal fluctuations. For one-electron orbitals (where kinetic correlation is neglected) we obtain an exact (albeit impractical) expression for the noninteracting kinetic energy as the sum of the classical kinetic energy and the Weizsacker term. The classical kinetic energy is seen to be explicitly dependent on the electron phase and this has implications for the development of accurate orbital-free kinetic-energy functionals. Also, there is a direct connection between the classical kinetic energy and the angular momentum and, across a row of the periodic table, the classical kinetic energy component of the noninteracting kinetic energy generally increases as Z increases.
Quantum tagging for tags containing secret classical data
Kent, Adrian [Centre for Quantum Information and Foundations, DAMTP, University of Cambridge, Cambridge (United Kingdom) and Perimeter Institute for Theoretical Physics, Waterloo, Ontario (Canada)
2011-08-15T23:59:59.000Z
Various authors have considered schemes for quantum tagging, that is, authenticating the classical location of a classical tagging device by sending and receiving quantum signals from suitably located distant sites, in an environment controlled by an adversary whose quantum information processing and transmitting power is potentially unbounded. All of the schemes proposed elsewhere in the literature assume that the adversary is able to inspect the interior of the tagging device. All of these schemes have been shown to be breakable if the adversary has unbounded predistributed entanglement. We consider here the case in which the tagging device contains a finite key string shared with distant sites but kept secret from the adversary, and show this allows the location of the tagging device to be authenticated securely and indefinitely. Our protocol relies on quantum key distribution between the tagging device and at least one distant site, and demonstrates a new practical application of quantum key distribution. It also illustrates that the attainable security in position-based cryptography can depend crucially on apparently subtle details in the security scenario considered.
Classical and Quantum Properties of Liouville Black Holes
R. B. Mann
1994-04-25T23:59:59.000Z
Black hole spacetimes can arise when a Liouville field is coupled to two- dimensional gravity. Exact solutions are obtained both classically and when quantum corrections due to back reaction effects are included. The black hole temperature depends upon the mass and the thermodynamic limit breaks down before evaporation of the black hole is complete, indicating that higher-loop effects must be included for a full description of the process.
Geometric phases in quantum control disturbed by classical stochastic processes
David Viennot
2012-08-01T23:59:59.000Z
We describe the geometric (Berry) phases arising when some quantum systems are driven by control classical parameters but also by outer classical stochastic processes (as for example classical noises). The total geometric phase is then divided into an usual geometric phase associated with the control parameters and a second geometric phase associated with the stochastic processes. The geometric structure in which these geometric phases take place is a composite bundle (and not an usual principal bundle), which is explicitely built in this paper. We explain why the composite bundle structure is the more natural framework to study this problem. Finally we treat a very simple example of a two level atom driven by a phase modulated laser field with a phase instability described by a gaussian white noise. In particular we compute the average geometric phase issued from the noise.
Thomas E. Skinner
2013-02-12T23:59:59.000Z
The dynamics of states representing arbitrary N-level quantum systems, including dissipative systems, can be modelled exactly by the dynamics of classical coupled oscillators. There is a direct one-to-one correspondence between the quantum states and the positions of the oscillators. Quantum coherence, expectation values, and measurement probabilities for system observables can therefore be realized from the corresponding classical states. The time evolution of an N-level system is represented as the rotation of a real state vector in hyperspace, as previously known for density matrix states but generalized here to Schrodinger states. A single rotor in n dimensions is then mapped directly to n oscillators in one physical dimension. The number of oscillators needed to represent N-level systems scales linearly with N for Schrodinger states, in contrast to N^2 for the density matrix formalism. Although the well-known equivalence (SU(2), SO(3) homomorphism) of 2-level quantum dynamics to a rotation in real, physical space cannot be generalized to arbitrary N-level systems, representing quantum dynamics by a system of coupled harmonic oscillators in one physical dimension is general for any N. Values for the classical coupling constants are readily obtained from the system Hamiltonian, allowing construction of classical mechanical systems that can provide visual insight into the dynamics of abstract quantum systems as well as a metric for characterizing the interface between quantum and classical mechanics.
Classical information storage in an $n$-level quantum system
Péter E. Frenkel; Mihály Weiner
2014-12-04T23:59:59.000Z
A game is played by a team of two --- say Alice and Bob --- in which the value of a random variable $x$ is revealed to Alice only, who cannot freely communicate with Bob. Instead, she is given a quantum $n$-level system, respectively a classical $n$-state system, which she can put in possession of Bob in any state she wishes. We evaluate how successfully they managed to store and recover the value of $x$ in the used system by requiring Bob to specify a value $z$ and giving a reward of value $ f(x,z)$ to the team. We show that whatever the probability distribution of $x$ and the reward function $f$ are, when using a quantum $n$-level system, the maximum expected reward obtainable with the best possible team strategy is equal to that obtainable with the use of a classical $n$-state system. The proof relies on mixed discriminants of positive matrices and --- perhaps surprisingly --- an application of the Supply--Demand Theorem for bipartite graphs. As a corollary, we get an infinite set of new, dimension dependent inequalities regarding positive operator valued measures and density operators on complex $n$-space. As a further corollary, we see that the greatest value, with respect to a given distribution of $x$, of the mutual information $I(x;z)$ that is obtainable using an $n$-level quantum system equals the analogous maximum for a classical $n$-state system.
Truhlar, Donald G
with a classical mechanical treatment of nuclear motion on coupled potential-energy surfaces. Whereas older mixedMixed quantum/classical investigation of the photodissociation of NH3,,A~ ... and a practical method for maintaining zero-point energy in classical trajectories David Bonhommeaua and Donald G
A Global Optimization Approach to Quantum Mechanics
Xiaofei Huang
2006-05-25T23:59:59.000Z
This paper presents a global optimization approach to quantum mechanics, which describes the most fundamental dynamics of the universe. It suggests that the wave-like behavior of (sub)atomic particles could be the critical characteristic of a global optimization method deployed by nature so that (sub)atomic systems can find their ground states corresponding to the global minimum of some energy function associated with the system. The classic time-independent Schrodinger equation is shown to be derivable from the global optimization method to support this argument.
A quantum mechanical version of Price's theorem for Gaussian states
Igor G. Vladimirov
2014-09-15T23:59:59.000Z
This paper is concerned with integro-differential identities which are known in statistical signal processing as Price's theorem for expectations of nonlinear functions of jointly Gaussian random variables. We revisit these relations for classical variables by using the Frechet differentiation with respect to covariance matrices, and then show that Price's theorem carries over to a quantum mechanical setting. The quantum counterpart of the theorem is established for Gaussian quantum states in the framework of the Weyl functional calculus for quantum variables satisfying the Heisenberg canonical commutation relations. The quantum mechanical version of Price's theorem relates the Frechet derivative of the generalized moment of such variables with respect to the real part of their quantum covariance matrix with other moments. As an illustrative example, we consider these relations for quadratic-exponential moments which are relevant to risk-sensitive quantum control.
Classical and Quantum Surgery of Geometries in an Open Inflationary Universe
Sang Pyo Kim
2000-05-09T23:59:59.000Z
We study classically and quantum mechanically the Euclidean geometries compatible with an open inflationary universe of a Lorentzian geometry. The Lorentzian geometry of the open universe with an ordinary matter state matches either an open or a closed Euclidean geometry at the cosmological singularity. With an exotic matter state it matches only the open Euclidean geometry and describes a genuine instanton regular at the boundary of a finite radius. The wave functions are found that describe the quantum creation of the open inflationary universe.
Symmetry and Relativity : From Classical Mechanics to Modern Particle Physics
Paris-Sud XI, Université de
Symmetry and Relativity : From Classical Mechanics to Modern Particle Physics Z.J. Ajaltouni to modern particle physics will be given and some open questions will be raised. Keywords: Symmetry that symmetry represents a methodology followed by Modern Physics in order to build coherent and successful
Bottleneck crossover between classical and quantum superfluid turbulence
L'vov, Victor S.; Rudenko, Oleksii [Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100 (Israel); Nazarenko, Sergei V. [Mathematics Institute, University of Warwick, Coventry CV4 7AL (United Kingdom)
2007-07-01T23:59:59.000Z
We consider superfluid turbulence near absolute zero of temperature generated by classical means, e.g., towed grid or rotation but not by counterflow. We argue that such turbulence consists of a polarized tangle of mutually interacting vortex filaments with quantized vorticity. For this system, we predict and describe a bottleneck accumulation of the energy spectrum at the classical-quantum crossover scale l. Demanding the same energy flux through scales, the value of the energy at the crossover scale should exceed the Kolmogorov-41 (K41) spectrum by a large factor ln{sup 10/3}(l/a{sub 0}) (l is the mean intervortex distance and a{sub 0} is the vortex core radius) for the classical and quantum spectra to be matched in value. One of the important consequences of the bottleneck is that it causes the mean vortex line density to be considerably higher than that based on K41 alone, and this should be taken into account in (re)interpretation of new (and old) experiments as well as in further theoretical studies.
Bottleneck crossover between classical and quantum superfluid turbulence
Victor S. L'vov; Sergei V. Nazarenko; Oleksii Rudenko
2007-06-25T23:59:59.000Z
We consider superfluid turbulence near absolute zero of temperature generated by classical means, e.g. towed grid or rotation but not by counterflow. We argue that such turbulence consists of a {\\em polarized} tangle of mutually interacting vortex filaments with quantized vorticity. For this system we predict and describe a bottleneck accumulation of the energy spectrum at the classical-quantum crossover scale $\\ell$. Demanding the same energy flux through scales, the value of the energy at the crossover scale should exceed the Kolmogorov-41 spectrum by a large factor $\\ln^{10/3} (\\ell/a_0)$ ($\\ell$ is the mean intervortex distance and $a_0$ is the vortex core radius) for the classical and quantum spectra to be matched in value. One of the important consequences of the bottleneck is that it causes the mean vortex line density to be considerably higher that based on K41 alone, and this should be taken into account in (re)interpretation of new (and old) experiments as well as in further theoretical studies.
Forrelation: A Problem that Optimally Separates Quantum from Classical Computing
Scott Aaronson; Andris Ambainis
2014-11-21T23:59:59.000Z
We achieve essentially the largest possible separation between quantum and classical query complexities. We do so using a property-testing problem called Forrelation, where one needs to decide whether one Boolean function is highly correlated with the Fourier transform of a second function. This problem can be solved using 1 quantum query, yet we show that any randomized algorithm needs ~sqrt(N)/log(N) queries (improving an ~N^{1/4} lower bound of Aaronson). Conversely, we show that this 1 versus ~sqrt(N) separation is optimal: indeed, any t-query quantum algorithm whatsoever can be simulated by an O(N^{1-1/2t})-query randomized algorithm. Thus, resolving an open question of Buhrman et al. from 2002, there is no partial Boolean function whose quantum query complexity is constant and whose randomized query complexity is linear. We conjecture that a natural generalization of Forrelation achieves the optimal t versus ~N^{1-1/2t} separation for all t. As a bonus, we show that this generalization is BQP-complete. This yields what's arguably the simplest BQP-complete problem yet known, and gives a second sense in which Forrelation "captures the maximum power of quantum computation."
A New Approach to The Quantum Mechanics
Yulei Feng
2013-02-15T23:59:59.000Z
In this paper, we try to give a new approach to the quantum mechanics(QM) on the framework of quantum field theory(QFT). Firstly, we make a detail study on the (non-relativistic) Schr\\"odinger field theory, obtaining the Schr\\"odinger equation as a field equation, after field quantization, the Heisenberg equations for the momentum and position operators of the particles excited from the (Schr\\"odinger) field and the Feynman path integral formula of QM are also obtained. We then give the probability concepts of quantum mechanics in terms of a statistical ensemble, realizing the ensemble(or statistical) interpretation. With these, we make a series of conceptual modifications to the standard quantum mechanics, especially propose a new assumption about the quantum measurement theory which can solve the EPR paradox from the view of the QFT. Besides, a field theoretical description to the double-slit interference experiment is developed, obtaining the required particle number distribution. In the end, we extend all the above concepts to the relativistic case so that the ensemble interpretation is still proper. Two extra topics are added, in the first one, an operable experiment is proposed to distinguish the Copenhagen interpretation from the ensemble one via very different experimental results. While the second topic concerns with the extensions of the concept of coherent state to both the Bosonic and Fermionic field cases, to obtain the corresponding classical fields. And in the concluding section, we make some general comparisons between the standard QM and the one derived from the QFT, from which we claim that the QFT is the fundamental theory.
The quantum field theory interpretation of quantum mechanics
Alberto C. de la Torre
2015-03-02T23:59:59.000Z
It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.
Classical and quantum chaos in a circular billiard with a straight cut
Suhan Ree; L. E. Reichl
1998-07-09T23:59:59.000Z
We study classical and quantum dynamics of a particle in a circular billiard with a straight cut. This system can be integrable, nonintegrable with soft chaos, or nonintegrable with hard chaos, as we vary the size of the cut. We use a quantum web to show differences in the quantum manifestations of classical chaos for these three different regimes.
Unstable trajectories and the quantum mechanical uncertainty
Moser, Hans R. [Physics Institute, University of Zuerich, Winterthurerstrasse 190, CH-8057 Zuerich (Switzerland)], E-mail: moser@physik.uzh.ch
2008-08-15T23:59:59.000Z
There is still an ongoing discussion about various seemingly contradictory aspects of classical particle motion and its quantum mechanical counterpart. One of the best accepted viewpoints that intend to bridge the gap is the so-called Copenhagen Interpretation. A major issue there is to regard wave functions as probability amplitudes (usually for the position of a particle). However, the literature also reports on approaches that claim a trajectory for any quantum mechanical particle, Bohmian mechanics probably being the most prominent one among these ideas. We introduce a way to calculate trajectories as well, but our crucial ingredient is their well controlled local (thus also momentaneous) degree of instability. By construction, at every moment their unpredictability, i.e., their local separation rates of neighboring trajectories, is governed by the local value of the given modulus square of a wave function. We present extensive numerical simulations of the H and He atom, and for some velocity-related quantities, namely angular momentum and total energy, we inspect their agreement with the values appearing in wave mechanics. Further, we interpret the archetypal double slit interference experiment in the spirit of our findings. We also discuss many-particle problems far beyond He, which guides us to a variety of possible applications.
Quantum mechanical time contradicts the uncertainty principle
Hitoshi Kitada
1999-11-17T23:59:59.000Z
The a priori time in conventional quantum mechanics is shown to contradict the uncertainty principle. A possible solution is given.
Positive contraction mappings for classical and quantum Schrodinger systems
Tryphon T. Georgiou; Michele Pavon
2014-10-07T23:59:59.000Z
The classical Schrodinger bridge seeks the most likely probability law for a diffusion process, in path space, that matches marginals at two end points in time; the likelihood is quantified by the relative entropy between the sought law and a prior, and the law dictates a controlled path that abides by the specified marginals. Schrodinger proved that the optimal steering of the density between the two end points is effected by a multiplicative functional transformation of the prior; this transformation represents an automorphism on the space of probability measures and has since been studied by Fortet, Beurling and others. A similar question can be raised for processes evolving in a discrete time and space as well as for processes defined over non-commutative probability spaces. The present paper builds on earlier work by Pavon and Ticozzi and begins with the problem of steering a Markov chain between given marginals. Our approach is based on the Hilbert metric and leads to an alternative proof which, however, is constructive. More specifically, we show that the solution to the Schrodinger bridge is provided by the fixed point of a contractive map. We approach in a similar manner the steering of a quantum system across a quantum channel. We are able to establish existence of quantum transitions that are multiplicative functional transformations of a given Kraus map, but only for the case of uniform marginals. As in the Markov chain case, and for uniform density matrices, the solution of the quantum bridge can be constructed from the fixed point of a certain contractive map. For arbitrary marginal densities, extensive numerical simulations indicate that iteration of a similar map leads to fixed points from which we can construct a quantum bridge. For this general case, however, a proof of convergence remains elusive.
Pairwise quantum and classical correlations in multi-qubits states via linear relative entropy
M. Daoud; R. Ahl Laamara; H. El Hadfi
2014-12-01T23:59:59.000Z
The pairwise correlations in a multi-qubit state are quantified through a linear variant of relative entropy. In particular, we derive the explicit expressions of total, quantum and classical bipartite correlations. Two different bi-partioning schemes are considered. We discuss the derivation of closest product, quantum-classical and quantum-classical product states. We also investigate the additivity relation between the various pairwise correlations existing in pure and mixed states. As illustration, some special cases are examined.
Phase space theory of quantum–classical systems with nonlinear and stochastic dynamics
Buri?, Nikola, E-mail: buric@ipb.ac.rs; Popovi?, Duška B.; Radonji?, Milan; Prvanovi?, Slobodan
2014-04-15T23:59:59.000Z
A novel theory of hybrid quantum–classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum–classical phase space. Both, the quantum and classical descriptions of the respective parts of the hybrid system are treated as fundamental. Therefore, the description of the quantum–classical interaction has to be postulated, and includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement. -- Highlights: •A novel theory of quantum–classical systems is developed. •Framework of quantum constrained dynamical systems is used. •A dynamical description of the measurement induced collapse is obtained.
Quantum Mechanics and Representation Theory Columbia University
Woit, Peter
Quantum Mechanics and Representation Theory Peter Woit Columbia University Texas Tech, November 21 2013 Peter Woit (Columbia University) Quantum Mechanics and Representation Theory November 2013 1 / 30, 1967 Peter Woit (Columbia University) Quantum Mechanics and Representation Theory November 2013 2 / 30
Classical and quantum Big Brake cosmology for scalar field and tachyonic models
Kamenshchik, A. Yu. [Dipartimento di Fisica e Astronomia and INFN, Via Irnerio 46, 40126 Bologna (Italy) and L.D. Landau Institute for Theoretical Physics of the Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow (Russian Federation); Manti, S. [Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa (Italy)
2013-02-21T23:59:59.000Z
We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical - quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bang and Big Crunch singularities are not traversable.
B?aszak, Maciej, E-mail: blaszakm@amu.edu.pl; Doma?ski, Ziemowit, E-mail: ziemowit@amu.edu.pl
2013-12-15T23:59:59.000Z
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. An explicit form of position and momentum operators as well as their appropriate ordering in arbitrary curvilinear coordinates is demonstrated. Finally, the extension of presented formalism onto non-flat case and related ambiguities of the process of quantization are discussed. -- Highlights: •An invariant quantization procedure of classical mechanics on the phase space over flat configuration space is presented. •The passage to an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. •Explicit form of position and momentum operators and their appropriate ordering in curvilinear coordinates is shown. •The invariant form of Hamiltonian operators quadratic and cubic in momenta is derived. •The extension of presented formalism onto non-flat case and related ambiguities of the quantization process are discussed.
The Quantum-Classical and Mind-Brain Linkages: The Quantum Zeno Effect in Binocular Rivalry
Henry P. Stapp
2007-11-05T23:59:59.000Z
A quantum mechanical theory of the relationship between perceptions and brain dynamics based on von Neumann's theory of measurments is applied to a recent quantum theoretical treatment of binocular rivaly that makes essential use of the quantum Zeno effect to give good fits to the complex available empirical data. The often-made claim that decoherence effects in the warm, wet, noisy brain must eliminate quantum effects at the macroscopic scale pertaining to perceptions is examined, and it is argued, on the basis of fundamental principles. that the usual decoherence effects will not upset the quantum Zeno effect that is being exploited in the cited work.
The M\\"obius Symmetry of Quantum Mechanics
Faraggi, Alon E
2015-01-01T23:59:59.000Z
The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under $D$--dimensional M\\"obius transformations with respect to the Euclidean or Minkowski metrics. The invariance under global M\\"obius transformations implies that spatial space is compact. Furthermore, it implies energy quantisation and undefinability of quantum trajectories without assuming any prior interpretation of the wave function. The approach may be viewed as conventional quantum mechanics with the caveat that spatial space is compact, as dictated by the M\\"obius symmetry, with the classical limit corresponding to the decompactification limit. Correspondingly, there exists a finite length scale in the formalism and consequently an intrinsic regularisation scheme. Evidence for the compactness of space may exist in the cosmic microwave background radiation.
Information Security and Quantum Mechanics: Security of Quantum Protocols
P. Oscar Boykin
2002-10-28T23:59:59.000Z
The problem of security of quantum key protocols is examined. In addition to the distribution of classical keys, the problem of encrypting quantum data and the structure of the operators which perform quantum encryption is studied. It is found that unitary bases are central to both encryption of quantum information, as well as the generation of states used in generalized quantum key distribution (which are called mutually unbiased bases). A one-to-one correspondence between certain unitary bases and mutually unbiased bases is found. Finally, a new protocol for making anonymous classical broadcasts is given along with a security proof. An experimental procedure to implement this protocol is also given. In order to prove these new results, some new bounds for accessible information of quantum sources are obtained.
Classical Mechanics of Collinear Positron-Hydrogen Scattering
Lee, Min-Ho; Moon, Jin-Sung; Choi, Nark Nyul; Kim, Dae-Soung
2015-01-01T23:59:59.000Z
We study the classical dynamics of the collinear positron-hydrogen scattering system below the three-body breakup threshold. Observing the chaotic behavior of scattering time signals, we in- troduce a code system appropriate to a coarse grained description of the dynamics. And, for the purpose of systematic analysis of the phase space structure, a surface of section is introduced being chosen to match the code system. Partition of the surface of section leads us to a surprising conjec- ture that the topological structure of the phase space of the system is invariant under exchange of the dynamical variables of proton with those of positron. It is also found that there is a finite set of forbidden patterns of symbol sequences. And the shortest periodic orbit is found to be stable, around which invariant tori form an island of stability in the chaotic sea. Finally we discuss a possible quantum manifestation of the classical phase space structure relevant to resonances in scattering cross sections.
Jianlan Wu; Fan Liu; Jian Ma; Robert J. Silbey; Jianshu Cao
2012-09-05T23:59:59.000Z
Following the calculation of optimal energy transfer in thermal environment in our first paper (Wu et al., New J. Phys., 2010, 12, 105012), full quantum dynamics and leading-order `classical' hopping kinetics are compared in the seven-site Fenna-Matthews-Olson (FMO) protein complex. The difference between these two dynamic descriptions is due to higher-order quantum corrections. Two thermal bath models, classical white noise (the Haken-Strobl-Reineker model) and quantum Debye model, are considered. In the seven-site FMO model, we observe that higher-order corrections lead to negligible changes in the trapping time or in energy transfer efficiency around the optimal and physiological conditions (2% in the HSR model and 0.1% in the quantum Debye model for the initial site at BChl 1). However, using the concept of integrated flux, we can identify significant differences in branching probabilities of the energy transfer network between hopping kinetics and quantum dynamics (26% in the HSR model and 32% in the quantum Debye model for the initial site at BChl 1). This observation indicates that the quantum coherence can significantly change the distribution of energy transfer pathways in the flux network with the efficiency nearly the same. The quantum-classical comparison of the average trapping time with the removal of the bottleneck site, BChl 4, demonstrates the robustness of the efficient energy transfer by the mechanism of multi-site quantum coherence. To reconcile with the latest eight-site FMO model, the quantum-classical comparison with the flux network analysis is summarized in the appendix. The eight-site FMO model yields similar trapping time and network structure as the seven-site FMO model but leads to a more disperse distribution of energy transfer pathways.
Flux formulation of loop quantum gravity: Classical framework
Bianca Dittrich; Marc Geiller
2014-12-11T23:59:59.000Z
We recently introduced a new representation for loop quantum gravity, which is based on the BF vacuum and is in this sense much nearer to the spirit of spin foam dynamics. In the present paper we lay out the classical framework underlying this new formulation. The central objects in our construction are the so-called integrated fluxes, which are defined as the integral of the electric field variable over surfaces of codimension one, and related in turn to Wilson surface operators. These integrated flux observables will play an important role in the coarse graining of states in loop quantum gravity, and can be used to encode in this context the notion of curvature-induced torsion. We furthermore define a continuum phase space as the modified projective limit of a family of discrete phase spaces based on triangulations. This continuum phase space yields a continuum (holonomy-flux) algebra of observables. We show that the corresponding Poisson algebra is closed by computing the Poisson brackets between the integrated fluxes, which have the novel property of being allowed to intersect each other.
Quantum mechanical effects from deformation theory
Much, A. [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)] [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)
2014-02-15T23:59:59.000Z
We consider deformations of quantum mechanical operators by using the novel construction tool of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a role. Furthermore, a quantum plane can be defined by using the deformation techniques. This in turn gives an experimentally verifiable effect.
Henry P. Stapp
2008-03-11T23:59:59.000Z
A simple exactly solvable model is given of the dynamical coupling between a person's classically described perceptions and that person's quantum mechanically described brain. The model is based jointly upon von Neumann's theory of measurement and the empirical findings of close connections between conscious intentions and synchronous oscillations in well separated parts of the brain. A quantum-Zeno-effect-based mechanism is described that allows conscious intentions to influence brain activity in a functionally appropriate way. The robustness of this mechanism in the face of environmental decoherence effects is emphasized.
Nano-wires with surface disorder: Giant localization lengths and quantum-to-classical crossover
J. Feist; A. Bäcker; R. Ketzmerick; S. Rotter; B. Huckestein; J. Burgdörfer
2006-09-14T23:59:59.000Z
We investigate electronic quantum transport through nano-wires with one-sided surface roughness. A magnetic field perpendicular to the scattering region is shown to lead to exponentially diverging localization lengths in the quantum-to-classical crossover regime. This effect can be quantitatively accounted for by tunneling between the regular and the chaotic components of the underlying mixed classical phase space.
A necessary and sufficient condition to play games in quantum mechanical settings
Sahin Kaya Ozdemir; Junichi Shimamura; Nobuyuki Imoto
2007-03-01T23:59:59.000Z
Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum measurement. By transferring two-player-two strategy (2x2) dilemma containing classical games into quantum realm, dilemmas can be resolved in quantum pure strategies if entanglement is distributed between the players who use quantum operations. Moreover, players receive the highest sum of payoffs available in the game, which are otherwise impossible in classical pure strategies. Encouraged by the observation of rich dynamics of physical systems with many interacting parties and the power of entanglement in quantum versions of 2x2 games, it became generally accepted that quantum versions can be easily extended to N-player situations by simply allowing N-partite entangled states. In this article, however, we show that this is not generally true because the reproducibility of classical tasks in quantum domain imposes limitations on the type of entanglement and quantum operators. We propose a benchmark for the evaluation of quantum and classical versions of games, and derive the necessary and sufficient conditions for a physical realization. We give examples of entangled states that can and cannot be used, and the characteristics of quantum operators used as strategies.
Treating Time Travel Quantum Mechanically
John-Mark A. Allen
2014-10-10T23:59:59.000Z
The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilising the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their non-linearity and time travel paradoxes. In particular, the "equivalent circuit model"---which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory---is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of new theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features---such as time travel paradoxes, the ability to distinguish non-orthogonal states with certainty, and the ability to clone or delete arbitrary pure states---that are present with D-CTCs and P-CTCs. The problems with non-linear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.
Classical and quantum chaotic angular-momentum pumps
T. Dittrich; F. L. Dubeibe
2015-02-10T23:59:59.000Z
We study directed transport of charge and intrinsic angular momentum by periodically driven scattering in the regime of fast and strong driving. A spin-orbit coupling through a kicked magnetic field confined to a compact region in space leads to irregular scattering and triggers spin flips in a spatially asymmetric manner which allows to generate polarized currents. The dynamical mechanisms responsible for the spin separation carry over to the quantum level and give rise to spin pumping. Our theory, based on the Floquet formalism, is confirmed by numerical solutions of the time-dependent inhomogeneous Schr\\"{o}dinger equation with a continuous source term.
Parameter scaling in a novel measure of quantum-classical difference for decohering chaotic systems
Nathan Wiebe; Parin Sripakdeevong; Arnaldo Gammal; Arjendu K. Pattanayak
2009-04-21T23:59:59.000Z
In this paper we introduce a diagnostic for measuring the quantum-classical difference for open quantum systems, which is the normalized size of the quantum terms in the Master equation for Wigner function evolution. For a driven Duffing oscillator, this measure shows remarkably precise scaling over long time-scales with the parameter $\\zeta_0=\\hbar^2/D$. We also see that, independent of $\\zeta_0$ the dynamics follows a similar pattern. For small $\\zeta_0$ all of our curves collapses to essentially a single curve when scaled by the maximum value of the quantum-classical difference. In both limits of large and small $\\zeta_0$ we see a saturation effect in the size of the quantum-classical difference; that is, the instantaneous difference between quantum and classical evolutions cannot be either too small or too large.
Transition to classical chaos in a coupled quantum system through continuous measurement
Ghose, Shohini; Alsing, Paul; Deutsch, Ivan; Bhattacharya, Tanmoy; Habib, Salman [Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131 (United States); T-8 Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2004-05-01T23:59:59.000Z
Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough that quantum backaction noise is negligible. We investigate the conditions under which classical dynamics emerges, via a continuous position measurement, for a particle moving in a harmonic well with its position coupled to internal spin. As a consequence of this coupling, we find that classical dynamics emerges only when the position and spin actions are both large compared to ({Dirac_h}/2{pi}). These conditions are quantified by placing bounds on the size of the covariance matrix which describes the delocalized quantum coherence over extended regions of phase space. From this result, it follows that a mixed quantum-classical regime (where one subsystem can be treated classically and the other not) does not exist for a continuously observed spin-(1/2) particle. When the conditions for classicality are satisfied (in the large-spin limit), the quantum trajectories reproduce both the classical periodic orbits as well as the classically chaotic phase space regions. As a quantitative test of this convergence, we compute the largest Lyapunov exponent directly from the measured quantum trajectories and show that it agrees with the classical value.
Consistency Tests of Classical and Quantum Models for a Quantum Annealer
Tameem Albash; Walter Vinci; Anurag Mishra; Paul A. Warburton; Daniel A. Lidar
2015-04-13T23:59:59.000Z
Recently the question of whether the D-Wave processors exhibit large-scale quantum behavior or can be described by a classical model has attracted significant interest. In this work we address this question by studying a 503 qubit D-Wave Two device in the "black box" model, i.e., by studying its input-output behavior. Our work generalizes an approach introduced in Boixo et al. [Nat. Commun. 4, 2067 (2013)], and uses groups of up to 20 qubits to realize a transverse Ising model evolution with a ground state degeneracy whose distribution acts as a sensitive probe that distinguishes classical and quantum models for the D-Wave device. Our findings rule out all classical models proposed to date for the device and provide evidence that an open system quantum dynamical description of the device that starts from a quantized energy level structure is well justified, even in the presence of relevant thermal excitations and a small value of the ratio of the single-qubit decoherence time to the annealing time.
On quantum capacity of erasure channel assisted by back classical communication
Debbie Leung; Joungkeun Lim; Peter Shor
2010-01-02T23:59:59.000Z
We present a communication protocol for the erasure channel assisted by backward classical communication, which achieves a significantly better rate than the best prior result. In addition, we prove an upper bound for the capacity of the channel. The upper bound is smaller than the capacity of the erasure channel when it is assisted by two-way classical communication. Thus, we prove the separation between quantum capacities assisted by backward classical communication and two-way classical communication.
Quantum Statistical Mechanics. III. Equilibrium Probability
Phil Attard
2014-04-10T23:59:59.000Z
Given are a first principles derivation and formulation of the probabilistic concepts that underly equilibrium quantum statistical mechanics. The transition to non-equilibrium probability is traversed briefly.
A Process Model of Quantum Mechanics
William Sulis
2014-04-21T23:59:59.000Z
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise through a non-uniform interpolation process. Standard non-relativistic quantum mechanics emerges under the limit of infinite information (the causal space grows to infinity) and infinitesimal scale (the separation between points goes to zero). The model has the potential to address several paradoxes in quantum mechanics while remaining computationally powerful.
Classical and Quantum Correlations of Scalar Field in the Inflationary Universe
Yasusada Nambu; Yuji Ohsumi
2011-08-01T23:59:59.000Z
We investigate classical and quantum correlations of a quantum field in the inflationary universe using a particle detector model. By considering the entanglement and correlations between two comoving detectors interacting with a scalar field, we find that the entanglement between the detectors becomes zero after their physical separation exceeds the Hubble horizon. Furthermore, the quantum discord, which is defined as the quantum part of total correlation, approaches zero on super horizon scale. These behaviors support appearance of classical nature of the quantum fluctuation generated during the inflationary era.
Classical and Quantum Correlations of Scalar Field in the Inflationary Universe
Nambu, Yasusada
2011-01-01T23:59:59.000Z
We investigate classical and quantum correlations of a quantum field in the inflationary universe using a particle detector model. By considering the entanglement and correlations between two comoving detectors interacting with a scalar field, we find that the entanglement between the detectors becomes zero after their physical separation exceeds the Hubble horizon. Furthermore, the quantum discord, which is defined as the quantum part of total correlation, approaches zero on super horizon scale. These behaviors support appearance of classical nature of the quantum fluctuation generated during the inflationary era.
Quantum mechanics and the direction of time
Hasegawa, H.; Petrosky, T. (Univ. of Texas, Austin (United States)); Prigogine, I. (Univ. of Texas, Austin (United States) International Solvay Inst. for Physics and Chemistry, Brussels (Belgium)); Tasaki, S. (International Solvay Inst. for Physics and Chemistry, Brussels (Belgium))
1991-03-01T23:59:59.000Z
In recent papers the authors have discussed the dynamical properties of large Poincare systems (LPS), that is, nonintegrable systems with a continuous spectrum (both classical and quantum). An interesting example of LPS is given by the Friedrichs model of field theory. As is well known, perturbation methods analytic in the coupling constant diverge because of resonant denominators. They show that this Poincare catastrophe can be eliminated by a natural time ordering of the dynamical states. They obtain then a dynamical theory which incorporates a privileged direction of time (and therefore the second law of thermodynamics). However, it is only in very simple situations that his time ordering can be performed in an extended Hilbert space. In general, they need to go to the Liouville space (superspace) and introduce a time ordering of dynamical states according to the number of particles involved in correlations. This leads then to a generalization of quantum mechanics in which the usual Heisenberg's eigenvalue problem is replaced by a complex eigenvalue problem in the Liouville space.
Martin Frimmer; Lukas Novotny
2014-09-26T23:59:59.000Z
Coherent control of a quantum mechanical two-level system is at the heart of magnetic resonance imaging, quantum information processing, and quantum optics. Among the most prominent phenomena in quantum coherent control are Rabi oscillations, Ramsey fringes and Hahn echoes. We demonstrate that these phenomena can be derived classically by use of a simple coupled harmonic oscillator model. The classical problem can be cast in a form that is formally equivalent to the quantum mechanical Bloch equations with the exception that the longitudinal and the transverse relaxation times ($T_1$ and $T_2$) are equal. The classical analysis is intuitive and well suited for familiarizing students with the basic concepts of quantum coherent control, while at the same time highlighting the fundamental differences between classical and quantum theories.
Quantum and Classical Superballistic Transport in a Relativistic Kicked-Rotor System
Qifang Zhao; Cord A. Muller; Jiangbin Gong
2014-05-27T23:59:59.000Z
As an unusual type of anomalous diffusion behavior, superballistic transport is not well known but has been experimentally simulated recently. Quantum superballistic transport models to date are mainly based on connected sublattices which are constructed to have different properties. In this work, we show that both quantum and classical superballistic transport in the momentum space can occur in a simple periodically driven Hamiltonian system, namely, a relativistic kicked-rotor system with a nonzero mass term. The nonzero mass term essentially realizes a junction-like scenario: regimes with low or high momentum values have different dispersion relations and hence different transport properties. It is further shown that the quantum and classical superballistic transport should occur under much different choices of the system parameters. The results are of interest to studies of anomalous transport, quantum and classical chaos, and the issue of quantum-classical correspondence.
Highlighting the mechanism of the quantum speedup by time-symmetric and relational quantum mechanics
Giuseppe Castagnoli
2014-12-11T23:59:59.000Z
Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. We explain it by extending the usual representation of the quantum algorithm, limited to the process of solving the problem, to the process of setting the problem. The number of the drawer with the ball becomes a unitary transformation of the random outcome of the preparation measurement. This brings in relational quantum mechanics: the extension is with respect to Bob and cannot be with respect to Alice. It would tell her the drawer number before she opens any drawer. To Alice, the projection of the quantum state due to the preparation measurement should be retarded at the end of her search; in the input state of the search, the drawer number is determined to Bob and undetermined to Alice. A second consequence is the emergence of an ambiguity. Either the preparation measurement or the final one required to read the solution selects the solution. For reasons of symmetry, we assume that the selection shares evenly between the two measurements. All is as if Alice, by reading the solution, selected half of the information that specifies the drawer number. This selection leaves the input state to Bob unaltered and projects that to Alice on a state of lower entropy where she knows that half in advance. The quantum algorithm is a sum over histories in each of which Alice knows in advance that the ball is in a pair of drawers and locates it by opening one of the two. More in general, given an oracle problem, this explanation of the speedup predicts the number of queries required to solve it in an optimal quantum way.
Andrei Khrennikov
2011-12-03T23:59:59.000Z
We present a purely wave model (based on classical random field) which reproduces quantum probabilities (given by the fundamental law of quantum mechanics, Born's rule) including probabilities for joint detection of a pair of quantum observables (e.g., spin or polarization projections). The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counteparts of the theoretical model. The presence of the background field (vacuum fluctuations) is also the key-element of our prequantum model. It is of the classical signal type and the methods of classical signal theory (including statistical radiophysics) are used for its development. We stress that our prequantum model is not objective, i.e., the values of observables (clicks of detectors) cannot be assigned in advance, i.e., before measurement. Hence, the dilemma, nonobjectivity or nonlocality, is resolved in favor of nonobjectivity (our model is local of the classical field type). In particular, we reproduce the probabilities for the EPR-experiment for photon polarization and, hence, violate CHSH inequality for classical random signals (measured by the threshold type and properly calibrated detectors acting in the presence of the background field).
Reality without Realism: On the Ontological and Epistemological Architecture of Quantum Mechanics
Plotnitsky, Arkady
2015-01-01T23:59:59.000Z
First, the article considers the nature of quantum reality (the reality responsible for quantum phenomena) and the concept of realism (our ability to represent this reality) in quantum theory, in conjunction with the roles of locality, causality, and probability and statistics there. Second, it offers two interpretations of quantum mechanics, developed by the authors of this article, the second of which is also a different (from quantum mechanics) theory of quantum phenomena. Both of these interpretations are statistical. The first interpretation, by A. Plotnitsky, "the statistical Copenhagen interpretation," is non-realist, insofar as the description or even conception of the nature of quantum objects and processes is precluded. The second, by A. Khrennikov, is ultimately realist, because it assumes that the quantum-mechanical level of reality is underlain by a deeper level of reality, described, in a realist fashion, by a model based on the pre-quantum classical statistical field theory (PCSFT), the predict...
Loop Quantum Gravity 1. Classical framework : Ashtekar-Barbero connection
Sart, Remi
gravity Why Quantum Gravity ? Gravitation vs. Quantum Physics : the two infinities Gravitation : large Quantum Gravity ? Gravitation vs. Quantum Physics : the two infinities Gravitation : large scales-perturbative renormalization Gravity is not a fundamental theory but it is effective (law energy) Â· it has to be modified
Superconformal quantum mechanics and the exterior algebra
Andrew Singleton
2014-09-11T23:59:59.000Z
We extend the differential form representation of N = (n,n) supersymmetric quantum mechanics to the superconformal case. We identify the superalgebras occurring for n = 1,2,4, give necessary and sufficient conditions for their existence, and give explicit geometric constructions of their generators and commutation relations. Quantum mechanics on the moduli space of instantons is considered as an example.
NONEQUILIBRIUM QUANTUM STATISTICAL MECHANICS AND THERMODYNAMICS #
NONEQUILIBRIUM QUANTUM STATISTICAL MECHANICS AND THERMODYNAMICS # Walid K. Abou Salem + Institut f recent progress in deriving the fundamental laws of thermodynamics (0 th , 1 st and 2 nd Âlaw) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and di#erent reversible
Entanglement in Classical Optics
Partha Ghose; Anirban Mukherjee
2013-09-12T23:59:59.000Z
The emerging field of entanglement or nonseparability in classical optics is reviewed, and its similarities with and differences from quantum entanglement clearly pointed out through a recapitulation of Hilbert spaces in general, the special restrictions on Hilbert spaces imposed in quantum mechanics and the role of Hilbert spaces in classical polarization optics. The production of Bell-like states in classical polarization optics is discussed, and new theorems are proved to discriminate between separable and nonseparable states in classical wave optics where no discreteness is involved. The influence of the Pancharatnam phase on a classical Bell-like state is deived. Finally, to what extent classical polarization optics can be used to simulate quantum information processing tasks is also discussed. This should be of great practical importance because coherence and entanglement are robust in classical optics but not in quantum systems.
Blume-Kohout, Robin; Zurek, Wojciech H. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA and Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125 (United States); Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2006-06-15T23:59:59.000Z
We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles of states for a model universe consisting of one system and many environments: the first consisting of arbitrary states, and the second consisting of 'singly branching' states consistent with a simple decoherence model. Typical states from the random ensemble do not store information about the system redundantly, but information stored in branching states has a redundancy proportional to the environment's size. We compute the specific redundancy for a wide range of model universes, and fit the results to a simple first-principles theory. Our results show that the presence of redundancy divides information about the system into three parts: classical (redundant); purely quantum; and the borderline, undifferentiated or 'nonredundant', information.
Improving Classical Authentication over a Quantum Channel F. M. Assis1
Lisboa, Universidade Técnica de
be used to replace Wegman-Carter's classical authentication scheme in quantum key distribution (QKD the QKD protocol to bootstrap. The authenti- cation scheme commonly used in QKD is the Wegman
Classical M-Fivebrane Dynamics and Quantum N=2 Yang-Mills
P. S. Howe; N. D. Lambert; P. C. West
1997-11-05T23:59:59.000Z
We obtain the complete quantum Seiberg-Witten effective action for N=2 supersymmetric SU(N) Yang-Mills theory from the classical M-fivebrane equations of motion with N threebranes moving in its worldvolume.
Polymer Quantum Mechanics and its Continuum Limit
Alejandro Corichi; Tatjana Vukasinac; Jose A. Zapata
2007-08-22T23:59:59.000Z
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle and a simple cosmological model.
Information Nano-Technologies: Transition from Classical to Quantum
Alexander Yu. Vlasov
2009-12-04T23:59:59.000Z
In this presentation are discussed some problems, relevant with application of information technologies in nano-scale systems and devices. Some methods already developed in quantum information technologies may be very useful here. Here are considered two illustrative models: representation of data by quantum bits and transfer of signals in quantum wires.
Effectiveness of classical spin simulations for describing NMR relaxation of quantum spins
Tarek A. Elsayed; Boris V. Fine
2014-09-29T23:59:59.000Z
We investigate the limits of effectiveness of classical spin simulations for predicting free induction decays (FIDs) measured by solid-state nuclear magnetic resonance (NMR) on systems of quantum nuclear spins. The specific limits considered are associated with the range of interaction, the size of individual quantum spins and the long-time behavior of the FID signals. We compare FIDs measured or computed for lattices of quantum spins (mainly spins 1/2) with the FIDs computed for the corresponding lattices of classical spins. Several cases of excellent quantitative agreement between quantum and classical FIDs are reported along with the cases of gradually decreasing quality of the agreement. We formulate semi-empirical criteria defining the situations, when classical simulations are expected to accurately reproduce quantum FIDs. Our findings indicate that classical simulations may be a quantitatively accurate tool of first principles calculations for a broad class of macroscopic systems, where individual quantum microscopic degrees of freedom are far from the classical limit.
A general method for implementing vibrationally adiabatic mixed quantum-classical simulations
Thompson, Ward H.
2003-01-06T23:59:59.000Z
and this procedure is repeated until the input and output e(t1dt/2) are the same to within a specified tolerance ~as measured, for example, by De5ueoutput(t1dt/2)2einput(t1dt/2)u2). Next, advance the momenta a full time step from t to t 1dt: P ja~ t1dt !5P ja~ t !1... to these coordinates are pr , pe 5(pex,pey,pez), and P5(P1 ,P2 ,. . . ,PN). At this point we wish to treat the diatom bond distance quantum mechanically while retaining a classical description for all the other degrees-of-freedom. Specifically, we can de- fine a...
A Process Algebra Approach to Quantum Mechanics
William H. Sulis
2014-09-07T23:59:59.000Z
The process approach to NRQM offers a fourth framework for the quantization of physical systems. Unlike the standard approaches (Schrodinger-Heisenberg, Feynman, Wigner-Gronewald-Moyal), the process approach is not merely equivalent to NRQM and is not merely a re-interpretation. The process approach provides a dynamical completion of NRQM. Standard NRQM arises as a asymptotic quotient by means of a set-valued process covering map, which links the process algebra to the usual space of wave functions and operators on Hilbert space. The process approach offers an emergentist, discrete, finite, quasi-non-local and quasi-non-contextual realist interpretation which appears to resolve many of the paradoxes and is free of divergences. Nevertheless, it retains the computational power of NRQM and possesses an emergent probability structure which agrees with NRQM in the asymptotic quotient. The paper describes the process algebra, the process covering map for single systems and the configuration process covering map for multiple systems. It demonstrates the link to NRQM through a toy model. Applications of the process algebra to various quantum mechanical situations - superpositions, two-slit experiments, entanglement, Schrodinger's cat - are presented along with an approach to the paradoxes and the issue of classicality.
Ching-Yi Lai; Chung-Chin Lu
2007-12-02T23:59:59.000Z
In quantum coding theory, stabilizer codes are probably the most important class of quantum codes. They are regarded as the quantum analogue of the classical linear codes and the properties of stabilizer codes have been carefully studied in the literature. In this paper, a new but simple construction of stabilizer codes is proposed based on syndrome assignment by classical parity-check matrices. This method reduces the construction of quantum stabilizer codes to the construction of classical parity-check matrices that satisfy a specific commutative condition. The quantum stabilizer codes from this construction have a larger set of correctable error operators than expected. Its (asymptotic) coding efficiency is comparable to that of CSS codes. A class of quantum Reed-Muller codes is constructed, which have a larger set of correctable error operators than that of the quantum Reed-Muller codes developed previously in the literature. Quantum stabilizer codes inspired by classical quadratic residue codes are also constructed and some of which are optimal in terms of their coding parameters.
Parallelism of quantum computations from prequantum classical statistical field theory (PCSFT)
Andrei Khrennikov
2008-03-10T23:59:59.000Z
This paper is devoted to such a fundamental problem of quantum computing as quantum parallelism. It is well known that quantum parallelism is the basis of the ability of quantum computer to perform in polynomial time computations performed by classical computers for exponential time. Therefore better understanding of quantum parallelism is important both for theoretical and applied research, cf. e.g. David Deutsch \\cite{DD}. We present a realistic interpretation based on recently developed prequantum classical statistical field theory (PCSFT). In the PCSFT-approach to QM quantum states (mixed as well as pure) are labels of special ensembles of classical fields. Thus e.g. a single (!) ``electron in the pure state'' $\\psi$ can be identified with a special `` electron random field,'' say $\\Phi_\\psi(\\phi).$ Quantum computer operates with such random fields. By one computational step for e.g. a Boolean function $f(x_1,...,x_n)$ the initial random field $\\Phi_{\\psi_0}(\\phi)$ is transformed into the final random field $\\Phi_{\\psi_f}(\\phi)$ ``containing all values'' of $f.$ This is the objective of quantum computer's ability to operate quickly with huge amounts of information -- in fact, with classical random fields.
Classical analogous of quantum cosmological perfect fluid models
Batista, A B; Gonçalves, S V B; Tossa, J
2001-01-01T23:59:59.000Z
Quantization in the mini-superspace of a gravity system coupled to a perfect fluid, leads to a solvable model which implies singularity free solutions through the construction of a superposition of the wavefunctions. We show that such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid with an equation of state $p_Q = \\rho_Q$ is present. This leads to speculate on the true nature of this quantization procedure. A perturbative analysis of the classical system reveals the condition for the stability of the classical system in terms of the existence of an anti-gravity phase.
Strange Bedfellows: Quantum Mechanics and Data Mining
Marvin Weinstein
2009-11-03T23:59:59.000Z
Last year, in 2008, I gave a talk titled {\\it Quantum Calisthenics}. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.
Study of classical mechanical systems with complex potentials
A. Sinha; D. Dutta; P. Roy
2011-01-08T23:59:59.000Z
We apply the factorization technique developed by Kuru and Negro [Ann. Phys. 323 (2008) 413] to study complex classical systems. As an illustration we apply the technique to study the classical analogue of the exactly solvable PT symmetric Scarf II model, which exhibits the interesting phenomenon of spontaneous breakdown of PT symmetry at some critical point. As the parameters are tuned such that energy switches from real to complex conjugate pairs, the corresponding classical trajectories display a distinct characteristic feature - the closed orbits become open ones.
Optimization Online - Quantum and classical coin-flipping protocols ...
Ashwin Nayak
2015-04-21T23:59:59.000Z
Apr 21, 2015 ... In this analogy, classical systems correspond to linear programming ... Moreover, if the product of Alice and Bob's optimal cheating probabilities is 1/2, then exactly one party can perfectly control the outcome of the protocol.
Wu Jianlan [Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027 (China); Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139 (United States); Liu Fan; Silbey, Robert J.; Cao Jianshu [Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139 (United States); Ma Jian [Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027 (China)
2012-11-07T23:59:59.000Z
Following the calculation of optimal energy transfer in thermal environment in our first paper [J. L. Wu, F. Liu, Y. Shen, J. S. Cao, and R. J. Silbey, New J. Phys. 12, 105012 (2010)], full quantum dynamics and leading-order 'classical' hopping kinetics are compared in the seven-site Fenna-Matthews-Olson (FMO) protein complex. The difference between these two dynamic descriptions is due to higher-order quantum corrections. Two thermal bath models, classical white noise (the Haken-Strobl-Reineker (HSR) model) and quantum Debye model, are considered. In the seven-site FMO model, we observe that higher-order corrections lead to negligible changes in the trapping time or in energy transfer efficiency around the optimal and physiological conditions (2% in the HSR model and 0.1% in the quantum Debye model for the initial site at BChl 1). However, using the concept of integrated flux, we can identify significant differences in branching probabilities of the energy transfer network between hopping kinetics and quantum dynamics (26% in the HSR model and 32% in the quantum Debye model for the initial site at BChl 1). This observation indicates that the quantum coherence can significantly change the distribution of energy transfer pathways in the flux network with the efficiency nearly the same. The quantum-classical comparison of the average trapping time with the removal of the bottleneck site, BChl 4, demonstrates the robustness of the efficient energy transfer by the mechanism of multi-site quantum coherence. To reconcile with the latest eight-site FMO model which is also investigated in the third paper [J. Moix, J. L. Wu, P. F. Huo, D. F. Coker, and J. S. Cao, J. Phys. Chem. Lett. 2, 3045 (2011)], the quantum-classical comparison with the flux network analysis is summarized in Appendix C. The eight-site FMO model yields similar trapping time and network structure as the seven-site FMO model but leads to a more disperse distribution of energy transfer pathways.
A Review of Student Difficulties in Upper-Level Quantum Mechanics
Singh, Chandralekha
2015-01-01T23:59:59.000Z
Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical mechanics and quantum mechanics are very different. Here, we review research on student reasoning difficulties in learning upper-level quantum mechanics and research on students' problem-solving and metacognitive skills in these courses. Some of these studies were multi-university investigations. The investigations suggest that there is large diversity in student performance in upper-level quantum mechanics regardless of the university, textbook, or instructor and many students in these courses have not acquired a functional understanding of the fundamental concepts. The nature of reasoning difficulties in learning quantum mechanics is analogous to reasoning difficulties...
Playing games in quantum mechanical settings: A necessary and sufficient condition
Junichi Shimamura; Sahin Kaya Ozdemir; Nobuyuki Imoto
2005-08-15T23:59:59.000Z
A number of recent studies have focused on novel features in game theory when the games are played using quantum mechanical toolbox (entanglement, unitary operators, measurement). Researchers have concentrated in two-player-two strategy, 2x2, dilemma containing classical games, and transferred them into quantum realm showing that in quantum pure strategies dilemmas in such games can be resolved if entanglement is distributed between the players armed with quantum operations. Moreover, it became clear that the players receive the highest sum of payoffs available in the game, which are otherwise impossible in classical pure strategies. Encouraged by the observation of rich dynamics of physical systems with many interacting parties and the power of entanglement in quantum versions of 2x2 games, it became generally accepted that quantum versions can be easily extended to N-player situations by simply allowing N-partite entangled states. In this article, however, we show that this is not generally true because the reproducibility of classical tasks in quantum domain imposes limitations on the type of entanglement and quantum operators. We propose a benchmark for the evaluation of quantum and classical versions of games, and derive the necessary and sufficient conditions for a physical realization. We give examples of entangled states that can and cannot be used, and the characteristics of quantum operators used as strategies.
Ulmer, W
2015-01-01T23:59:59.000Z
Friction incorporates the close connection between classical mechanics in irreversible thermodynamics. The translation to a quantum mechanical foundation is not trivial and requires a generalization of the Lagrange function. A change to electromagnetic circuits appears to more adequate, since the electric analogue (Ohms law) is related to scatter of electrons at lattice vibrations.
Prasenjit Deb; Manik Banik
2014-11-16T23:59:59.000Z
Quantum correlation lies at the very heart of almost all the non-classical phenomena exhibited by quantum systems composed of more than one subsystem. In the recent days it has been pointed out that there exists quantum correlation, namely discord which is more general than entanglement. Some authors have investigated that for certain initial states the quantum correlations as well as classical correlation exhibit sudden change under simple Markovian noise. We show that, this dy- namical behavior of the both types of correlations can be explained using the idea of complementary correlations introduced in [arXiv:1408.6851]. We also show that though certain class of mixed en- tangled states can resist the monotonic decay of quantum correlations,it is not true for all mixed states. Moreover, pure entangled states of two qubits will never exhibit such sudden change.
Gibbs Free Energy Analysis of a Quantum Analog of the Classical Binary Symmetric Channel
David K. Ford
2009-01-19T23:59:59.000Z
The Gibbs free energy properties of a quantum {\\it send, receive} communications system are studied. The communications model resembles the classical Ising model of spins on a lattice in that the joint state of the quantum system is the product of sender and receiver states. However, the system differs from the classical case in that the sender and receiver spin states are quantum superposition states coupled by a Hamiltonian operator. A basic understanding of these states is directly relevant to communications theory and indirectly relevant to computation since the product states form a basis for entangled states. Highlights of the study include an exact method for decimation for quantum spins. The main result is that the minimum Gibbs free energy of the quantum system in the product state is higher (lower capacity) than a classical system with the same parameter values. The result is both surprising and not. The channel characteristics of the quantum system in the product state are markedly inferior to those of the classical Ising system. Intuitively, it would seem that capacity should suffer as a result. Yet, one would expect entangled states, built from product states, to have better correlation properties.
Classical-like behavior in quantum walks with inhomogeneous, time-dependent coin operators
Miquel Montero
2015-05-29T23:59:59.000Z
Although quantum walks exhibit distinctive properties that distinguish them from random walks, classical behavior can be recovered by destroying the coherence of the pure state associated to the quantum system. Here I show that this is not the only way: I introduce a quantum walk driven by an inhomogeneous, time-dependent coin operator, which mimics the statistical properties of a random walk. The quantum particle undergoes unitary evolution and, in fact, the coherence evidenced by the wave function can be used to revert the outcome of an accidental measure of its chirality.
Classical and quantum dynamics in the (non-Hermitian) Swanson oscillator
Eva-Maria Graefe; Hans Jürgen Korsch; Alexander Rush; Roman Schubert
2014-12-21T23:59:59.000Z
The non-Hermitian quadratic oscillator studied by Swanson is one of the popular $PT$-symmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine the classical symplectic flow for Hermitian systems with a dissipative metric flow for the anti-Hermitian part. Closed form expressions for the metric and phase-space trajectories are presented which are found to be periodic in time. Since the Hamiltonian is only quadratic the classical dynamics exactly describes the quantum dynamics of Gaussian wave packets. It is shown that the classical metric and trajectories as well as the quantum wave functions can diverge in finite time even though the $PT$-symmetry is unbroken, i.e., the eigenvalues are purely real.
Unified analysis of terminal-time control in classical and quantum systems
Alexander Pechen; Herschel Rabitz
2010-11-04T23:59:59.000Z
Many phenomena in physics, chemistry, and biology involve seeking an optimal control to maximize an objective for a classical or quantum system which is open and interacting with its environment. The complexity of finding an optimal control for maximizing an objective is strongly affected by the possible existence of sub-optimal maxima. Within a unified framework under specified conditions, control objectives for maximizing at a terminal time physical observables of open classical and quantum systems are shown to be inherently free of sub-optimal maxima. This attractive feature is of central importance for enabling the discovery of controls in a seamless fashion in a wide range of phenomena transcending the quantum and classical regimes.
Mossbauer neutrinos in quantum mechanics and quantum field theory
Kopp, Joachim
2009-01-01T23:59:59.000Z
We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations. First, we compute the combined rate $\\Gamma$ of Mossbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for $\\Gamma$ is identical to the one obtained previously (Akhmedov et al., arXiv:0802.2513) for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Mossbauer neutrinos and show that the oscillation, coherence and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detecti...
Classical and Quantum Aspects of 1+1 Gravity
T. Kloesch; P. Schaller; T. Strobl
1996-08-02T23:59:59.000Z
We present a classification of all global solutions (with Lorentzian signature) for any general 2D dilaton gravity model. For generic choices of potential-like terms in the Lagrangian one obtains maximally extended solutions on arbitrary non-compact two-manifolds, including various black-hole and kink configurations. We determine all physical quantum states in a Dirac approach. In some cases the spectrum of the (black-hole) mass operator is found to be sensitive to the signature of the theory, which may be relevant in view of current attempts to implement a generalized Wick-rotation in 4D quantum gravity.
Noncommutative Quantum Mechanics from Noncommutative Quantum Field Theory
Pei-Ming Ho; Hsien-Chung Kao
2001-10-26T23:59:59.000Z
We derive noncommutative multi-particle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Paricles of opposite charges are found to have opposite noncommutativity. As a result, there is no noncommutative correction to the hydrogen atom spectrum at the tree level. We also comment on the obstacles to take noncommutative phenomenology seriously, and propose a way to construct noncommutative SU(5) grand unified theory.
Dmitry Gavinsky; Julia Kempe; Ronald de Wolf
2006-07-25T23:59:59.000Z
We give an exponential separation between one-way quantum and classical communication complexity for a Boolean function. Earlier such a separation was known only for a relation. A very similar result was obtained earlier but independently by Kerenidis and Raz [KR06]. Our version of the result gives an example in the bounded storage model of cryptography, where the key is secure if the adversary has a certain amount of classical storage, but is completely insecure if he has a similar amount of quantum storage.
Noise in Classical and Quantum Photon-Correlation
Teich, Malvin C.
.2.2 Van CittertZernike theorem 21.2.3 Hanbury-Brown-Twiss interferometer 21.3 Quantum Photon is stellar imaging using a Hanbury- BrownTwiss intensity-correlation interferometer.47 More recently, two
Geometric potentials in quantum optics: A semi-classical interpretation
analysis may help for the design and the implementation of novel geometric forces. Cold atomic gases are considered as efficient simulators of quantum condensed matter systems (for a review, see e.g. [1 in the implementation of these simulators is the possibil- ity to apply a gauge field to the cold atomic gas in or- der
Standard Quantum Limit for Probing Mechanical Energy Quantization
Corbitt, Thomas R.
We derive a standard quantum limit for probing mechanical energy quantization in a class of systems with mechanical modes parametrically coupled to external degrees of freedom. To resolve a single mechanical quantum, it ...
Graeme Smith
2007-05-25T23:59:59.000Z
We study the symmetric-side-channel-assisted private capacity of a quantum channel, for which we provide a single-letter formula. This capacity is additive, convex, and, for degradable channels, equal to the unassisted private capacity. While a channel's (unassisted) capacity for for private classical communication may be strictly larger than its quantum capacity, we will show that these capacities are equal for degradable channels, thus demonstrating the equivalence of privacy and quantum coherence in this context. We use these ideas to find new bounds on the key rate of quantum key distribution protocols with one-way classical post-processing. For the Bennett-Brassard-84 (BB84) protocol, our results demonstrate that collective attacks are strictly stronger than individual attacks.
Nonlinear Quantum Mechanics at the Planck Scale
George Svetlichny
2004-10-27T23:59:59.000Z
I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear effects can be of comparable magnitude to the linear ones and still be highly suppressed at low energies. This can offer alternative approaches to quantum gravity and to the evolution of the early universe.
Mossbauer neutrinos in quantum mechanics and quantum field theory
Joachim Kopp
2009-06-12T23:59:59.000Z
We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations. First, we compute the combined rate $\\Gamma$ of Mossbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for $\\Gamma$ is identical to the one obtained previously (Akhmedov et al., arXiv:0802.2513) for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Mossbauer neutrinos and show that the oscillation, coherence, and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detection cross section, including localization and Lamb-Mossbauer terms, cannot be predicted in quantum mechanics and have to be put in by hand.
3D gravity with dust: classical and quantum theory
Viqar Husain; Jonathan Ziprick
2015-06-02T23:59:59.000Z
We study the Einstein gravity and dust system in three spacetime dimensions as an example of a non-perturbative quantum gravity model with local degrees of freedom. We derive the Hamiltonian theory in the dust time gauge and show that it has a rich class of exact solutions. These include the Ba\\~nados-Teitelboim-Zanelli black hole, static solutions with naked singularities and travelling wave solutions with dynamical horizons. We give a complete quantization of the wave sector of the theory, including a definition of a self-adjoint spacetime metric operator. This operator is used to demonstrate the quantization of deficit angle and the fluctuation of dynamical horizons.
Environment--Induced Decoherence, Classicality and Consistency of Quantum Histories
Juan Pablo Paz; Wojciech Hubert Zurek
1993-04-20T23:59:59.000Z
We prove that for an open system, in the Markovian regime, it is always possible to construct an infinite number of non trivial sets of histories that exactly satisfy the probability sum rules. In spite of being perfectly consistent, these sets manifest a very non--classical behavior: they are quite unstable under the addition of an extra instant to the list of times defining the history. To eliminate this feature --whose implications for the interpretation of the formalism we discuss-- and to achieve the stability that characterizes the quasiclassical domain, it is necessary to separate the instants which define the history by time intervals significantly larger than the typical decoherence time. In this case environment induced superselection is very effective and the quasiclassical domain is characterized by histories constructed with ``pointer projectors''.
Xie, Weiwei; Xu, Yang; Zhu, Lili; Shi, Qiang, E-mail: qshi@iccas.ac.cn [Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190 (China)] [Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190 (China)
2014-05-07T23:59:59.000Z
We present mixed quantum classical calculations of the proton transfer (PT) reaction rates represented by a double well system coupled to a dissipative bath. The rate constants are calculated within the so called nontraditional view of the PT reaction, where the proton motion is quantized and the solvent polarization is used as the reaction coordinate. Quantization of the proton degree of freedom results in a problem of non-adiabatic dynamics. By employing the reactive flux formulation of the rate constant, the initial sampling starts from the transition state defined using the collective reaction coordinate. Dynamics of the collective reaction coordinate is treated classically as over damped diffusive motion, for which the equation of motion can be derived using the path integral, or the mixed quantum classical Liouville equation methods. The calculated mixed quantum classical rate constants agree well with the results from the numerically exact hierarchical equation of motion approach for a broad range of model parameters. Moreover, we are able to obtain contributions from each vibrational state to the total reaction rate, which helps to understand the reaction mechanism from the deep tunneling to over the barrier regimes. The numerical results are also compared with those from existing approximate theories based on calculations of the non-adiabatic transmission coefficients. It is found that the two-surface Landau-Zener formula works well in calculating the transmission coefficients in the deep tunneling regime, where the crossing point between the two lowest vibrational states dominates the total reaction rate. When multiple vibrational levels are involved, including additional crossing points on the free energy surfaces is important to obtain the correct reaction rate using the Landau-Zener formula.
Modified Bennett-Brassard 1984 Quantum Key Distribution With Two-way Classical Communications
Kai Wen; Gui Lu Long
2005-08-27T23:59:59.000Z
The quantum key distribution protocol without public announcement of bases is equipped with a two-way classical communication symmetric entanglement purification protocol. This modified key distribution protocol is unconditionally secure and has a higher tolerable error rate of 20%, which is higher than previous scheme without public announcement of bases.
Janke, Wolfhard
and quantum compass model Sandro Wenzel* and Wolfhard Janke Institut für Theoretische Physik and Centre compass model on the square lattice is performed for classical and quantum spin degrees of freedom using and critical exponents. In a preinvestigation we recon- sider the classical compass model where we study
Kenji Nakahira; Tsuyoshi Sasaki Usuda
2015-01-26T23:59:59.000Z
We study the discrimination of multipartite quantum states by local operations and classical communication. We derive that any optimal discrimination of quantum states spanning a two-dimensional Hilbert space in which each party's space is finite dimensional is possible by local operations and one-way classical communication, regardless of the optimality criterion used and how entangled the states are.
Phil Attard
2013-11-25T23:59:59.000Z
The probability operator is derived from first principles for an equilibrium quantum system. It is also shown that the superposition states collapse into a mixture of states giving the conventional von Neumann trace form for the quantum average. The mechanism for the collapse is found to be quite general: it results from the conservation law for a conserved, exchangeable variable (such as energy) and the entanglement of the total system wave function that necessarily follows. The relevance of the present results to the einselection mechanism for decoherence, to the quantum measurement problem, and to the classical nature of the macroscopic world are discussed.
The ramifications of diffusive volume transport in classical fluid mechanics
Bielenberg, James R. (James Ronald), 1976-
2004-01-01T23:59:59.000Z
The thesis that follows consists of a collection of work supporting and extending a novel reformulation of fluid mechanics, wherein the linear momentum per unit mass in a fluid continuum, m, is supposed equal to the volume ...
Prants, S. V.; Uleysky, M. Yu.; Argonov, V. Yu. [Laboratory of Nonlinear Dynamical Systems, V.I. Il'ichev Pacific Oceanological Institute of the Russian Academy of Sciences, 690041 Vladivostok (Russian Federation)
2006-02-15T23:59:59.000Z
Stability and instability of quantum evolution are studied in the interaction between a two-level atom with photon recoil and a quantized field mode in an ideal cavity, the basic model of cavity quantum electrodynamics. It is shown that the Jaynes-Cummings dynamics can be unstable in the regime of chaotic motion of the atomic center of mass in the quantized field of a standing wave in the absence of any kind of interaction with environment. This kind of quantum instability manifests itself in strong variations of reduced quantum purity and entropy, correlating with the respective classical Lyapunov exponent, and in exponential sensitivity of fidelity of quantum states to small variations in the atom-field detuning. The connection between quantum entanglement and fidelity and the center-of-mass motion is clarified analytically and numerically for a few regimes of that motion. The results are illustrated with two specific initial field states: the Fock and coherent ones. Numerical experiments demonstrate various manifestations of the quantum-classical correspondence, including dynamical chaos and fractals, which can be, in principle, observed in real experiments with atoms and photons in high-finesse cavities.
On the classical character of control fields in quantum information processing
S. J. van Enk; H. J. Kimble
2001-07-17T23:59:59.000Z
Control fields in quantum information processing are virtually always, almost by definition, assumed to be classical. In reality, however, when such a field is used to manipulate the quantum state of qubits, the qubits never remain completely unentangled with the field. For quantum information processing this is an undesirable property, as it precludes perfect quantum computing and quantum communication. Here we consider the interaction of atomic qubits with laser fields and quantify atom-field entanglement in various cases of interest. We find that the entanglement decreases with the average number of photons $\\bar{n}$ in a laser beam as $E\\propto\\log_2 \\bar{n}/\\bar{n}$ for $\\bar{n}\\to\\infty$.
Multiparty quantum secret sharing of classical messages based on entanglement swapping
Zhang Zhanjun [School of Physics and Material Science, Anhui University, Hefei 230039 (China); Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071 (China); Man Zhongxiao [Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071 (China)
2005-08-15T23:59:59.000Z
A multiparty quantum secret sharing (QSS) protocol of classical messages (i.e., classical bits) is proposed by using swapping quantum entanglement of Bell states. The secret messages are imposed on Bell states by local unitary operations. The secret messages are split into several parts, and each part is distributed to a separate party so that no action of a subset of all the parties without the cooperation of the entire group is able to read out the secret messages. In addition, dense coding is used in this protocol to achieve a high efficiency. The security of the present multiparty QSS against eavesdropping has been analyzed and confirmed even in a noisy quantum channel.
Spin Glass: A Bridge between quantum computation and statistical mechanics
Masayuki Ohzeki
2012-04-24T23:59:59.000Z
We show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Second, we show another interesting technique to employ quantum nature, quantum annealing. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.
A Signal Processing Model of Quantum Mechanics
Chris Thron; Johnny Watts
2012-05-08T23:59:59.000Z
This paper develops a deterministic model of quantum mechanics as an accumulation-and-threshold process. The model arises from an analogy with signal processing in wireless communications. Complex wavefunctions are interpreted as expressing the amplitude and phase information of a modulated carrier wave. Particle transmission events are modeled as the outcome of a process of signal accumulation that occurs in an extra (non-spacetime) dimension. Besides giving a natural interpretation of the wavefunction and the Born rule, the model accommodates the collapse of the wave packet and other quantum paradoxes such as EPR and the Ahanorov-Bohm effect. The model also gives a new perspective on the 'relational' nature of quantum mechanics: that is, whether the wave function of a physical system is "real" or simply reflects the observer's partial knowledge of the system. We simulate the model for a 2-slit experiment, and indicate possible deviations of the model's predictions from conventional quantum mechanics. We also indicate how the theory may be extended to a field theory.
Deformation Quantization: From Quantum Mechanics to Quantum Field Theory
P. Tillman
2006-10-31T23:59:59.000Z
The aim of this paper is to give a basic overview of Deformation Quantization (DQ) to physicists. A summary is given here of some of the key developments over the past thirty years in the context of physics, from quantum mechanics to quantum field theory. Also, we discuss some of the conceptual advantages of DQ and how DQ may be related to algebraic quantum field theory. Additionally, our previous results are summarized which includes the construction of the Fedosov star-product on dS/AdS. One of the goals of these results was to verify that DQ gave the same results as previous analyses of these spaces. Another was to verify that the formal series used in the conventional treatment converged by obtaining exact and nonperturbative results for these spaces.
Mechanisms of classical crystal growth theory explain quartz and silicate dissolution behavior
Dove, Patricia M.
Mechanisms of classical crystal growth theory explain quartz and silicate dissolution behavior processes was previously unknown for oxides or silicates, our mechanism-based findings are consistent, the geochemistry of earth systems is, in large part, controlled by the kinetics of silicate mineral dissolution
Campos, Leonardo
The advent of few-layer graphene has given rise to a new family of two-dimensional systems with emergent electronic properties governed by relativistic quantum mechanics. The multiple carbon sublattices endow the electronic ...
The classical limit of quantum optics: not what it seems at first sight
Yakir Aharonov; Alonso Botero; Shmuel Nussinov; Sandu Popescu; Jeff Tollaksen; Lev Vaidman
2013-05-01T23:59:59.000Z
What is light and how to describe it has always been a central subject in physics. As our understanding has increased, so have our theories changed: Geometrical optics, wave optics and quantum optics are increasingly sophisticated descriptions, each referring to a larger class of phenomena than its predecessor. But how exactly are these theories related? How and when wave optics reduces to geometric optics is a rather simple problem. Similarly, how quantum optics reduces to wave optics has been considered to be a very simple business as well. It's not so. As we show here the classical limit of quantum optics is a far more complicated issue; it is in fact dramatically more involved and it requires a complete revision of all our intuitions. The revised intuitions can then serve as a guide to finding novel quantum effects.
Quantum Mechanics, Gravity, and the Multiverse
Yasunori Nomura
2012-07-30T23:59:59.000Z
The discovery of accelerating expansion of the universe has led us to take the dramatic view that our universe may be one of the many universes in which low energy physical laws take different forms: the multiverse. I explain why/how this view is supported both observationally and theoretically, especially by string theory and eternal inflation. I then describe how quantum mechanics plays a crucial role in understanding the multiverse, even at the largest distance scales. The resulting picture leads to a revolutionary change of our view of spacetime and gravity, and completely unifies the paradigm of the eternally inflating multiverse with the many worlds interpretation of quantum mechanics. The picture also provides a solution to a long-standing problem in eternal inflation, called the measure problem, which I briefly describe.
Latyshev, A V
2015-01-01T23:59:59.000Z
From Vlasov kinetic equation for collisionless plasmas distribution function in square-law approximation on size of electromagnetic field is received. Formulas for calculation electric current at any temperature (any degree of degeneration of electronic gas) are deduced. The case of small values of the wave numbers is considered. It is shown, that the nonlinearity account leads to occurrence the longitudinal electric current directed along a wave vector. This longitudinal current orthogonal to known transversal classical current, received at the linear analysis. From the kinetic equation with Wigner integral for collisionless quantum plasma distribution function is received in square-law on vector potential approximation. Formulas for calculation electric current at any temperature are deduced. The case of small values of wave number is considered. It is shown, that size of a longitudinal current at small values of wave number and for classical plasma and for quantum plasma coincide. Graphic comparison of dim...
Classical simulation of measurement-based quantum computation on higher-genus surface-code states
Leonard Goff; Robert Raussendorf
2012-10-31T23:59:59.000Z
We consider the efficiency of classically simulating measurement-based quantum computation on surface-code states. We devise a method for calculating the elements of the probability distribution for the classical output of the quantum computation. The operational cost of this method is polynomial in the size of the surface-code state, but in the worst case scales as $2^{2g}$ in the genus $g$ of the surface embedding the code. However, there are states in the code space for which the simulation becomes efficient. In general, the simulation cost is exponential in the entanglement contained in a certain effective state, capturing the encoded state, the encoding and the local post-measurement states. The same efficiencies hold, with additional assumptions on the temporal order of measurements and on the tessellations of the code surfaces, for the harder task of sampling from the distribution of the computational output.
Classical and Quantum Gravity in 1+1 Dimensions, Part I: A Unifying Approach
T. Kloesch; T. Strobl
1997-08-11T23:59:59.000Z
We provide a concise approach to generalized dilaton theories with and without torsion and coupling to Yang-Mills fields. Transformations on the space of fields are used to trivialize the field equations locally. In this way their solution becomes accessible within a few lines of calculation only. In this first of a series of papers we set the stage for a thorough global investigation of classical and quantum aspects of more or less all available 2D gravity-Yang-Mills models.
Quantum versus classical descriptions of sub-Poissonian light generation in three-wave mixing
Jiri Bajer; Adam Miranowicz
2001-07-20T23:59:59.000Z
Sub-Poissonian light generation in the non-degenerate three-wave mixing is studied numerically and analytically within quantum and classical approaches. Husimi Q-functions and their classical trajectory simulations are analysed to reveal a special regime corresponding to the time-stable sub-Poissonian photocount statistics of the sum-frequency mode. Conditions for observation of this regime are discussed. Theoretical predictions of the Fano factor and explanation of the extraordinary stabilization of the sub-Poissonian photocount behavior are obtained analytically by applying the classical trajectories. Scaling laws for the maximum sub-Poissonian behavior are found. Noise suppression levels in the non-degenerate vs degenerate three-wave mixing are discussed on different time scales compared to the revival times. It is shown that the non-degenerate conversion offers much better stabilization of the suppressed noise in comparison to that of degenerate process.
Smooth quantum-classical transition in photon subtraction and addition processes
A. V. Dodonov; S. S. Mizrahi
2009-01-28T23:59:59.000Z
Recently Parigi et al. [Science 317, 1890 (2007)] implemented experimentally the photon subtraction and addition processes from/to a light field in a conditional way, when the required operations were produced successfully only upon the positive outcome of a separate measurement. It was verified that for a low intensity beam (quantum regime) the bosonic annihilation operator does indeed describe a single photon subtraction, while the creation operator describes a photon addition. Nonetheless, the exact formal expressions for these operations do not always reduce to these simple identifications, and in this connection here we deduce the general superoperators for multiple photons subtraction and addition processes and analyze the statistics of the resulting states for classical field states having an arbitrary intensity. We obtain closed analytical expressions and verify that for classical fields with high intensity (classical regime) the operators that describe photon subtraction and addition processes deviate significantly from simply annihilation and creation operators. Complementarily, we analyze in details such a smooth quantum-classical transition as function of beam intensity for both processes.
Dinner, Aaron
Abstract. We present a method to treat the solvent ef- ficiently in hybrid quantum mechanical, the central reactive region is treated quan- tum mechanically to allow key bonds to be made and broken, while the surrounding non-reactive region is treated classically to make the calculations computa- tionally feasible
R. Fedele; M. A. Man'ko; V. I. Man'ko; V. G. Vaccaro
2002-07-30T23:59:59.000Z
It is shown that the transmission line technology can be suitably used for simulating quantum mechanics. Using manageable and at the same time non-expensive technology, several quantum mechanical problems can be simulated for significant tutorial purposes. The electric signal envelope propagation through the line is governed by a Schrodinger-like equation for a complex function, representing the low-frequency component of the signal, In this preliminary analysis, we consider two classical examples, i.e. the Frank-Condon principle and the Ramsauer effect.
Quantum mechanics with coordinate dependent noncommutativity
Kupriyanov, V. G. [CMCC, Universidade Federal do ABC, Santo André, SP (Brazil)] [CMCC, Universidade Federal do ABC, Santo André, SP (Brazil)
2013-11-15T23:59:59.000Z
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.
Non-equilibrium transition from dissipative quantum walk to classical random walk
Marco Nizama; Manuel O. Cáceres
2012-06-26T23:59:59.000Z
We have investigated the time-evolution of a free particle in interaction with a phonon thermal bath, using the tight-binding approach. A dissipative quantum walk can be defined and many important non-equilibrium decoherence properties can be investigated analytically. The non-equilibrium statistics of a pure initial state have been studied. Our theoretical results indicate that the evolving wave-packet shows the suppression of Anderson's boundaries (ballistic peaks) by the presence of dissipation. Many important relaxation properties can be studied quantitatively, such as von Neumann's entropy and quantum purity. In addition, we have studied Wigner's function. The time-dependent behavior of the quantum entanglement between a free particle -in the lattice- and the phonon bath has been characterized analytically. This result strongly suggests the non-trivial time-dependence of the off-diagonal elements of the reduced density matrix of the system. We have established a connection between the quantum decoherence and the dissipative parameter arising from interaction with the phonon bath. The time-dependent behavior of quantum correlations has also been pointed out, showing continuous transition from quantum random walk to classical random walk, when dissipation increases.
Quantum mechanism helps agents combat "bad" social choice rules
Haoyang Wu
2011-04-22T23:59:59.000Z
Quantum strategies have been successfully applied to game theory for years. However, as a reverse problem of game theory, the theory of mechanism design is ignored by physicists. In this paper, the theory of mechanism design is generalized to a quantum domain. The main result is that by virtue of a quantum mechanism, agents who satisfy a certain condition can combat "bad" social choice rules instead of being restricted by the traditional mechanism design theory.
The rate constant for radiative association of HF: Comparing quantum and classical dynamics
Gustafsson, Magnus, E-mail: magngu@chem.gu.se; Monge-Palacios, M.; Nyman, Gunnar [Department of Chemistry and Molecular Biology, University of Gothenburg, 41296 Gothenburg (Sweden)] [Department of Chemistry and Molecular Biology, University of Gothenburg, 41296 Gothenburg (Sweden)
2014-05-14T23:59:59.000Z
Radiative association for the formation of hydrogen fluoride through the A{sup 1}? ? X{sup 1}?{sup +} and X{sup 1}?{sup +} ? X{sup 1}?{sup +} transitions is studied using quantum and classical dynamics. The total thermal rate constant is obtained for temperatures from 10 K to 20 000 K. Agreement between semiclassical and quantum approaches is observed for the A{sup 1}? ? X{sup 1}?{sup +} rate constant above 2000 K. The agreement is explained by the fact that the corresponding cross section is free of resonances for this system. At temperatures below 2000 K we improve the agreement by implementing a simplified semiclassical expression for the rate constant, which includes a quantum corrected pair distribution. The rate coefficient for the X{sup 1}?{sup +} ? X{sup 1}?{sup +} transition is calculated using Breit–Wigner theory and a classical formula for the resonance and direct contributions, respectively. In comparison with quantum calculations the classical formula appears to overestimate the direct contribution to the rate constant by about 12% for this transition. Below about 450 K the resonance contribution is larger than the direct, and above that temperature the opposite holds. The biggest contribution from resonances is at the lowest temperature in the study, 10 K, where it is more than four times larger than the direct. Below 1800 K the radiative association rate constant due to X{sup 1}?{sup +} ? X{sup 1}?{sup +} transitions dominates over A{sup 1}? ? X{sup 1}?{sup +}, while above that temperature the situation is the opposite.
arXiv:cond-mat/0208233v418Nov2003 Classical and quantum pumping in closed systems
Cohen, Doron
arXiv:cond-mat/0208233v418Nov2003 Classical and quantum pumping in closed systems Doron Cohen version [1], follow up [2]) Pumping of charge (Q) in a closed ring geometry is not quantized even and the adiabatic contributions to Q. As an application we bring examples for classical dissipative pumping
Gogonea, V.; Merz, K.M. Jr. [Pennsylvania State Univ., University Park, PA (United States). Dept. of Chemistry] [Pennsylvania State Univ., University Park, PA (United States). Dept. of Chemistry
1999-07-01T23:59:59.000Z
In this paper the authors report a method for solving the Schroedinger equation for large molecules in solution which involved merging a linear scaling divide and conquer (D and C) semiempirical algorithm with the Poisson-Boltzmann (PB) equation. They then assess the performance of their self-consistent reaction field (SCRF) approach by comparing the D and C-PB calculations for a set of 29 neutral and 36 charged molecules with those obtained by ab initio GVB and DFT (B3LYP) methods, Cramer and Truhlar`s semiempirical generalized-Born SM5 model, and with the experimental solvation free energies. Furthermore, the authors show that their SCRF method can be used to perform fully quantum mechanical calculations of proteins in solution in a reasonable amount of time on a modern workstation. They believe that all electrostatic interactions in biological systems require a quantum mechanical description in order to obtain an accurate representation. Thus, their new SCRF method should have an impact on the computational study of physical and chemical phenomena occurring in proteins and nuclei acids, which are, in general, strongly influenced by electrostatic interactions. Moreover, this may lead to novel insights into classic problems like protein folding or drug design.
5.74 Introductory Quantum Mechanics II, Spring 2007
Tokmakoff, Andrei
Time-dependent quantum mechanics and spectroscopy. Topics covered include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, ...
5.74 Introductory Quantum Mechanics II, Spring 2003
Tokmakoff, Andrei
Time-dependent quantum mechanics and spectroscopy. Topics covered include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, ...
The Multiverse Interpretation of Quantum Mechanics
Raphael Bousso; Leonard Susskind
2011-07-22T23:59:59.000Z
We argue that the many-worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics. Decoherence - the modern version of wave-function collapse - is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the "environment". In fact decoherence is absent in the complete description of any region larger than the future light-cone of a measurement event. However, if one restricts to the causal diamond - the largest region that can be causally probed - then the boundary of the diamond acts as a one-way membrane and thus provides a preferred choice of environment. We argue that the global multiverse is a representation of the many-worlds (all possible decoherent causal diamond histories) in a single geometry. We propose that it must be possible in principle to verify quantum-mechanical predictions exactly. This requires not only the existence of exact observables but two additional postulates: a single observer within the universe can access infinitely many identical experiments; and the outcome of each experiment must be completely definite. In causal diamonds with finite surface area, holographic entropy bounds imply that no exact observables exist, and both postulates fail: experiments cannot be repeated infinitely many times; and decoherence is not completely irreversible, so outcomes are not definite. We argue that our postulates can be satisfied in "hats" (supersymmetric multiverse regions with vanishing cosmological constant). We propose a complementarity principle that relates the approximate observables associated with finite causal diamonds to exact observables in the hat.
Clocks And Dynamics In Quantum Mechanics
Michael York
2014-07-11T23:59:59.000Z
We argue that (1) our perception of time through change and (2) the gap between reality and our observation of it are at the heart of both quantum mechanics and the dynamical mechanism of physical systems. We suggest that the origin of quantum uncertainty lies with the absence of infinities or infinitesimals in observational data and that our concept of time derives from observing changing data (events). We argue that the fundamentally important content of the Superposition Principle is not the "probability amplitude" of posterior state observation but future state availability conditional only on prior information. Since event detection also implies posterior conditions (e.g. a specific type of detectable event occurred) as well as prior conditions, the probabilities of detected outcomes are also conditional on properties of the posterior properties of the observation. Such posterior conditions cannot affect the prior state availabilities and this implies violation of counter-factual definiteness. A component of a quantum system may be chosen to represent a clock and changes in other components can then be expected to be correlated with clocks with which they are entangled. Instead of traditional time-dependent equations of motion we provide a specific mechanism whereby evolution of data is instead quasi-causally related to the relative \\availability\\ of states and equations of motion are expressed in terms of quantized clock variables. We also suggest that time-reversal symmetry-breaking in weak interactions is an artifice of a conventional choice of co-ordinate time-function. Analysis of a "free" particle suggests that conventional co-ordinate space-time emerges from how we measure the separation of objects and events.
Ivanov, Mikhail [PSL Research University, Observatoire de Paris, Sorbonne Universités, UPMC Univ Paris 06, ENS, UCP, CNRS, UMR8112, LERMA, 5 Place Janssen, 92195 Meudon (France) [PSL Research University, Observatoire de Paris, Sorbonne Universités, UPMC Univ Paris 06, ENS, UCP, CNRS, UMR8112, LERMA, 5 Place Janssen, 92195 Meudon (France); Department of Chemistry, Marquette University, Milwaukee, Wisconsin 53201-1881 (United States); Dubernet, Marie-Lise [PSL Research University, Observatoire de Paris, Sorbonne Universités, UPMC Univ Paris 06, ENS, UCP, CNRS, UMR8112, LERMA, 5 Place Janssen, 92195 Meudon (France)] [PSL Research University, Observatoire de Paris, Sorbonne Universités, UPMC Univ Paris 06, ENS, UCP, CNRS, UMR8112, LERMA, 5 Place Janssen, 92195 Meudon (France); Babikov, Dmitri, E-mail: dmitri.babikov@mu.edu [Department of Chemistry, Marquette University, Milwaukee, Wisconsin 53201-1881 (United States)] [Department of Chemistry, Marquette University, Milwaukee, Wisconsin 53201-1881 (United States)
2014-04-07T23:59:59.000Z
The mixed quantum/classical theory (MQCT) formulated in the space-fixed reference frame is used to compute quenching cross sections of several rotationally excited states of water molecule by impact of He atom in a broad range of collision energies, and is tested against the full-quantum calculations on the same potential energy surface. In current implementation of MQCT method, there are two major sources of errors: one affects results at energies below 10 cm{sup ?1}, while the other shows up at energies above 500 cm{sup ?1}. Namely, when the collision energy E is below the state-to-state transition energy ?E the MQCT method becomes less accurate due to its intrinsic classical approximation, although employment of the average-velocity principle (scaling of collision energy in order to satisfy microscopic reversibility) helps dramatically. At higher energies, MQCT is expected to be accurate but in current implementation, in order to make calculations computationally affordable, we had to cut off the basis set size. This can be avoided by using a more efficient body-fixed formulation of MQCT. Overall, the errors of MQCT method are within 20% of the full-quantum results almost everywhere through four-orders-of-magnitude range of collision energies, except near resonances, where the errors are somewhat larger.
Classical noise assists the flow of quantum energy by `momentum rejuvenation'
Ying Li; Filippo Caruso; Erik Gauger; Simon C. Benjamin
2014-06-13T23:59:59.000Z
An important challenge in quantum science is to fully understand the efficiency of energy flow in networks. Here we present a simple and intuitive explanation for the intriguing observation that optimally efficient networks are not purely quantum, but are assisted by some interaction with a `noisy' classical environment. By considering the system's dynamics in both the site-basis and the momentum-basis, we show that the effect of classical noise is to sustain a broad momentum distribution, countering the depletion of high mobility terms which occurs as energy exits from the network. This picture predicts that the optimal level of classical noise is reciprocally related to the linear dimension of the lattice; our numerical simulations verify this prediction to high accuracy for regular 1D and 2D networks over a range of sizes up to thousands of sites. This insight leads to the discovery that dramatic further improvements in performance occur when a driving field targets noise at the low mobility components.
Non-representative quantum mechanical weak values
B. E. Y. Svensson
2015-03-06T23:59:59.000Z
The operational definition of a weak value for a quantum mechanical system involves the limit of the weak measurement strength tending to zero. I study how this limit compares to the situation for the undisturbed (no weak measurement) system. Under certain conditions, which I investigate, this limit is discontinuous in the sense that it does not merge smoothly to the Hilbert space description of the undisturbed system. Hence, in these discontinuous cases, the weak value does not represent the undisturbed system. As a result, conclusions drawn from such weak values regarding the properties of the studied system cannot be upheld. Examples are given.
Scattering in PT-symmetric quantum mechanics
Cannata, Francesco [Istituto Nazionale di Fisica Nucleare, Sezione di Bologna and Dipartimento di Fisica dell' Universita, Via Irnerio 46, I 40126 Bologna (Italy)]. E-mail: Francesco.Cannata@bo.infn.it; Dedonder, Jean-Pierre [GMPIB Universite Paris 7 - Denis-Diderot, 2 Place Jussieu, F-75251, Paris Cedex 05 (France)]. E-mail: dedonder@paris7.jussieu.fr; Ventura, Alberto [Ente Nuove Tecnologie, Energia e Ambiente, Bologna and Istituto Nazionale di Fisica Nucleare, Sezione di Bologna (Italy)]. E-mail: Alberto.Ventura@bologna.enea.it
2007-02-15T23:59:59.000Z
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with Hermiticity, T invariance and PT invariance.
Simonovic, N.S. [Institute of Physics, P.O. Box 57, 11001 Belgrade (Serbia and Montenegro)
2006-01-07T23:59:59.000Z
Relations between quantum-mechanical and classical properties of open systems with a saddle-type potential, for which at a given energy only one unstable periodic orbit exists, are studied. By considering the convergence of the Gutzwiller trace formula [J. Math. Phys. 12, 343 (1971)] it is confirmed that both for homogeneous and inhomogeneous potentials the poles of the formula are located below the real energy axis, i.e., these kind of potentials do not support bound states, in general. Within the harmonic approximation the widths of resonant (transition) states are proportional to the values of Lyapunov exponent of the single periodic orbit calculated at the energies which are equal to the resonance positions. The accuracy of the semiclassical relation is discussed and demonstrated for several examples.
Kauffman, Stuart
2014-01-01T23:59:59.000Z
I wish to discuss a large, interwoven set of topics pointed at in the title above. Much of what I say is highly speculative, some is testable, some is, at present, surely not. It is, I hope, useful, to set these ideas forth for our consideration. What I shall say assumes quantum measurement is real, and that Bohm's interpretation of Quantum Mechanics is not true. The Stalemate: In our contemporary neurobiology and much of the philosophy of mind post Descartes we are classical physics machines and either mindless, or mind is at best epiphenomenal and can have no consequences for the physical world. The first main point of this paper is that we are not forced to this conclusion, but must give up total reliance on classical physics.
Larkin, Teresa L.
Materials* Yan Wang** and Teresa L. Hein American University In this paper we will present our experiences using a portion of the materials developed by the Visual Quantum Mechanics (VQM) project1 as part of our materials were utilized in a new second-tier introductory course for non-science majors at American
Decoherence and the quantum-classical limit in the presence of chaos
Toscano, F.; Matos Filho, R.L. de; Davidovich, L. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68.528, 21.941-972, Rio de Janeiro (Brazil)
2005-01-01T23:59:59.000Z
We investigate how decoherence affects the short-time separation between quantum and classical dynamics for classically chaotic systems, within the framework of a specific model. For a wide range of parameters, the distance between the corresponding phase-space distributions depends on a single parameter {chi} that relates an effective Planck constant ({Dirac_h}/2{pi}){sub eff}, the Lyapunov coefficient, and the diffusion constant. This distance peaks at a time that depends logarithmically on ({Dirac_h}/2{pi}){sub eff}, in agreement with previous estimations of the separation time for Hamiltonian systems. However, for {chi} < or approx. 1, the separation remains small, going down with ({Dirac_h}/2{pi}){sub eff}{sup 2}, so the concept of separation time loses its meaning.
H. Hernández-Saldaña
2012-12-21T23:59:59.000Z
A calculation of the classical analogue for the quantum wave function and local denity of states, in energy representation, is presented for simple Hamiltonian systems. Sucha analogous were proposed by M. V. Berry and A. voros considering the intersection of energy shells of two systems as the only semiclassical object which can give support to eigenfunctions. One of them is the system unser study and the other is the "unperturbed system" used to express the wave functions, even in the case that both systems are not close. For simple systems and as for scalable ones analytical expressions are obtainable. In the present work we offer examples of both.
Quantum Mechanics and the Principle of Least Radix Economy
Vladimir Garcia-Morales
2015-01-08T23:59:59.000Z
A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this concept in a unified way. The principle reinterprets and generalizes the principle of least action yielding two classes of physical solutions: least action paths and quantum wavefunctions. A new physical foundation of the Hilbert space of quantum mechanics is then accomplished and it is used to derive the Schr\\"odinger and Dirac equations and the breaking of the commutativity of spacetime geometry. The formulation provides an explanation of how determinism and random statistical behavior coexist in spacetime and a framework is developed that allows dynamical processes to be formulated in terms of chains of digits. These methods lead to a new (pre-geometrical) foundation for Lorentz transformations and special relativity. The Parker-Rhodes combinatorial hierarchy is encompassed within our approach and this leads to an estimate of the interaction strength of the electromagnetic and gravitational forces that agrees with the experimental values to an error of less than one thousandth. Finally, it is shown how the principle of least-radix economy naturally gives rise to Boltzmann's principle of classical statistical thermodynamics. A new expression for a general (path-dependent) nonequilibrium entropy is proposed satisfying the Second Law of Thermodynamics.
Quantum Dynamical Model for Wave Function Reduction in Classical and Macroscopic Limits
Chang-Pu Sun
1993-03-22T23:59:59.000Z
In this papper, a quantum dynamical model describing the quantum measurement process is presented as an extensive generalization of the Coleman-Hepp model. In both the classical limit with very large quantum number and macroscopic limit with very large particle number in measuring instrument, this model generally realizes the wave packet collapse in quantum measurement as a consequence of the Schrodinger time evolution in either the exactly-solvable case or the non-(exactly-)solvable case. For the latter, its quasi-adiabatic case is explicitly analysed by making use of the high-order adiabatic approximation method and then manifests the wave packet collapse as well as the exactly-solvable case. By highlighting these analysis, it is finally found that an essence of the dynamical model of wave packet collapse is the factorization of the Schrodinger evolution other than the exact solvability. So many dynamical models including the well-known ones before, which are exactly-solvable or not, can be shown only to be the concrete realizations of this factorizability
Magnetic monopoles and dyons revisited: A useful contribution to the study of classical mechanics
Santos, Renato P dos
2015-01-01T23:59:59.000Z
Graduate level physics curricula in many countries around the world, as well as senior-level undergraduate ones in some major institutions, include Classical Mechanics courses, mostly based on Goldstein's textbook masterpiece. During the discussion of central force motion, however, the Kepler problem is virtually the only serious application presented. In this paper, we present another problem that is also soluble, namely the interaction of Schwinger's dual-charged (dyon) particles. While the electromagnetic interaction of magnetic monopoles and electric charges was studied in detail some 40 years ago, we consider that a pedagogical discussion of it from an essentially classical mechanics point of view is a useful contribution for students. Following a path that generalizes Kepler's problem and Rutherford scattering, we show that they exhibit remarkable properties such as stable non-planar orbits, as well as rainbow and glory scattering, which are not present in the ordinary scattering of two singly charged p...
The ideal energy of classical lattice dynamics
Margolus, Norman
2015-01-01T23:59:59.000Z
We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change. In two example dynamics, we see that these rates evolve like classical mechanical energy and momentum.
A Causal Net Approach to Relativistic Quantum Mechanics
R. D. Bateson
2012-05-13T23:59:59.000Z
In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on Reichenbach-like conjunctive forks in proper time we can exactly derive the 1+1 dimension Dirac equation for a relativistic fermion and correctly model quantum mechanical statistics. Symmetries of the net provide various quantum mechanical effects such as quantum uncertainty and wavefunction, phase, spin, negative energy states and the effect of a potential. The causal net can be embedded in 3+1 dimensions and is consistent with the conventional Dirac equation. In the low velocity limit the causal net approximates to the Schrodinger equation and Pauli equation for an electromagnetic field. Extending to different momentum states the net is compatible with the Feynman path integral approach to quantum mechanics that allows calculation of well known quantum phenomena such as diffraction.
Green's Functions and Their Applications to Quantum Mechanics
Morrow, James A.
Green's Functions and Their Applications to Quantum Mechanics Jeff Schueler June 2, 2011 Contents 1 Green's Functions in Quantum Mechanics and Many-body Theory 8 3.1 Time Independent Green's Fuctions . . . . . . . . . . . . . . 8 3.2 Solving the Schr¨odinger Equation Using Green's Functions . . 12 4 Conclusion 13 1 #12
Environment-Induced Decoherence in Noncommutative Quantum Mechanics
Joao Nuno Prata; Nuno Costa Dias
2006-12-02T23:59:59.000Z
We address the question of the appearence of ordinary quantum mechanics in the context of noncommutative quantum mechanics. We obtain the noncommutative extension of the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators. We consider the particular case of an Ohmic regime.
Kimichika Fukushima; Hikaru Sato
2014-10-04T23:59:59.000Z
This article reports an explicit function form for confining classical Yang-Mills vector potentials and quantum fluctuations around the classical field. The classical vector potential, which is composed of a confining localized function and an unlocalized function, satisfies the classical Yang-Mills equation. The confining localized function contributes to the Wilson loop, while the unlocalized function makes no contribution to this loop. The confining linear potential between a heavy fermion and antifermion is due to (1) the Lie algebra and (2) the form of the confining localized function which has opposite signs at the positions of the particle and antiparticle along the Wilson loop in the time direction. Some classical confining parts of vector potentials also change sign on inversion of the coordinates of the axis perpendicular to the axis joining the two particles. The localized parts of the vector potentials are squeezed around the axis connecting the two particles, and the string tension of the confining linear potential is derived. Quantum fluctuations are formulated using a field expression in terms of local basis functions in real spacetime. The quantum path integral gives the Coulomb potential between the two particles in addition to the linear potential due to the classical fields.
Rotation in classical zero-point radiation and in quantum vacuum
Yefim S. Levin
2006-06-02T23:59:59.000Z
Two reference systems (RS) are defined and used as the basis for investigating thermal effects of rotation through both random classical zero point radiation and quantum vacuum. Both RSs consist of an infinite number of instantaneous global inertial reference frames (RF). The RFs do not accompany the detector and are defined so that at each moment of proper time of the detector there are two RFs belonging with different RSs. These RFs agree momentarily, are connected by a Lorentz transformation with the detector velocity as a parameter, and with origins at the detector location at the same proper time. The two- field correlation functions (CF) measured by the observer rotating through a random classical zero point radiation have been calculated and presented in terms of elementary functions for both electromagnetic and massless scalar fields. If the CFs are periodic with a period of rotation the observer finds the spectrum which is very similar, but not identical, to Plank spectrum. If both fields of such a two-field periodic CF, for both electromagnetic and massless scalar case, are taken at the same point then its convergent part is shown, using Abel-Plana summation formula, to have Planck spectrum with the temperature T= hw/k, where w is an angular velocity of the detector. It is shown that the vacuum of the quantized massless scalar field in rotating RS is not equivalent to the vacuum of the field in the laboratory system because the respective Bogolubov transformation is not a zero.
High-efficiency quantum state transfer and quantum memory using a mechanical oscillator
Eyob A. Sete; H. Eleuch
2015-03-30T23:59:59.000Z
We analyze an optomechanical system that can be used to efficiently transfer a quantum state between an optical cavity and a distant mechanical oscillator coupled to a second optical cavity. We show that for a moderate mechanical Q-factor it is possible to achieve a transfer efficiency of $99.4\\%$ by using adjustable cavity damping rates and destructive interference. We also show that the quantum mechanical oscillator can be used as a quantum memory device with an efficiency of $96\\%$ employing a pulsed optomechanical coupling. Although the mechanical dissipation slightly decreases the efficiency, its effect can be significantly reduced by designing a high-Q mechanical oscillator.
Goddard III, William A.
Mechanism of Selective Oxidation of Propene to Acrolein on Bismuth Molybdates from Quantum for understanding the fundamental chemical mechanisms underlying the selective oxidation of propene to acrolein to form acrolein, and acrolein desorption. The formation of -allyl intermediate is reversible
Adrian A. Budini
2010-05-20T23:59:59.000Z
In this paper, we develop a quantum-jump approach for describing the photon-emission process of single fluorophore systems coupled to complex classically fluctuating reservoirs. The formalism relies on an open quantum system approach where the dynamic of the system and the reservoir fluctuations are described through a density matrix whose evolution is defined by a Lindblad rate equation. For each realization of the photon measurement processes it is possible to define a conditional system state (stochastic density matrix) whose evolution depends on both the photon detection events and the fluctuations between the configurational states of the reservoir. In contrast to standard fluorescent systems the photon-to-photon emission process is not a renewal one, being defined by a (stochastic) waiting time distribution that in each recording event parametrically depends on the conditional state. The formalism allows calculating experimental observables such as the full hierarchy of joint probabilities associated to the time intervals between consecutive photon recording events. These results provide a powerful basis for characterizing different situations arising in single-molecule spectroscopy, such as spectral fluctuations, lifetime fluctuations, and light assisted processes.
Quantum information processing in continuous time
Childs, Andrew MacGregor, 1977-
2004-01-01T23:59:59.000Z
Quantum mechanical computers can solve certain problems asymptotically faster than any classical computing device. Several fast quantum algorithms are known, but the nature of quantum speedup is not well understood, and ...
Nikolopoulos, Georgios M.; Ranade, Kedar S.; Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, 64289 Darmstadt (Germany)
2006-03-15T23:59:59.000Z
We investigate the error tolerance of quantum cryptographic protocols using d-level systems. In particular, we focus on prepare-and-measure schemes that use two mutually unbiased bases and a key-distillation procedure with two-way classical communication. For arbitrary quantum channels, we obtain a sufficient condition for secret-key distillation which, in the case of isotropic quantum channels, yields an analytic expression for the maximally tolerable error rate of the cryptographic protocols under consideration. The difference between the tolerable error rate and its theoretical upper bound tends slowly to zero for sufficiently large dimensions of the information carriers.
Numerical integration of functions originating from quantum mechanics
Armiento, Rickard
Numerical integration of functions originating from quantum mechanics R. Armiento Department Applications in quantum physics commonly involve large batches of integrals of smooth but very oscillatory for evaluating such integrals. The routines studied include: two from the QUADPACK package based on Gauss
Born series and unitarity in noncommutative quantum mechanics
Bemfica, F. S.; Girotti, H. O. [Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 - Porto Alegre, Rio Grande do Sul (Brazil)
2008-01-15T23:59:59.000Z
This paper is dedicated to present model independent results for noncommutative quantum mechanics. We determine sufficient conditions for the convergence of the Born series and, in the sequel, unitarity is proved in full generality.
Nonlinear coupling of nano mechanical resonators to Josephson quantum circuits
Xingxiang Zhou; Ari Mizel
2006-05-01T23:59:59.000Z
We propose a technique to couple the position operator of a nano mechanical resonator to a SQUID device by modulating its magnetic flux bias. By tuning the magnetic field properly, either linear or quadratic couplings can be realized, with a discretely adjustable coupling strength. This provides a way to realize coherent nonlinear effects in a nano mechanical resonator by coupling it to a Josephson quantum circuit. As an example, we show how squeezing of the nano mechanical resonator state can be realized with this technique. We also propose a simple method to measure the uncertainty in the position of the nano mechanical resonator without quantum state tomography.
Structure/Function Studies of Proteins Using Linear Scaling Quantum Mechanical Methodologies
Merz, K. M.
2004-07-19T23:59:59.000Z
We developed a linear-scaling semiempirical quantum mechanical (QM) program (DivCon). Using DivCon we can now routinely carry out calculations at the fully QM level on systems containing up to about 15 thousand atoms. We also implemented a Poisson-Boltzmann (PM) method into DivCon in order to compute solvation free energies and electrostatic properties of macromolecules in solution. This new suite of programs has allowed us to bring the power of quantum mechanics to bear on important biological problems associated with protein folding, drug design and enzyme catalysis. Hence, we have garnered insights into biological systems that have been heretofore impossible to obtain using classical simulation techniques.
Sensible Quantum Mechanics: Are Probabilities only in the Mind?
Don N. Page
1995-07-11T23:59:59.000Z
Quantum mechanics may be formulated as {\\it Sensible Quantum Mechanics} (SQM) so that it contains nothing probabilistic except conscious perceptions. Sets of these perceptions can be deterministically realized with measures given by expectation values of positive-operator-valued {\\it awareness operators}. Ratios of the measures for these sets of perceptions can be interpreted as frequency-type probabilities for many actually existing sets. These probabilities generally cannot be given by the ordinary quantum ``probabilities'' for a single set of alternatives. {\\it Probabilism}, or ascribing probabilities to unconscious aspects of the world, may be seen to be an {\\it aesthemamorphic myth}.
Quantum network of superconducting qubits through opto-mechanical interface
Zhang-qi Yin; W. L. Yang; L. Sun; L. M. Duan
2015-01-08T23:59:59.000Z
We propose a scheme to realize quantum networking of superconducting qubits based on the opto-mechanical interface. The superconducting qubits interact with the microwave photons, which then couple to the optical photons through the opto-mechanical interface. The interface generates a quantum link between superconducting qubits and optical flying qubits with tunable pulse shapes and carrier frequencies, enabling transmission of quantum information to other superconducting or atomic qubits. We show that the scheme works under realistic experimental conditions and it also provides a way for fast initialization of the superconducting qubits under 1 K instead of 20 mK operation temperature.
Assessing the Montevideo Interpretation of Quantum Mechanics
Jeremy Butterfield
2014-06-17T23:59:59.000Z
This paper gives a philosophical assessment of the Montevideo interpretation of quantum theory, advocated by Gambini, Pullin and co-authors. This interpretation has the merit of linking its proposal about how to solve the measurement problem to the search for quantum gravity: namely by suggesting that quantum gravity makes for fundamental limitations on the accuracy of clocks, which imply a type of decoherence that "collapses the wave-packet". I begin (Section 2) by sketching the topics of decoherence, and quantum clocks, on which the interpretation depends. Then I expound the interpretation, from a philosopher's perspective (Sections 3, 4 and 5). Finally, in Section 6, I argue that the interpretation, at least as developed so far, is best seen as a form of the Everett interpretation: namely with an effective or approximate branching, that is induced by environmental decoherence of the familiar kind, and by the Montevideans' "temporal decoherence".
Quantum Statistical Mechanics. II. Stochastic Schrodinger Equation
Phil Attard
2014-06-02T23:59:59.000Z
The stochastic dissipative Schrodinger equation is derived for an open quantum system consisting of a sub-system able to exchange energy with a thermal reservoir. The resultant evolution of the wave function also gives the evolution of the density matrix, which is an explicit, stochastic form of the Lindblad master equation. A quantum fluctuation-dissipation theorem is also derived. The time correlation function is discussed.
EFT Beyond the Horizon: Stochastic Inflation and How Primordial Quantum Fluctuations Go Classical
C. P. Burgess; R. Holman; G. Tasinato; M. Williams
2014-11-04T23:59:59.000Z
We identify the effective theory describing inflationary super-Hubble scales and show it to be a special case of effective field theories appropriate to open systems. Open systems allow information to be exchanged between the degrees of freedom of interest and those that are integrated out, such as for particles moving through a fluid. Strictly speaking they cannot in general be described by an effective lagrangian; rather the appropriate `low-energy' limit is instead a Lindblad equation describing the evolution of the density matrix of the slow degrees of freedom. We derive the equation relevant to super-Hubble modes of quantum fields in near-de Sitter spacetimes and derive two implications. We show the evolution of the diagonal density-matrix elements quickly approaches the Fokker-Planck equation of Starobinsky's stochastic inflationary picture. This provides an alternative first-principles derivation of this picture's stochastic noise and drift, as well as its leading corrections. (An application computes the noise for systems with a sub-luminal sound speed.) We argue that the presence of interactions drives the off-diagonal density-matrix elements to zero in the field basis. This shows why the field basis is the `pointer basis' for the decoherence of primordial quantum fluctuations while they are outside the horizon, thus allowing them to re-enter as classical fluctuations, as assumed when analyzing CMB data. The decoherence process is efficient, occurring after several Hubble times even for interactions as weak as gravitational-strength. Crucially, the details of the interactions largely control only the decoherence time and not the nature of the final late-time stochastic state, much as interactions can control the equilibration time for thermal systems but are largely irrelevant to the properties of the resulting equilibrium state.
Whether quantum mechanics can be almighty even in information science
Koji Nagata; Tadao Nakamura
2008-11-28T23:59:59.000Z
We discuss that there is a crucial contradiction within quantum mechanics. We derive a proposition concerning a quantum expectation value under the assumption of the existence of the directions in a spin-1/2 system. The quantum predictions within the formalism of von Neumann's projective measurement cannot coexist with the proposition concerning the existence of the directions. Therefore, we have to give up either the existence of the directions or the formalism of von Neumann's projective measurement. Hence there is a crucial contradiction within the Hilbert space formalism of the quantum theory. This implies that there is no axiomatic system for the quantum theory. This also reveals that we need new physical theories in order to explain the handing of raw experimental data. We discuss that this crucial contradiction makes the quantum-theoretical formulation of Deutsch's algorithm questionable.
Quantum mechanical Hamiltonian models of the computation process
Benioff, P.
1983-01-01T23:59:59.000Z
As noted in the proceedings of this conference it is of importance to determine if quantum mechanics imposes fundamental limits on the computation process. Some aspects of this problem have been examined by the development of different types of quantum mechanical Hamiltonian models of Turing machines. (Benioff 1980, 1982a, 1982b, 1982c). Turing machines were considered because they provide a standard representation of all digital computers. Thus, showing the existence of quantum mechanical models of all Turing machines is equivalent to showing the existence of quantum mechanical models of all digital computers. The types of models considered all had different properties. Some were constructed on two-dimensional lattices of quantum spin systems of spin 1/2 (Benioff 1982b, 1982c) or higher spins (Benioff 1980). All the models considered Turing machine computations which were made reversible by addition of a history tape. Quantum mechanical models of Bennett's reversible machines (Bennett 1973) in which the model makes a copy of the computation result and then erases the history and undoes the computation in lockstep to recover the input were also developed (Benioff 1982a). To avoid technical complications all the types of models were restricted to modelling an arbitrary but finite number of computation steps.
An ultra-low dissipation micro-oscillator for quantum opto-mechanics
E. Serra; A. Borrielli; F. S. Cataliotti; F. Marin; F. Marino; A. Pontin; G. A. Prodi; M. Bonaldi
2012-08-30T23:59:59.000Z
Generating non-classical states of light by opto-mechanical coupling depends critically on the mechanical and optical properties of micro-oscillators and on the minimization of thermal noise. We present an oscillating micro-mirror with a mechanical quality factor Q = 2.6x10^6 at cryogenic temperature and a Finesse of 65000, obtained thanks to an innovative approach to the design and the control of mechanical dissipation. Already at 4 K with an input laser power of 2 mW, the radiation-pressure quantum fluctuations become the main noise source, overcoming thermal noise. This feature makes our devices particularly suitable for the production of pondero-motive squeezing.
Towards Quantifying Complexity with Quantum Mechanics
Ryan Tan; Daniel R. Terno; Jayne Thompson; Vlatko Vedral; Mile Gu
2014-09-23T23:59:59.000Z
While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified by the complexity of its simplest mathematical model - the model that requires the least past information for optimal future prediction. Here we review how such models, known as $\\epsilon$-machines can be further simplified through quantum logic, and explore the resulting consequences for understanding complexity. In particular, we propose a new measure of complexity based on quantum $\\epsilon$-machines. We apply this to a simple system undergoing constant thermalization. The resulting quantum measure of complexity aligns more closely with our intuition of how complexity should behave.
Quantum micro-mechanics with ultracold atoms
Thierry Botter; Daniel Brooks; Subhadeep Gupta; Zhao-Yuan Ma; Kevin L. Moore; Kater W. Murch; Tom P. Purdy; Dan M. Stamper-Kurn
2008-10-21T23:59:59.000Z
In many experiments isolated atoms and ions have been inserted into high-finesse optical resonators for the study of fundamental quantum optics and quantum information. Here, we introduce another application of such a system, as the realization of cavity optomechanics where the collective motion of an atomic ensemble serves the role of a moveable optical element in an optical resonator. Compared with other optomechanical systems, such as those incorporating nanofabricated cantilevers or the large cavity mirrors of gravitational observatories, our cold-atom realization offers direct access to the quantum regime. We describe experimental investigations of optomechanical effects, such as the bistability of collective atomic motion and the first quantification of measurement backaction for a macroscopic object, and discuss future directions for this nascent field.
Can absolute freedom save quantum mechanics?
Marek Czachor
1997-05-30T23:59:59.000Z
A classical system violating the Bell inequality is discussed. The system is local, deterministic, observers have free will, and detectors are ideal so that no data are lost. The trick is based on two elements. First, a state of one observer is locally influenced by a "particle". Second, random variables used in the experiment are complementary. A relation of this effect to nonlocality is discussed.
Sewell, T. D. (Thomas D.); Gan, C. K. (Chee Kwan); Jaramillo, E. (Eugenio); Strachan, A. H. (Alejandro H.)
2004-01-01T23:59:59.000Z
We are using classical molecular dynamics and condensed phase electronic-structure methods to predict some of the thermophysical and mechanical properties that are needed as input to realistic mesoscale models for plastic-bonded explosives. The main materials studied to date are HMX, PETN, Estane copolymer, and bi(2,2-dinitropropyl) formal/acetal (BDNPF/A). Emphasis is placed on non-reactive properties and thermodynamic states relevant to cookoff and shock initiation phenomena. Both crystal and liquid-state properties are of interest. Typical simulation sizes and times are {approx}10{sup 2} molecules and 2-10 ns, respectively. The overarching goal is to develop internally consistent model thermodynamic and elastic mechanical descriptions for the materials. Prioritization among the set of properties amenable to atomistic simulation is made based on ongoing interactions with mesoscale modelers at Los Alamos and elsewhere. Recent work will be summarized and our view of profitable directions for future research will be discussed, including preliminary results for large-scale molecular dynamics simulations of shock response of crystalline HMX.
SISSA/ISAS/100/93/EP Quantum mechanics and quantum
;b and Dingping Li a International School for Advanced studies, SISSA, IÂ34014 Trieste, Italy a Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Trieste, Trieste, Italy b Abstract The quantum mechanics
H. Makino; S. Tasaki
2004-03-26T23:59:59.000Z
Along the line of thoughts of Berry and Robnik\\cite{[1]}, we investigated the gap distribution function of systems with infinitely many independent components, and discussed the level-spacing distribution of classically integrable quantum systems. The level spacing distribution is classified into three cases: Case 1: Poissonian if $\\bar{\\mu}(+\\infty)=0$, Case 2: Poissonian for large $S$, but possibly not for small $S$ if $0statistically independent, non-Poisson level spacing distributions are possible.
A deformation quantization theory for noncommutative quantum mechanics
Costa Dias, Nuno; Prata, Joao Nuno [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Av. Campo Grande, 376, 1749-024 Lisboa (Portugal) and Grupo de Fisica Matematica, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa (Portugal); Gosson, Maurice de [NuHAG Fakultaet fuer Mathematik, Universitaet Wien, Wien 1090 (Austria); Luef, Franz [NuHAG Fakultaet fuer Mathematik, Universitaet Wien, Wien 1090 (Austria); Department of Mathematics, UC Berkeley, 847 Evans Hall, Berkeley, California 94720-3840 (United States)
2010-07-15T23:59:59.000Z
We show that the deformation quantization of noncommutative quantum mechanics previously considered by Dias and Prata ['Weyl-Wigner formulation of noncommutative quantum mechanics', J. Math. Phys. 49, 072101 (2008)] and Bastos, Dias, and Prata ['Wigner measures in non-commutative quantum mechanics', e-print arXiv:math-ph/0907.4438v1; Commun. Math. Phys. (to appear)] can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef ['A new approach to the *-genvalue equation', Lett. Math. Phys. 85, 173-183 (2008)].
Comment on 'Nonlocality, Counterfactuals and Quantum Mechanics'
Stapp, H.P.
1999-04-14T23:59:59.000Z
A recent proof [H. P. Stapp, Am. J. Phys. 65, 300 (1997)], formulated in the symbolic language of modal logic, claims to show that contemporary quantum theory, viewed as a set of rules that allow us to calculate statistical predictions among certain kinds of observations, cannot be imbedded in any rational framework that conforms to the principles that (1) the experimenters' choices of which experiments they will perform can be considered to be free choices, (2) outcomes of measurements are unique, and (3) the free choices just mentioned have no backward-in-time effects of any kind. This claim is similar to Bell's theorem, but much stronger, because no reality assumption alien to quantum philosophy is used. The paper being commented on [W. Unruh, Phys. Rev. A 59, 126 (1999)] argues that some such reality assumption has been ''smuggled'' in. That argument is examined here and shown, I believe, to be defective.
Mind-Body Interpretation of Quantum Mechanics
Raoul Nakhmanson
2001-11-13T23:59:59.000Z
The wave-particle duality is a mind-body one. In the real 3D-space there exists only the particle, the wave exists in its consciousness. If there are many particles, their distribution in accordance with the wave function represents a real wave in real space. Many worlds, Schroedinger cat, etc., exist only as mental constructions. The "waves of matter" are non-material. Feynman et al. taught quantum world "is like neither". Alas, they forgot living matter.
Free-fall in a uniform gravitational field in non-commutative quantum mechanics
K. H. C. Castello-Branco; A. G. Martins
2011-05-23T23:59:59.000Z
We study the free-fall of a quantum particle in the context of noncommutative quantum mechanics (NCQM). Assuming noncommutativity of the canonical type between the coordinates of a two-dimensional configuration space, we consider a neutral particle trapped in a gravitational well and exactly solve the energy eigenvalue problem. By resorting to experimental data from the GRANIT experiment, in which the first energy levels of freely falling quantum ultracold neutrons were determined, we impose an upper-bound on the noncommutativity parameter. We also investigate the time of flight of a quantum particle moving in a uniform gravitational field in NCQM. This is related to the weak equivalence principle. As we consider stationary, energy eigenstates, i.e., delocalized states, the time of flight must be measured by a quantum clock, suitably coupled to the particle. By considering the clock as a small perturbation, we solve the (stationary) scattering problem associated and show that the time of flight is equal to the classical result, when the measurement is made far from the turning point. This result is interpreted as an extension of the equivalence principle to the realm of NCQM.
Free-fall in a uniform gravitational field in noncommutative quantum mechanics
Castello-Branco, K. H. C. [Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, Av. Trabalhador Sao-Carlense, 400, Sao Carlos, Sao Paulo 13560-970 (Brazil); Martins, A. G. [Departamento de Ciencias Naturais, Universidade do Estado do Para, Av. Djalma Dutra, s/n, Belem, Para 66113-200 (Brazil)
2010-10-15T23:59:59.000Z
We study the free-fall of a quantum particle in the context of noncommutative quantum mechanics (NCQM). Assuming noncommutativity of the canonical type between the coordinates of a two-dimensional configuration space, we consider a neutral particle trapped in a gravitational well and exactly solve the energy eigenvalue problem. By resorting to experimental data from the GRANIT experiment, in which the first energy levels of freely falling quantum ultracold neutrons were determined, we impose an upper-bound on the noncommutativity parameter. We also investigate the time of flight of a quantum particle moving in a uniform gravitational field in NCQM. This is related to the weak equivalence principle. As we consider stationary, energy eigenstates, i.e., delocalized states, the time of flight must be measured by a quantum clock, suitably coupled to the particle. By considering the clock as a small perturbation, we solve the (stationary) scattering problem associated and show that the time of flight is equal to the classical result, when the measurement is made far from the turning point. This result is interpreted as an extension of the equivalence principle to the realm of NCQM.
Quantum Thermodynamic Cycles and Quantum Heat Engines (II)
H. T. Quan
2009-03-09T23:59:59.000Z
We study the quantum mechanical generalization of force or pressure, and then we extend the classical thermodynamic isobaric process to quantum mechanical systems. Based on these efforts, we are able to study the quantum version of thermodynamic cycles that consist of quantum isobaric process, such as quantum Brayton cycle and quantum Diesel cycle. We also consider the implementation of quantum Brayton cycle and quantum Diesel cycle with some model systems, such as single particle in 1D box and single-mode radiation field in a cavity. These studies lay the microscopic (quantum mechanical) foundation for Szilard-Zurek single molecule engine.
Non-classical properties of quantum wave packets propagating in a Kerr-like medium
C. Sudheesh; S. Lakshmibala; V. Balakrishnan
2005-02-08T23:59:59.000Z
We investigate non-classical effects such as fractional revivals, squeezing and higher-order squeezing of photon-added coherent states propagating through a Kerr-like medium.The Wigner functions corresponding to these states at the instants of fractional revivals are obtained, and the extent of non-classicality quantified.
Spin-Statistics Connection for Relativistic Quantum Mechanics
A. F. Bennett
2015-04-20T23:59:59.000Z
The spin-statistics connection has been proved for nonrelativistic quantum mechanics (Jabs, A., 2010: Found. Phys., {\\bf 40}, 776-792). The proof is extended here to the relativistic regime using the parametrized Dirac equation. A causality condition is not required.
Quantum-mechanical theory of optomechanical Brillouin cooling
Tomes, Matthew; Bahl, Gaurav; Carmon, Tal [Department of Electrical Engineering, University of Michigan, Ann Arbor, Michigan 48109 (United States); Marquardt, Florian [Institut fuer Theoretische Physik, Universitaet Erlangen-Nuernberg, Staudtstrasse 7, D-91058 Erlangen (Germany); Max Planck Institute for the Science of Light, Guenther-Scharowsky-Strasse 1/Bau 24, D-91058 Erlangen (Germany)
2011-12-15T23:59:59.000Z
We analyze how to exploit Brillouin scattering of light from sound for the purpose of cooling optomechanical devices and present a quantum-mechanical theory for Brillouin cooling. Our analysis shows that significant cooling ratios can be obtained with standard experimental parameters. A further improvement of cooling efficiency is possible by increasing the dissipation of the optical anti-Stokes resonance.
Graphene and Quantum Mechanics University of California, Berkeley
Zworski, Maciej
Graphene and Quantum Mechanics Minjae Lee University of California, Berkeley lee.minjae@math.berkeley.edu March 31, 2014 Minjae Lee (UC Berkeley) Graphene March 31, 2014 1 / 9 #12;Carbon structures Graphite 3 Berkeley) Graphene March 31, 2014 2 / 9 #12;Graphene Graphene A single layer of graphite The thinnest 2D
Transition state theory, Siegert eigenstates, and quantum mechanical reaction rates
Miller, William H.
Transition state theory, Siegert eigenstates, and quantum mechanical reaction rates Tamar Seideman variables associated with a transition state (i.e., the saddle point of a potential energy surface), on which a general semiclassical transition state theory is based, are shown to be the semiclassical
Lagrangian Approaches of Dirac and Feynman to Quantum Mechanics
Y. G. Yi
2006-03-23T23:59:59.000Z
A unified exposition of the Lagrangian approach to quantum mechanics is presented, embodying the main features of the approaches of Dirac and of Feynman. The arguments of the exposition address the relation of the Lagrangian approach to the Hamiltonian operator and how the correspondence principle fits into each context.
Harmonic Superfields in N=4 Supersymmetric Quantum Mechanics
Evgeny A. Ivanov
2011-02-11T23:59:59.000Z
This is a brief survey of applications of the harmonic superspace methods to the models of N=4 supersymmetric quantum mechanics (SQM). The main focus is on a recent progress in constructing SQM models with couplings to the background non-Abelian gauge fields. Besides reviewing and systemizing the relevant results, we present some new examples and make clarifying comments.
Quantum statistics as geometry: Conflict, Mechanism, Interpretation, and Implication
Daniel C. Galehouse
2015-01-29T23:59:59.000Z
The conflict between the determinism of geometry in general relativity and the essential statistics of quantum mechanics blocks the development of a unified theory. Electromagnetic radiation is essential to both fields and supplies a common meeting ground. It is proposed that a suitable mechanism to resolve these differences can be based on the use of a time-symmetric treatment for the radiation. Advanced fields of the absorber can be interpreted to supply the random character of spontaneous emission. This allows the statistics of the Born rule to come from the spontaneous emission that occurs during a physical measurement. When the absorber is included, quantum mechanics is completely deterministic. It is suggested that the peculiar properties of kaons may be induced by the advanced effects of the neutrino field. Schr\\"odinger's cat loses its enigmatic personality and the identification of mental processes as an essential component of a measurement is no longer needed.
Armand Rundquist; Michal Bajcsy; Arka Majumdar; Tomas Sarmiento; Kevin Fischer; Konstantinos G. Lagoudakis; Sonia Buckley; Alexander Y. Piggott; Jelena Vuckovic
2014-08-12T23:59:59.000Z
We use the third- and fourth-order autocorrelation functions $g^{(3)}(\\tau_1,\\tau_2)$ and $g^{(4)}(\\tau_1,\\tau_2, \\tau_3)$ to detect the non-classical character of the light transmitted through a photonic-crystal nanocavity containing a strongly-coupled quantum dot probed with a train of coherent light pulses. We contrast the value of $g^{(3)}(0, 0)$ with the conventionally used $g^{(2)}(0)$ and demonstrate that in addition to being necessary for detecting two-photon states emitted by a low-intensity source, $g^{(3)}$ provides a more clear indication of the non-classical character of a light source. We also present preliminary data that demonstrates bunching in the fourth-order autocorrelation function $g^{(4)}(\\tau_1,\\tau_2, \\tau_3)$ as the first step toward detecting three-photon states.
Noncommutative unification of general relativity and quantum mechanics
Heller, Michael; Pysiak, Leszek; Sasin, Wieslaw [Vatican Observatory, Vatican City, V-00120 Vatican City, Rome (Italy); Department of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw (Poland)
2005-12-15T23:59:59.000Z
We present a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry is developed in terms of a noncommutative algebra A which is defined on a transformation groupoid {gamma} given by the action of a noncompact group G on the total space E of a principal fiber bundle over space-time M. The case is important since to obtain physical effects predicted by the model we should assume that G is a Lorentz group or some of its representations. We show that the generalized Einstein equation of the model has the form of the eigenvalue equation for the generalized Ricci operator, and all relevant operators in the quantum sector of the model are random operators; we study their dynamics. We also show that the model correctly reproduces general relativity and the usual quantum mechanics. It is interesting that the latter is recovered by performing the measurement of any observable. In the act of such a measurement the model 'collapses' to the usual quantum mechanics.
Semi-classical measures on Quantum graphs and the Gau map of the determinant manifold
Boyer, Edmond
believed that QE does not hold in general for a FIXED quantum graph. In [BKW04], it is proved that QE does
New version of $q$-deformed supersymmetric quantum mechanics
Gavrilik, A M; Lukash, A V
2013-01-01T23:59:59.000Z
A new version of the q-deformed supersymmetric quantum mechanics (q-SQM), which is inspired by the Tamm--Dankoff-type (TD-type) deformation of quantum harmonic oscillator, is constructed. The obtained algebra of q-SQM is similar to that in Spiridonov's approach. However, within our version of q-SQM, the ground state found explicitly in the special case of superpotential yiealding q-superoscillator turns out to be non-Gaussian and takes the form of special (TD-type) q-deformed Gaussian.
On a Model of Quantum Mechanics and the Mind
J. Acacio de Barros
2014-04-16T23:59:59.000Z
In this paper I discuss Stapp's (2014) interesting proposal of using the Quantum Zeno Effect to account for the mind/matter interaction. In particular, I discuss some of the motivations for it, and then argue that, in his current version, his model is circular (a solution to this, proposed by Kathryn Laskey, is presented), insofar as the mind/matter problem is concerned. I also present an alternative approach to some of the appealing aspects of using quantum mechanics to think about consciousness.
Quantum mechanical perspectives and generalization of the fractional Fourier Transformation
Jun-Hua Chen; Hong-Yi Fan
2014-08-23T23:59:59.000Z
Fourier and fractional-Fourier transformations are widely used in theoretical physics. In this paper we make quantum perspectives and generalization for the fractional Fourier transformation (FrFT). By virtue of quantum mechanical representation transformation and the method of integration within normal ordered product (IWOP) of operators, we find the key point for composing FrFT, and reveal the structure of FrFT. Following this procedure, a full family of generalized fractional transformations are discovered with the usual FrFT as one special case. The eigen-functions of arbitrary GFrT are derived explicitly.
Hiroaki Matsueda
2014-08-27T23:59:59.000Z
An information-geometrical interpretation of AdS3/CFT2 correspondence is given. In particular, we consider an inverse problem in which the classical spacetime metric is given in advance and then we find what is the proper quantum information that is well stored into the spacetime. We see that the Fisher metric plays a central role on this problem. Actually, if we start with the two-dimensional hyperbolic space, a constant-time surface in AdS3, the resulting singular value spectrum of the quantum state shows power law for the correlation length with conformal dimension proportional to the curvature radius in the gravity side. Furthermore, the entanglement entropy data embedded into the hyperbolic space agree well with the Ryu-Takayanagi formula. These results show that the relevance of the AdS/CFT correspondence can be represented by the information-gemetrical approach based on the Fisher metric.
Substrate Hydroxylation in Methane Monooxygenase: Quantitative Modeling via Mixed Quantum Mechanics/
Gherman, Benjamin F.
at an atomic level of detail.4-7 In particular, the use of ab initio quantum chemical methods based on densitySubstrate Hydroxylation in Methane Monooxygenase: Quantitative Modeling via Mixed Quantum Mechanics with mixed quantum mechanics/molecular mechanics (QM/MM) methods, the hydroxylation of methane
Quantum capacity of lossy channel with additive classical Gaussian noise : a perturbation approach
Xiao-yu Chen
2007-10-02T23:59:59.000Z
For a quantum channel of additive Gaussian noise with loss, in the general case of $n$ copies input, we show that up to first order perturbation, any non-Gaussian perturbation to the product thermal state input has a less quantum information transmission rate when the input energy tend to infinitive.
Bell's theorem tells us NOT what quantum mechanics IS, but what quantum mechanics IS NOT
Zukowski, Marek
2015-01-01T23:59:59.000Z
Non-locality, or quantum-non-locality, are buzzwords in the community of quantum foundation and information scientists, which purportedly describe the implications of Bell's theorem. When such phrases are treated seriously, that is it is claimed that Bell's theorem reveals non-locality as an inherent trait of the quantum description of the micro-world, this leads to logical contradictions, which will be discussed here. In fact, Bell's theorem, understood as violation of Bell inequalities by quantum predictions, is consistent with Bohr's notion of complementarity. Thus, if it points to anything, then it is rather the significance of the principle of Bohr, but even this is not a clear implication. Non-locality is a necessary consequence of Bell's theorem only if we reject complementarity by adopting some form of realism, be it additional hidden variables, additional hidden causes, etc., or counterfactual definiteness. The essay contains two largely independent parts. The first one is addressed to any reader int...
Classical and quantum behaviour of Skyrmions This is a proposal for a University PhD Studentship
Banaji,. Murad
, neutrons and atomic nuclei. The study of the Skyrme model involves sophisticated numerical simulations. Since protons and neutrons obey the laws of quantum mechanics, the Skyrme model with its Skyrmions also of nuclear physics experiments is concerned with the scattering of atomic nuclei - for example hitting
The Measurement Problem and the Reduction Postulate of Quantum Mechanics
Rodolfo Gambini
1998-06-18T23:59:59.000Z
It is well known, that the causal Schr\\"odinger evolution of a quantum state is not compatible with the reduction postulate, even when decoherence is taken into account. The violation of the causal evolution, introduced by the standard reduction postulate distinguishes certain systems (as the measurement devices), whose states are very close to statistical mixtures (as the ones resulting from the process of decoherence). In these systems, this violation has not any observable effect. In arbitrary quantum systems, the transition from the initial density matrix to a diagonal matrix predicted by the standard reduction postulate, would lead to a complete breakdown of the Schr\\"odinger evolution, and consequently would destroy all the predictive power of quantum mechanics. What we show here, is that there is a modified version of the postulate that allows to treat all the quantum mechanical systems on equal footing. The standard reduction postulate may be considered as a good approximation, useful for practical purposes, of this modified version which is consistent with the Schr\\"odinger evolution and via decoherence with the experimental results. Within this approach, the physical role played by the reduction postulate is as a tool for the computation of relative probabilities and consequently for the determination of the probabilities of consistent histories.
An investigation of precision and scaling issues in nuclear spin and trapped-ion quantum simulators
Clark, Robert J., Ph. D. Massachusetts Institute of Technology
2009-01-01T23:59:59.000Z
Quantum simulation offers the possibility of using a controllable quantum-mechanical system to implement the dynamics of another quantum system, performing calculations that are intractable on classical computers for all ...
Zero-Branes, Quantum Mechanics and the Cosmological Constant
Andrew Chamblin; Neil D. Lambert
2001-07-25T23:59:59.000Z
We analyse some dynamical issues in a modified type IIA supergravity, recently proposed as an extension of M-theory that admits de Sitter space. In particular we find that this theory has multiple zero-brane solutions. This suggests a microscopic quantum mechanical matrix description which yields a massive deformation of the usual M(atrix) formulation of M-theory and type IIA string theory.
Noncommutative Field Theory from Quantum Mechanical Space-Space Noncommutativity
Marcos Rosenbaum; J. David Vergara; L. Roman Juarez
2007-09-21T23:59:59.000Z
We investigate the incorporation of space noncommutativity into field theory by extending to the spectral continuum the minisuperspace action of the quantum mechanical harmonic oscillator propagator with an enlarged Heisenberg algebra. In addition to the usual $\\star$-product deformation of the algebra of field functions, we show that the parameter of noncommutativity can occur in noncommutative field theory even in the case of free fields without self-interacting potentials.
Physics 268r: Classical and Quantum Phase Transitions 7th lecture: February 23th Monday, 2009
and all down. won't modify universality)? as ! 0,B ! 1 and coupling becomes large, bubble elongated 3 ) mapping to Bose model becomes exact at large nMI (each quantum dot, insulated state, coulomb
Semi-classical measures on Quantum graphs and the Gau map of the determinant manifold
Recanati, Catherine
believed that QE does not hold in general for a FIXED quantum graph. This is proved for star graphs in [BKW to what people do in several papers like [BG00, BKW04, BW08, Ba12, BB13]. Let
Formulation of quantum mechanics in terms of gauge transformations
S. R. Vatsya
2014-05-29T23:59:59.000Z
Formulations of quantum mechanics incorporating the Weyl gauge transformations are studied in this article and developed further. In the process, impact of the method of observation on its outcome is interpreted in terms of the assigned gauges by incorporating properties of the corresponding experimental arrangement in defining them. Further, the assigned gauge is explicitly incorporated in the Feynman path integral formulation of quantum mechanics. The resulting wavefunction, which is not uniquely defined, represents a gauge equivalence class. The representative wavefunction is still obtained by the original path integral method. Methods to obtain the pertinent information about the assigned gauges supplementing the representative wavefunction are discussed. The probability density is shown to be a uniquely defined gauge invariant quantity but at the expense of some information describing the observable effects contained in gauge factors. In the standard quantum mechanics, a wavefunction is assumed to be defined within a phase factor while the probability density is phase-independent, paralleling these results. Also, the path integral method is used to deduce the Klein-Gordon equation for the representative wavefunction in the Riemannian spaces in a more streamlined manner than the previous derivations.
From quantum ladder climbing to classical autoresonance G. Marcus, L. Friedland, and A. Zigler
Friedland, Lazar
to guarantee the stability of the time varying, phase-locked excited state. Furthermore, in mi- croscopic 2003; published 21 January 2004 The autoresonance phenomenon allows excitation of a classical importance in spectroscopy and chemical dynamics 1 . Direct excitation of high vibrational levels
California at Santa Cruz, University of
addition Alejandro Morales and Alejandro Amaya-Tapia Centro de Ciencias Fi´sicas, Universidad Nacional Auto 1999 We perform an analysis of a graphical representation for the addition of two angular momenta addition of angular momenta may be represented using classical-like diagrams. © 1999 American Association
Karl Svozil
2001-06-29T23:59:59.000Z
Three extensions and reinterpretations of nonclassical probabilities are reviewed. (i) We propose to generalize the probability axiom of quantum mechanics to self-adjoint positive operators of trace one. Furthermore, we discuss the Cartesian and polar decomposition of arbitrary normal operators and the possibility to operationalize the corresponding observables. Thereby we review and emphasize the use of observables which maximally represent the context. (ii) In the second part, we discuss Pitowsky polytopes for automaton logic as well as for generalized urn models and evaluate methods to find the resulting Boole-Bell type (in)equalities. (iii) Finally, so-called ``parameter cheats'' are introduced, whereby parameters are transformed bijectively and nonlinearly in such a way that classical systems mimic quantum correlations and vice versa. It is even possible to introduce parameter cheats which violate the Boole-Bell type inequalities stronger than quantum ones, thereby trespassing the Tsirelson limit. The price to be paid is nonuniformity.
Nonclassical polarization dynamics in classical-like states
Alfredo Luis; Angel S. Sanz
2014-12-23T23:59:59.000Z
Quantum polarization is investigated by means of a trajectory picture based on the Bohmian formulation of quantum mechanics. Relevant examples of classical-like two-mode field states are thus examined, namely Glauber and SU(2) coherent states. Although these states are often regarded as classical, the analysis here shows that the corresponding electric-field polarization trajectories display topologies very different from those expected from classical electrodynamics. Rather than incompatibility with the usual classical model, this result demonstrates the dynamical richness of quantum motions, determined by local variations of the system quantum phase in the corresponding (polarization) configuration space, absent in classical-like models. These variations can be related to the evolution in time of the phase, but also to its dependence on configurational coordinates, which is the crucial factor to generate motion in the case of stationary states like those here considered. In this regard, for completeness these results are compared those obtained from nonclassical N00N states.
Phase Space Quantum Mechanics on the Anti-De Sitter Spacetime and its Poincaré Contraction
A. M. El Gradechi; S. De Bièvre
1992-10-26T23:59:59.000Z
In this work we propose an alternative description of the quantum mechanics of a massive and spinning free particle in anti-de~Sitter spacetime, using a phase space rather than a spacetime representation. The regularizing character of the curvature appears clearly in connection with a notion of localization in phase space which is shown to disappear in the zero curvature limit. We show in particular how the anti-de~Sitter optimally localized (coherent) states contract to plane waves as the curvature goes to zero. In the first part we give a detailed description of the classical theory {\\it \\a la Souriau\\/}. This serves as a basis for the quantum theory which is constructed in the second part using methods of geometric quantization. The invariant positive K\\"ahler polarization that selects the anti-de~Sitter quantum elementary system is shown to have as zero curvature limit the Poincar\\'e polarization which is no longer K\\"ahler. This phenomenon is then related to the disappearance of the notion of localization in the zero curvature limit.
Natural star-products on symplectic manifolds and related quantum mechanical operators
B?aszak, Maciej, E-mail: blaszakm@amu.edu.pl; Doma?ski, Ziemowit, E-mail: ziemowit@amu.edu.pl
2014-05-15T23:59:59.000Z
In this paper is considered a problem of defining natural star-products on symplectic manifolds, admissible for quantization of classical Hamiltonian systems. First, a construction of a star-product on a cotangent bundle to an Euclidean configuration space is given with the use of a sequence of pair-wise commuting vector fields. The connection with a covariant representation of such a star-product is also presented. Then, an extension of the construction to symplectic manifolds over flat and non-flat pseudo-Riemannian configuration spaces is discussed. Finally, a coordinate free construction of related quantum mechanical operators from Hilbert space over respective configuration space is presented. -- Highlights: •Invariant representations of natural star-products on symplectic manifolds are considered. •Star-products induced by flat and non-flat connections are investigated. •Operator representations in Hilbert space of considered star-algebras are constructed.
Scale invariance and efficient classical simulation of the quantum Fourier transform
Kieran J. Woolfe; Charles D. Hill; Lloyd C. L. Hollenberg
2014-06-04T23:59:59.000Z
We provide numerical evidence that the quantum Fourier transform can be efficiently represented in a matrix product operator with a size growing relatively slowly with the number of qubits. Additionally, we numerically show that the tensors in the operator converge to a common tensor as the number of qubits in the transform increases. Together these results imply that the application of the quantum Fourier transform to a matrix product state with $n$ qubits of maximum Schmidt rank $\\chi$ can be simulated in $O(n (log(n))^2 \\chi^2)$ time. We perform such simulations and quantify the error involved in representing the transform as a matrix product operator and simulating the quantum Fourier transform of periodic states.
Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
Troels Harmark; Marta Orselli
2014-10-31T23:59:59.000Z
We introduce a new quantum mechanical theory called Spin Matrix theory (SMT). The theory is interacting with a single coupling constant g and is based on a Hilbert space of harmonic oscillators with a spin index taking values in a Lie (super)algebra representation as well as matrix indices for the adjoint representation of U(N). We show that SMT describes N=4 super-Yang-Mills theory (SYM) near zero-temperature critical points in the grand canonical phase diagram. Equivalently, SMT arises from non-relativistic limits of N=4 SYM. Even though SMT is a non-relativistic quantum mechanical theory it contains a variety of phases mimicking the AdS/CFT correspondence. Moreover, the infinite g limit of SMT can be mapped to the supersymmetric sector of string theory on AdS_5 x S^5. We study SU(2) SMT in detail. At large N and low temperatures it is a theory of spin chains that for small g resembles planar gauge theory and for large g a non-relativistic string theory. When raising the temperature a partial deconfinement transition occurs due to finite-N effects. For sufficiently high temperatures the partially deconfined phase has a classical regime. We find a matrix model description of this regime at any coupling g. Setting g=0 it is a theory of N^2+1 harmonic oscillators while for large g it becomes 2N harmonic oscillators.
Donnelly, R.J.; LaMar, M.M.
1987-11-01T23:59:59.000Z
We discuss the use of rotating-cylinder viscometers to determine absolute shear viscosities of classical fluids and of helium II in the context of past and current knowledge of the stability and flow of these fluids between concentric cylinders. We identify a problem in measuring the absolute viscosity when the inner cylinder is rotating and the outer cylinder is at rest. We conclude by discussing the design of viscometers for absolute viscosity measurements in helium I and helium II.
Quantum states built on classical nonlinear resonances for slowly deforming billiards
Jha, Nandan [High Pressure and Synchrotron Radiation Physics Division, Bhabha Atomic Research Centre, Mumbai 400085 (India); Jain, Sudhir R. [Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400085 (India)
2014-10-15T23:59:59.000Z
We study the modification in the energy spectrum of a closed, adiabatic Hamiltonian system due to the presence of classical nonlinear resonances. A number of resonances are shown to appear in the neighbourhood of the unperturbed energy levels. The unperturbed system is a simple rectangular billiard, subjected to adiabatic rotations and vibrations. We believe that the results hold equally well for a generic unperturbed system expressible in action variables alone, and perturbed there from.
Dark current mechanism of terahertz quantum-well photodetectors
Jia, J. Y.; Gao, J. H.; Hao, M. R.; Wang, T. M.; Shen, W. Z.; Zhang, Y. H., E-mail: yuehzhang@sjtu.edu.cn [Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China); Cao, J. C.; Guo, X. G. [Key Laboratory of Terahertz Solid-State Technology, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050 (China); Schneider, H., E-mail: h.schneider@hzdr.de [Helmholtz-Zentrum Dresden-Rossendorf, Institute of Ion Beam Physics and Materials Research, P.O. Box 510119, 01314 Dresden (Germany)
2014-10-21T23:59:59.000Z
Dark current mechanisms of terahertz quantum-well photodetectors (THz QWPs) are systematically investigated experimentally and theoretically by measuring two newly designed structures combined with samples reported previously. In contrast to previous investigations, scattering-assisted tunneling dark current is found to cause significant contributions to total dark current. A criterion is also proposed to determine the major dark current mechanism at different peak response frequencies. We further determine background limited performance (BLIP) temperatures, which decrease both experimentally and theoretically as the electric field increases. This work gives good description of dark current mechanism for QWPs in the THz region and is extended to determine the transition fields and BLIP temperatures with response peaks from 3 to 12 THz.
Quantum and Classical Chirps in an Anharmonic Oscillator Yoni Shalibo,1
Friedland, Lazar
phase locking between the system and the drive, yielding a con- trollable excitation as the system the state dynamics of a tunable anharmonic quantum system, the Josephson phase circuit, under the excitation excited states, held by the drive. At large anharmonicity, we observe sharp steps, corresponding
Classical Phase Space Density for the Relativistic Hydrogen Atom
Th. M. Nieuwenhuizen
2005-11-15T23:59:59.000Z
Quantum mechanics is considered to arise from an underlying classical structure (``hidden variable theory'', ``sub-quantum mechanics''), where quantum fluctuations follow from a physical noise mechanism. The stability of the hydrogen ground state can then arise from a balance between Lorentz damping and energy absorption from the noise. Since the damping is weak, the ground state phase space density should predominantly be a function of the conserved quantities, energy and angular momentum. A candidate for this phase space density is constructed for ground state of the relativistic hydrogen problem of a spinless particle. The first excited states and their spherical harmonics are also considered in this framework. The analytic expression of the ground state energy can be reproduced, provided averages of certain products are replaced by products of averages. This analysis puts forward that quantum mechanics may arise from an underlying classical level as a slow variable theory, where each new quantum operator relates to a new, well separated time interval.
Comment on ''Secret-key-assisted private classical communication capacity over quantum channels''
Wilde, Mark M. [School of Computer Science, McGill University, Montreal, Quebec H3A 2A7 (Canada)
2011-04-15T23:59:59.000Z
The paper of Hsieh, Luo, and Brun (HLB) [Phys. Rev. A 78, 042306 (2008)] contains several issues with the capacity theorem presented there, one of which is the suggestion that a sender and receiver can achieve entanglement-assisted classical capacity without any entanglement at all, and another of which is a violation of the Holevo bound. There is also an issue with the converse proof of the capacity theorem. In this comment, I point out these issues and provide revisions of the capacity theorem and the converse proof.
Comment on 'Multiparty quantum secret sharing of classical messages based on entanglement swapping'
Lin Song [School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876 (China); School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007 (China); Gao Fei; Guo Fenzhuo; Wen Qiaoyan [School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876 (China); Zhu Fuchen [National Laboratory for Modern Communications, P.O. Box 810, Chengdu 610041 (China)
2007-09-15T23:59:59.000Z
In a recent paper [Z. J. Zhang and Z. X. Man, Phys. Rev. A 72, 022303 (2005)], a multiparty quantum secret sharing protocol based on entanglement swapping was presented. However, as we show, this protocol is insecure in the sense that an unauthorized agent group can recover the secret from the dealer. Hence we propose an improved version of this protocol which can stand against this kind of attack.
Poincaré Invariant Quantum Mechanics based on Euclidean Green functions
W. N. Polyzou; Phil Kopp
2010-08-31T23:59:59.000Z
We investigate a formulation of Poincar\\'e invariant quantum mechanics where the dynamical input is Euclidean invariant Green functions or their generating functional. We argue that within this framework it is possible to calculate scattering observables, binding energies, and perform finite Poincar\\'e transformations without using any analytic continuation. We demonstrate, using a toy model, how matrix elements of $e^{-\\beta H}$ in normalizable states can be used to compute transition matrix elements for energies up to 2 GeV. We discuss some open problems.
Machine Learning for Quantum Mechanical Properties of Atoms in Molecules
Rupp, Matthias; von Lilienfeld, O Anatole
2015-01-01T23:59:59.000Z
We introduce machine learning models of quantum mechanical observables of atoms in molecules. Instant out-of-sample predictions for proton and carbon nuclear chemical shifts, atomic core level excitations, and forces on atoms reach accuracies on par with density functional theory reference. Locality is exploited within non-linear regression via local atom-centered coordinate systems. The approach is validated on a diverse set of 9k small organic molecules. Linear scaling is demonstrated for saturated polymers with up to sub-mesoscale lengths.
Matrix Quantum Mechanics and Soliton Regularization of Noncommutative Field Theory
Giovanni Landi; Fedele Lizzi; Richard J. Szabo
2004-01-20T23:59:59.000Z
We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is applied to the perturbative dynamics of scalar field theory, to tachyon dynamics in string field theory, and to the Hamiltonian dynamics of noncommutative gauge theory in two dimensions. We also describe the adiabatic dynamics of solitons on the noncommutative torus and compare various classes of noncommutative solitons on the torus and the plane.
CM Rohwer; FG Scholtz
2012-06-06T23:59:59.000Z
In this thesis we shall demonstrate that a measurement of position alone in non-commutative space cannot yield complete information about the quantum state of a particle. Indeed, the formalism used entails a description that is non-local in that it requires all orders of positional derivatives through the star product that is used ubiquitously to map operator multiplication onto function multiplication in non-commutative systems. It will be shown that there exist several equivalent local descriptions, which are arrived at via the introduction of additional degrees of freedom. Consequently non-commutative quantum mechanical position measurements necessarily confront us with some additional structure which is necessary to specify quantum states completely. The remainder of the thesis, will involve investigations into the physical interpretation of these additional degrees of freedom. For one particular local formulation, the corresponding classical theory will be used to demonstrate that the concept of extended, structured objects emerges quite naturally and unavoidably there. This description will be shown to be equivalent to one describing a two-charge harmonically interacting composite in a strong magnetic field found by Susskind. It will be argued that these notions also extend naturally to the quantum level, and constraints will be shown to arise there. A further local formulation will be introduced, with an interpretation in terms of objects located at a point with a certain angular momentum about that point. This again enforces the idea of particles that are not point-like. Both local descriptions make explicit the additional structure which is encoded more subtly in the non-local description. Additional degrees of freedom introduced by local descriptions may also be thought of as gauge degrees of freedom in a gauge-invariant formulation of the theory.
Rosenberg, Danna [Los Alamos National Laboratory; Peterson, Charles G [Los Alamos National Laboratory; Dallmann, Nicholas [Los Alamos National Laboratory; Hughes, Richard J [Los Alamos National Laboratory; Mccabe, Kevin P [Los Alamos National Laboratory; Nordholt, Jane E [Los Alamos National Laboratory; Tyagi, Hush T [Los Alamos National Laboratory; Peters, Nicholas A [TELCORDIA TECHNOLOGIES; Toliver, Paul [TELCORDIA TECHNOLOGIES; Chapman, Thomas E [TELCORDIA TECHNOLOGIES; Runser, Robert J [TELCORDIA TECHNOLOGIES; Mcnown, Scott R [TELCORDIA TECHNOLOGIES
2008-01-01T23:59:59.000Z
To move beyond dedicated links and networks, quantum communications signals must be integrated into networks carrying classical optical channels at power levels many orders of magnitude higher than the quantum signals themselves. We demonstrate transmission of a 1550-nm quantum channel with up to two simultaneous 200-GHz spaced classical telecom channels, using ROADM (reconfigurable optical <1dd drop multiplexer) technology for multiplexing and routing quantum and classical signals. The quantum channel is used to perform quantum key distribution (QKD) in the presence of noise generated as a by-product of the co-propagation of classical channels. We demonstrate that the dominant noise mechanism can arise from either four-wave mixing or spontaneous Raman scattering, depending on the optical path characteristics as well <1S the classical channel parameters. We quantity these impairments and discuss mitigation strategies.
On quantum theories of the mind
Henry P. Stapp
1997-11-26T23:59:59.000Z
Replies are given to arguments advanced in this journal that claim to show that it is to nonlinear classical mechanics rather than quantum mechanics that one must look for the physical underpinnings of consciousness.
J. H. Field
2005-03-02T23:59:59.000Z
Feynman's laws of quantum dynamics are concisely stated, discussed in comparison with other formulations of quantum mechanics and applied to selected problems in the physical optics of photons and massive particles as well as flavour oscillations. The classical wave theory of light is derived from these laws for the case in which temporal variation of path amplitudes may be neglected, whereas specific experiments, sensitive to the temporal properties of path amplitudes, are suggested. The reflection coefficient of light from the surface of a transparent medium is found to be markedly different to that predicted by the classical Fresnel formula. Except for neutrino oscillations, good agreement is otherwise found with previous calculations of spatially dependent quantum interference effects.
N + 1 dimensional quantum mechanical model for a closed universe
T. R. Mongan
1999-02-10T23:59:59.000Z
A quantum mechanical model for an N + 1 dimensional universe arising from a quantum fluctuation is outlined. (3 + 1) dimensions are a closed infinitely-expanding universe and the remaining N - 3 dimensions are compact. The (3 + 1) non-compact dimensions are modeled by quantizing a canonical Hamiltonian description of a homogeneous isotropic universe. It is assumed gravity and the strong-electro-weak (SEW) forces had equal strength in the initial state. Inflation occurred when the compact N -3 dimensional space collapsed after a quantum transition from the initial state of the univers, during its evolution to the present state where gravity is much weaker than the SEW force. The model suggests the universe has no singularities and the large size of our present universe is determined by the relative strength of gravity and the SEW force today. A small cosmological constant, resulting from the zero point energy of the scalar field corresponding to the compact dimensions, makes the model universe expand forever.
Generating function method and its applications to Quantum, Nuclear and the Classical Groups
Boyer, Edmond
mechanics has the starting point the meeting of a very rich Tycho Brahe passion for astrophysics the death of Tycho Brahe and the results were Kepler's laws and the death of Kepler poverty. Then Galileo
A general-purpose pulse sequencer for quantum computing
Pháº¡m, Paul Tân Tháº¿
2005-01-01T23:59:59.000Z
Quantum mechanics presents a more general and potentially more powerful model of computation than classical systems. Quantum bits have many physically different representations which nonetheless share a common need for ...
Quantum mechanical observer and superstring/M theory
M. Dance
2008-12-31T23:59:59.000Z
Terms are suggested for inclusion in a Lagrangian density as seen by an observer O2, to represent the dynamics of a quantum mechanical observer O1 that is an initial stage in an observation process. This paper extends an earlier paper which suggested that the centre-of-mass kinetic energy of O1 could correspond to, and possibly underlie, the Lagrangian density for bosonic string theory, where the worldsheet coordinates are the coordinates which O1 can observe. The present paper considers a fermion internal to O1, in addition to O1's centre of mass. It is suggested that quantum mechanical uncertainties in the transformation between O1's and O2's reference systems might require O2 to use $d$ spinor fields for this fermion, where $d$ is the number of spacetime dimensions. If this is the case, and if the symmetry/observability arguments in arXiv:hep-th/0601104 apply, the resulting Lagrangian density for the dynamics of O1 might resemble, or even underlie, superstring/M theory.
NMR quantum information processing
Dawei Lu; Aharon Brodutch; Jihyun Park; Hemant Katiyar; Tomas Jochym-O'Connor; Raymond Laflamme
2015-01-07T23:59:59.000Z
Quantum computing exploits fundamentally new models of computation based on quantum mechanical properties instead of classical physics, and it is believed that quantum computers are able to dramatically improve computational power for particular tasks. At present, nuclear magnetic resonance (NMR) has been one of the most successful platforms amongst all current implementations. It has demonstrated universal controls on the largest number of qubits, and many advanced techniques developed in NMR have been adopted to other quantum systems successfully. In this review, we show how NMR quantum processors can satisfy the general requirements of a quantum computer, and describe advanced techniques developed towards this target. Additionally, we review some recent NMR quantum processor experiments. These experiments include benchmarking protocols, quantum error correction, demonstrations of algorithms exploiting quantum properties, exploring the foundations of quantum mechanics, and quantum simulations. Finally we summarize the concepts and comment on future prospects.
ECE 350 / 450 -Fall 2010 Applied Quantum Mechanics for Engineers (3)
Gilchrist, James F.
ECE 350 / 450 - Fall 2010 Applied Quantum Mechanics for Engineers (3) Instructor: Prof. Nelson (for ECE 450-level) in engineering (Electical and Computer Engineering, Material Science Engineering
Upper Bound on Fidelity of Classical Sagnac Gyroscope
Thomas B. Bahder
2011-01-24T23:59:59.000Z
Numerous quantum mechanical schemes have been proposed that are intended to improve the sensitivity to rotation provided by the classical Sagnac effect in gyroscopes. A general metric is needed that can compare the performance of the new quantum systems with the classical systems. The fidelity (Shannon mutual information between the measurement and the rotation rate) is proposed as a metric that is capable of this comparison. A theoretical upper bound is derived for the fidelity of an ideal classical Sagnac gyroscope. This upper bound for the classical Sagnac gyroscope should be used as a benchmark to compare the performance of proposed enhanced classical and quantum rotation sensors. In fact, the fidelity is general enough to compare the quality of two different apparatuses (two different experiments) that attempt to measure the same quantity.
Chen, Jie; Yin, Hongyun; Wang, Dunyou; Valiev, Marat
2013-02-20T23:59:59.000Z
The OH- (H2O) + CCl4 reaction in aqueous solution was investigated using the combined quantum mechanical and molecular mechanics approach. The reaction mechanism of OH- (H2O) + CCl4 consists of two concerted steps - formation of OH- in the favorable attack conformation via the proton transfer process, and the nucleophilic substitution process in which the newly formed OH- attacks the CCl4. The free energy activation barrier is 38.2 kcal/mol at CCSD(T)/MM level of theory for this reaction, which is about 10.3 kcal/mol higher than that of the direct nucleophilic substitution mechanism of the OH- + CCl4 reaction in aqueous solution.
Goddard III, William A.
Quantum mechanics based force field for carbon ,,QMFF-Cx... validated to reproduce the mechanical mechanics based force field for carbon QMFF-Cx by fitting to results from density functional theory . A third, eclipsed geometry is calculated to be much higher in energy. The QMFF-Cx force field leads
Model checking quantum Markov chains
Yuan Feng; Nengkun Yu; Mingsheng Ying
2013-11-14T23:59:59.000Z
Although the security of quantum cryptography is provable based on the principles of quantum mechanics, it can be compromised by the flaws in the design of quantum protocols and the noise in their physical implementations. So, it is indispensable to develop techniques of verifying and debugging quantum cryptographic systems. Model-checking has proved to be effective in the verification of classical cryptographic protocols, but an essential difficulty arises when it is applied to quantum systems: the state space of a quantum system is always a continuum even when its dimension is finite. To overcome this difficulty, we introduce a novel notion of quantum Markov chain, specially suited to model quantum cryptographic protocols, in which quantum effects are entirely encoded into super-operators labelling transitions, leaving the location information (nodes) being classical. Then we define a quantum extension of probabilistic computation tree logic (PCTL) and develop a model-checking algorithm for quantum Markov chains.
Model checking quantum Markov chains
Feng, Yuan; Ying, Mingsheng
2012-01-01T23:59:59.000Z
Although the security of quantum cryptography is provable based on the principles of quantum mechanics, it can be compromised by the flaws in the design of quantum protocols and the noise in their physical implementations. So, it is indispensable to develop techniques of verifying and debugging quantum cryptographic systems. Model-checking has proved to be effective in the verification of classical cryptographic protocols, but an essential difficulty arises when it is applied to quantum systems: the state space of a quantum system is always a continuum even when its dimension is finite. To overcome this difficulty, we introduce a novel notion of quantum Markov chain, specially suited to model quantum cryptographic protocols, in which quantum effects are entirely encoded into super-operators labelling transitions, leaving the location information (nodes) being classical. Then we define a quantum extension of probabilistic computation tree logic (PCTL) and develop a model-checking algorithm for quantum Markov c...
Thermodynamics of quantum jump trajectories in systems driven by classical fluctuations
Adrian A. Budini
2010-12-03T23:59:59.000Z
The large-deviation method can be used to study the measurement trajectories of open quantum systems. For optical arrangements this formalism allows to describe the long time properties of the (non-equilibrium) photon counting statistics in the context of a (equilibrium) thermodynamic approach defined in terms of dynamical phases and transitions between them in the trajectory space [J.P. Garrahan and I. Lesanovsky, Phys. Rev. Lett. 104, 160601 (2010)]. In this paper, we study the thermodynamic approach for fluorescent systems coupled to complex reservoirs that induce stochastic fluctuations in their dynamical parameters. In a fast modulation limit the thermodynamics corresponds to that of a Markovian two-level system. In a slow modulation limit, the thermodynamic properties are equivalent to those of a finite system that in an infinite-size limit is characterized by a first-order transition. The dynamical phases correspond to different intensity regimes, while the size of the system is measured by the transition rate of the bath fluctuations. As a function of a dimensionless intensive variable, the first and second derivative of the thermodynamic potential develop an abrupt change and a narrow peak respectively. Their scaling properties are consistent with a double-Gaussian probability distribution of the associated extensive variable.
Frame transforms, star products and quantum mechanics on phase space
P. Aniello; V. I. Man'ko; G. Marmo
2008-04-10T23:59:59.000Z
Using the notions of frame transform and of square integrable projective representation of a locally compact group $G$, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier Hilbert space of the representation into the space of square integrable functions on the direct product group $G\\times G$. These transforms have remarkable properties. In particular, their ranges are reproducing kernel Hilbert spaces endowed with a suitable 'star product' which mimics, at the level of functions, the original product of operators. A 'phase space formulation' of quantum mechanics relying on the frame transforms introduced in the present paper, and the link of these maps with both the Wigner transform and the wavelet transform are discussed.
Generally covariant quantum mechanics on noncommutative configuration spaces
Kopf, Tomas; Paschke, Mario [Mathematical Institute, Silesian University, Na Rybnicku 1, 74601 Opava (Czech Republic); Institut fuer Mathematik, Einsteinstrasse 62, 48149 Muenster (Germany)
2007-11-15T23:59:59.000Z
We generalize the previously given algebraic version of 'Feynman's proof of Maxwell's equations' to noncommutative configuration spaces. By doing so, we also obtain an axiomatic formulation of nonrelativistic quantum mechanics over such spaces, which, in contrast to most examples discussed in the literature, does not rely on a distinguished set of coordinates. We give a detailed account of several examples, e.g., C{sup {infinity}}(Q)xM{sub n}(C) which leads to non-Abelian Yang-Mills theories, and of noncommutative tori T{sub {theta}}{sup d}. Moreover, we examine models over the Moyal-deformed plane R{sub {theta}}{sup 2}. Assuming the conservation of electrical charges, we show that in this case the canonical uncertainty relation [x{sub k},x{sub l}]=ig{sub kl} with metric g{sub kl} is only consistent if g{sub kl} is constant.
Solomon Akaraka Owerre; M. B Paranjape
2014-07-02T23:59:59.000Z
We study the phase transition of the escape rate of exchange-coupled dimer of single-molecule magnets which are coupled either ferromagnetic ally or antiferromagnetically in a staggered magnetic field and an easy $z$-axis anisotropy. The Hamiltonian for this system has been used to study molecular dimer nanomagnets [Mn$_4$]$_2$. We generalize the method of mapping a single-molecule magnetic spin problem onto a quantum-mechanical particle to dimeric molecular nanomagnets. The problem is mapped to a single particle quantum-mechanical Hamiltonian in terms of the relative coordinate and a coordinate dependent reduced mass. It is shown that the presence of the external staggered magnetic field creates a phase boundary separating the first- from the second-order transition. With the set of parameters used by R. Tiron, $\\textit{et al}$, \\prl {\\bf 91}, 227203 (2003), and S. Hill, $\\textit{et al}$ science {\\bf 302}, 1015 (2003) to fit experimental data for [Mn$_{4}$]$_2$ dimer we find that the critical temperature at the phase boundary is $T^{(c)}_0 =0.29K$. Therefore, thermally activated transitions should occur for temperatures greater than $T^{(c)}_0$.
Optics, Mechanics and Quantization of Reparametrization Systems
M. Navarro; J. Guerrero; V. Aldaya
1994-04-20T23:59:59.000Z
In this paper we regard the dynamics obtained from Fermat principle as begin the classical theory of light. We (first-)quantize the action and show how close we can get to the Maxwell theory. We show that Quantum Geometric Optics is not a theory of fields in curved space. Considering Classical Mechanics to be on the same footing, we show the parallelism between Quantum Mechanics and Quantum Geometric Optics. We show that, due to the reparametrization invariance of the classical theories, the dynamics of the quantum theories is given by a Hamiltonian constraint. Some implications of the above analogy in the quantization of true reparameterization invariant systems are discussed.
Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion Florian Marquardt,1
Clerk, Aashish
using bulk refrigeration, but it may be feasible using nonequilibrium cooling techniques analo- gousQuantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion Florian Marquardt,1 Joe P (Received 22 January 2007; published 28 August 2007) We present a quantum-mechanical theory of the cooling
Mechanism for thermoelectric figure-of-merit enhancement in regimented quantum dot superlattices
Mechanism for thermoelectric figure-of-merit enhancement in regimented quantum dot superlattices propose a mechanism for enhancement of the thermoelectric figure-of-merit in regimented quantum dot, as a result, to the thermoelectric figure-of-merit enhancement. To maximize the improvement, one has to tune
Elio Conte
2011-06-14T23:59:59.000Z
We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the and Clifford algebras. This last algebra gives proof of the von Neumann basic postulates on the quantum measurement explaining thus in an algebraic manner the wave function collapse postulated in standard quantum theory. In this manner we reach the objective to expose a self-consistent version of quantum mechanics. We give proof of the quantum like Heisenberg uncertainty relations, the phenomenon of quantum Mach Zender interference as well as quantum collapse in some cases of physical interest We also discuss the problem of time evolution of quantum systems as well as the changes in space location. We also give demonstration of the Kocken-Specher theorem, and also we give an algebraic formulation and explanation of the EPR . By using the same approach we also derive Bell inequalities. Our formulation is strongly based on the use of idempotents that are contained in Clifford algebra. Their counterpart in quantum mechanics is represented by the projection operators that are interpreted as logical statements, following the basic von Neumann results. Using the Clifford algebra we are able to invert such result. According to the results previously obtained by Orlov in 1994, we are able to give proof that quantum mechanics derives from logic. We show that indeterminism and quantum interference have their origin in the logic.
Quantum mechanical approaches to in silico enzyme characterization and drug design
Nilmeier, J P; Fattebert, J L; Jacobson, M P; Kalyanaraman, C
2012-01-17T23:59:59.000Z
The astonishing, exponentially increasing rates of genome sequencing has led to one of the most significant challenges for the biological and computational sciences in the 21st century: assigning the likely functions of the encoded proteins. Enzymes represent a particular challenge, and a critical one, because the universe of enzymes is likely to contain many novel functions that may be useful for synthetic biology, or as drug targets. Current approaches to protein annotation are largely based on bioinformatics. At the simplest level, this annotation involves transferring the annotations of characterized enzymes to related sequences. In practice, however, there is no simple, sequence based criterion for transferring annotations, and bioinformatics alone cannot propose new enzymatic functions. Structure-based computational methods have the potential to address these limitations, by identifying potential substrates of enzymes, as we and others have shown. One successful approach has used in silico 'docking' methods, more commonly applied in structure-based drug design, to identify possible metabolite substrates. A major limitation of this approach is that it only considers substrate binding, and does not directly assess the potential of the enzyme to catalyze a particular reaction using a particular substrate. That is, substrate binding affinity is necessary but not sufficient to assign function. A reaction profile is ultimately what is needed for a more complete quantitative description of function. To address this rather fundamental limitation, they propose to use quantum mechanical methods to explicitly compute transition state barriers that govern the rates of catalysis. Although quantum mechanical, and mixed quantum/classical (QM/MM), methods have been used extensively to investigate enzymatic reactions, the focus has been primarily on elucidating complex reaction mechanisms. Here, the key catalytic steps are known, and they use these methods quantify substrate specificity. That is, we bring the power of quantum mechanics to bear on the problem of annotating enzyme function, which is a novel approach. Although it has been clear to us at the Jacobson group for some time that enzyme specificity may be encoded in transition states, rather than simply substrate recognition, the main limitation has always been computational expense. Using a hierarchy of different methods, they can reduce the list of plausible substrates of an enzyme to a small number in most cases, but even identifying the transition states for a dozen plausible substrates requires significant computational effort, beyond what is practical using standard QM/MM methods. For this project, they have chosen two enzyme superfamilies which they have used as 'model systems' for functional assignment. The enolase superfamily is a large group of {alpha}-{beta} barrel enzymes with highly diverse substrates and chemical transformations. Despite decades of work, over a third of the superfamily remains unassigned, which means that the remaining cases are by definition difficult to assign. They have focused on acid sugar dehydratases, and have considerable expertise on the matter. They are also interested in the isoprenoid synthase superfamily, which is of central interest to the synthetic biology community, because these enzymes are used by nature to create complex rare natural products of medicinal value. the most notable example of this is the artemisinin, an antimalarial compound that is found in trace amounts in the wormwod root. From the standpoint of enzyme function assignment, these enzymes are intriguing because they use a small number of chemically simple substrates to generate, potentially, tens of thousands of different products. Hence, substrate binding specificity is only a small part of the challenge; the key is determining how the enzyme directs the carbocation chemistry to specific products. These more complex modeling approaches clearly require quantum mechanical methods.
On the explanation for quantum statistics
Simon Saunders
2005-11-15T23:59:59.000Z
The concept of classical indistinguishability is analyzed and defended against a number of well-known criticisms, with particular attention to the Gibbs' paradox. Granted that it is as much at home in classical as in quantum statistical mechanics, the question arises as to why indistinguishability, in quantum mechanics but not in classical mechanics, forces a change in statistics. The answer, illustrated with simple examples, is that the equilibrium measure on classical phase space is continuous, whilst on Hilbert space it is discrete. The relevance of names, or equivalently, properties stable in time that can be used as names, is also discussed.
Sussman, Joel L.
and Benzene Clifford Felder, Hua-Liang Jiang,,§,|, Wei-Liang Zhu,§,| Kai-Xian Chen,§ Israel Silman, Simone A-methyl groups with a benzene ring, by use of density-functional theory (DFT) methods B3LYP/6-31G* and B3LYP/6 profiles of the complex as benzene was moved away from TMA in 0.2 Å intervals. Hence it is possible to use
Quantum Mechanics as a Classical Theory XVI: Positive-Definite Densities
L. S. F. Olavo
1997-04-02T23:59:59.000Z
In this paper we will turn our attention to the problem of obtaining phase-space probability density functions. We will show that it is possible to obtain functions which assume only positive values over all its domain of definition.
State Transfer Between a Mechanical Oscillator and Microwave Fields in the Quantum Regime
T. A. Palomaki; J. W. Harlow; J. D. Teufel; R. W. Simmonds; K. W. Lehnert
2012-06-25T23:59:59.000Z
Recently, macroscopic mechanical oscillators have been coaxed into a regime of quantum behavior, by direct refrigeration [1] or a combination of refrigeration and laser-like cooling [2, 3]. This exciting result has encouraged notions that mechanical oscillators may perform useful functions in the processing of quantum information with superconducting circuits [1, 4-7], either by serving as a quantum memory for the ephemeral state of a microwave field or by providing a quantum interface between otherwise incompatible systems [8, 9]. As yet, the transfer of an itinerant state or propagating mode of a microwave field to and from a mechanical oscillator has not been demonstrated owing to the inability to agilely turn on and off the interaction between microwave electricity and mechanical motion. Here we demonstrate that the state of an itinerant microwave field can be coherently transferred into, stored in, and retrieved from a mechanical oscillator with amplitudes at the single quanta level. Crucially, the time to capture and to retrieve the microwave state is shorter than the quantum state lifetime of the mechanical oscillator. In this quantum regime, the mechanical oscillator can both store and transduce quantum information.
Techniques for noise suppression and robust control in spin-based quantum information processors
Borneman, Troy William
2013-01-01T23:59:59.000Z
Processing information quantum mechanically allows the relatively efficient solution of many important problems thought to be intractable on a classical computer. A primary challenge in experimentally implementing a quantum ...
Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians
Al-Hashimi, M.H., E-mail: hashimi@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Salman, M., E-mail: msalman@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Shalaby, A., E-mail: amshalab@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Physics Department, Faculty of Science, Mansoura University (Egypt); Wiese, U.-J., E-mail: wiese@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA (United States)
2013-10-15T23:59:59.000Z
We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant. -- Highlights: •Self-adjoint extension theory and contact interactions. •Application of self-adjoint extensions to supersymmetry. •Contact interactions in finite volume with Robin boundary condition.
Quantum-mechanical nonequivalence of metrics of centrally symmetric uncharged gravitational field
M. V. Gorbatenko; V. P. Neznamov
2013-08-02T23:59:59.000Z
Quantum-mechanical analysis shows that the metrics of a centrally symmetric uncharged gravitational field, which are exact solutions of the general relativity equations, are physically non-equivalent. The classical Schwarzschield metric and the Schwarzschild metrics in isotropic and harmonic coordinates provide for the existence of stationary bound states of Dirac particles with a real energy spectrum. The Hilbert condition g_{00}>0 is responsible for zero values of the wave functions under the "event horizon" that leads to the absence of Hawking radiation. For the Eddington-Finkelstein and Painleve-Gullstrand metrics, stationary bound states of spin-half particles cannot exist because Dirac Hamiltonians are non-Hermitian. For these metrics, the condition g_{00}>0 also leads to the absence of Hawking evaporation. For the Finkelstein-Lemaitre and Kruskal metrics, Dirac Hamiltonians are explicitly time-dependent, and stationary bound states of spin-half particles cannot exist for them. The Hilbert condition for these metrics does not place any constraints on the domains of the wave functions. Hawking evaporation of black holes is possible in this case. The results can lead to revisiting some concepts of the standard cosmological model related to the evolution of the universe and interaction of collapsars with surrounding matter.
Semiclassical analysis of quantum dynamics
Siyang Yang
2011-11-15T23:59:59.000Z
Simulating the molecular dynamics (MD) using classical or semi-classical trajectories provides important details for the understanding of many chemical reactions, protein folding, drug design, and solvation effects. MD simulations using trajectories have achieved great successes in the computer simulations of various systems, but it is difficult to incorporate quantum effects in a robust way. Therefore, improving quantum wavepacket dynamics and incorporating nonadiabatic transitions and quantum effects into classical and semi-classical molecular dynamics is critical as well as challenging. In this paper, we present a MD scheme in which a new set of equations of motion (EOM) are proposed to effectively propagate nuclear trajectories while conserving quantum mechanical energy which is critical for describing quantum effects like tunneling. The new quantum EOM is tested on a one-state one-dimensional and a two-state two-dimensional model nonadiabatic systems. The global quantum force experienced by each trajectory promotes energy redistribution among the bundle of trajectories, and thus helps the individual trajectory tunnel through the potential barrier higher than the energy of the trajectory itself. Construction of the new quantum force and EOM also provides a better way to treat the issue of back-reaction in mixed quantum-classical (MQC) methods, i.e. self-consistency between quantum degrees of freedom (DOF) and classical DOF.
Cosmological Rotation of Quantum-Mechanical Origin and Anisotropy of the Microwave Background
L. P. Grishchuk
1993-10-06T23:59:59.000Z
It is shown that rotational cosmological perturbations can be generated in the early Universe, similarly to gravitational waves. The generating mechanism is quantum-mechanical in its nature, and the created perturbations should now be placed in squeezed vacuum quantum states. The physical conditions under which the phenomenon can occur are formulated. The generated perturbations can contribute to the large-angular-scale anisotropy of the cosmic microwave background radiation. An exact formula is derived for the angular correlation function of the temperature variations caused by the quantum-mechanically generated rotational perturbations. The multipole expansion begins from the dipole component. The comparison with the case of gravitational waves is made.
Reginald B. Little
2014-03-27T23:59:59.000Z
A comprehensive theory of superconductivity (SC) and superfluidity (SF) is presented of new types III and IV at temperatures into millions of degrees involving phase transitions of fermions in heat reservoirs to form general relativistic triple quasi-particles of 3 fermions interacting to boson-fermion pairs. Types 0, I, and II SC/SF are deduced from such triples as: thermally dressed, relativistic fermionic vortices; spin coupled, dressed, fermionic vortical pairs (diamagnetic bosons); and spinrevorbitally coupled, dressed fermionic, vortical pairs (ferromagnetic bosons). All known SC, SF and trends in critical temperatures (Tc) are thereby explained. The recently observed SC/SF in nano-graphene systems is explained. The above room temperature SC/SF is predicted and modeled by transformations of intense thermal boson populations of heat reservoirs to relativistic mass, weight, spin and magnetism for further reasoning over compression to electricity, weak phenomena and strong phenomena for connecting general relativism and quantum mechanics.
Reginald B. Little
2015-04-23T23:59:59.000Z
A comprehensive theory of superconductivity (SC) and superfluidity (SF) is presented of new types III and IV at temperatures into millions of degrees involving phase transitions of fermions in heat reservoirs to form general relativistic triple quasi-particles of 3 fermions interacting to boson-fermion pairs. Types 0, I, and II SC/SF are deduced from such triples as: thermally dressed, relativistic fermionic vortices; spin coupled, dressed, fermionic vortical pairs (diamagnetic bosons); and spinrevorbitally coupled, dressed fermionic, vortical pairs (ferromagnetic bosons). All known SC, SF and trends in critical temperatures (Tc) are thereby explained. The recently observed SC/SF in nano-graphene systems is explained. The above room temperature SC/SF is predicted and modeled by transformations of intense thermal boson populations of heat reservoirs to relativistic mass, weight, spin and magnetism for further reasoning over compression to electricity, weak phenomena and strong phenomena for connecting general relativism and quantum mechanics.
Dynamical Wave Function Collapse Models in Quantum Measure Theory
Fay Dowker; Yousef Ghazi-Tabatabai
2008-05-15T23:59:59.000Z
The structure of Collapse Models is investigated in the framework of Quantum Measure Theory, a histories-based approach to quantum mechanics. The underlying structure of coupled classical and quantum systems is elucidated in this approach which puts both systems on a spacetime footing. The nature of the coupling is exposed: the classical histories have no dynamics of their own but are simply tied, more or less closely, to the quantum histories.
Coherent states in the quantum multiverse
S. Robles-Perez; Y. Hassouni; P. F. Gonzalez-Diaz
2009-11-24T23:59:59.000Z
In this paper, we study the role of coherent states in the realm of quantum cosmology, both in a second-quantized single universe and in a third-quantized quantum multiverse. In particular, most emphasis will be paid to the quantum description of multiverses made up of accelerated universes. We have shown that the quantum states involved at a quantum mechanical multiverse whose single universes are accelerated are given by squeezed states having no classical analogs.
Neirotti, Juan Pablo
: AM30ME School: Engineering and Applied Science Module Type: Standard Module New Module? No Module in both written and oral form. 2. Structure, order and classify materials, information, dataApproved Module Information for AM30ME, 2014/5 Module Title/Name: Classical Mechanics Module Code
Khan, Shabbir A
2013-01-01T23:59:59.000Z
Quantum plasma physics is a rapidly evolving research field with a very inter-disciplinary scope of potential applications, ranging from nano-scale science in condensed matter to the vast scales of astrophysical objects. The theoretical description of quantum plasmas relies on various approaches, microscopic or macroscopic, some of which have obvious relation to classical plasma models. The appropriate model should, in principle, incorporate the quantum mechanical effects such as diffraction, spin statistics and correlations, operative on the relevant scales. However, first-principle approaches such as quantum Monte Carlo and density functional theory or quantum-statistical methods such as quantum kinetic theory or non-equilibrium Green's functions require substantial theoretical and computational efforts. Therefore, for selected problems, alternative simpler methods have been put forward. In particular, the collective behavior of many-body systems is usually described within a self-consistent scheme of parti...
Energy Inequalities in Quantum Field Theory
Christopher J. Fewster
2005-01-31T23:59:59.000Z
Quantum fields are known to violate all the pointwise energy conditions of classical general relativity. We review the subject of quantum energy inequalities: lower bounds satisfied by weighted averages of the stress-energy tensor, which may be regarded as the vestiges of the classical energy conditions after quantisation. Contact is also made with thermodynamics and related issues in quantum mechanics, where such inequalities find analogues in sharp Gaarding inequalities.
Superradiant Quantum Heat Engine
Ali Ü. C. Hardal; Özgür E. Müstecapl?oglu
2015-04-22T23:59:59.000Z
Quantum physics revolutionized classical disciplines of mechanics, statistical physics, and electrodynamics. One branch of scientific knowledge however seems untouched: thermodynamics. Major motivation behind thermodynamics is to develop efficient heat engines. Technology has a trend to miniaturize engines, reaching to quantum regimes. Development of quantum heat engines (QHEs) requires emerging field of quantum thermodynamics. Studies of QHEs debate whether quantum coherence can be used as a resource. We explore an alternative where it can function as an effective catalyst. We propose a QHE which consists of a photon gas inside an optical cavity as the working fluid and quantum coherent atomic clusters as the fuel. Utilizing the superradiance, where a cluster can radiate quadratically faster than a single atom, we show that the work output becomes proportional to the square of the number of the atoms. In addition to practical value of cranking up QHE, our result is a fundamental difference of a quantum fuel from its classical counterpart.
Quantum Ground State and Single Phonon Control of a Mechanical Resonator
Martinis, John M.
-limited measurements must then be demonstrated. Here, using conventional cryo- genic refrigeration, we show that we can, eases the stringent temperature requirements, and when combined with quantum optics-based refrigeration conventional cryogenic refrigeration, we show that we can demonstrably cool a mechanical mode to its quantum
A Short-Time Quantum Mechanical Expansion Approach to Vibrational Relaxation Eran Rabani*,
Rabani, Eran
A Short-Time Quantum Mechanical Expansion Approach to Vibrational Relaxation Eran Rabani*, School" molecule embedded in a "quantum" host is approached from the perspective of a short-time expansion that depend on both position and momentum. A simple ansatz is used to connect the short-time and long
Quantum-mechanical description of Lense-Thirring effect for relativistic scalar particles
Alexander J. Silenko
2014-08-10T23:59:59.000Z
Exact expression for the Foldy-Wouthuysen Hamiltonian of scalar particles is used for a quantum-mechanical description of the relativistic Lense-Thirring effect. The exact evolution of the angular momentum operator in the Kerr field approximated by a spatially isotropic metric is found. The quantum-mechanical description of the full Lense-Thirring effect based on the Laplace-Runge-Lenz vector is given in the nonrelativistic and weak-field approximation. Relativistic quantum-mechanical equations for the velocity and acceleration operators are obtained. The equation for the acceleration defines the Coriolis-like and centrifugal-like accelerations and presents the quantum-mechanical description of the frame-dragging effect.
Liao, Rongzhen
Tungsten-dependent formaldehyde ferredoxin oxidoreductase: Reaction mechanism from quantum chemical theory Enzyme catalysis Formaldehyde ferredoxin oxidoreductase from Pyrococcus furiosus is a tungsten the formaldehyde substrate binds directly to the tungsten ion. WVI =O then performs a nucleophilic attack
Application of quantum theory of electrons to the mechanical and thermal properties of metals
Peng, Hwan-Wu
The first successful application of quantum mechanics to the problem of metallic cohesion was made by Wigner and Seitz (1938) They appoximated sodium metal by a number of isolated spheres of equal atomic volume and integrated, ...
Unitary dilation models of Turing machines in quantum mechanics
Benioff, P. [Environmental Assessment Division, Building 900, Argonne National Laboratory, Argonne, Illinois 60439 (United States)] [Environmental Assessment Division, Building 900, Argonne National Laboratory, Argonne, Illinois 60439 (United States)
1995-05-01T23:59:59.000Z
A goal of quantum-mechanical models of the computation process is the description of operators that model changes in the information-bearing degrees of freedom. Iteration of the operators should correspond to steps in the computation, and the final state of halting computations should be stable under iteration. The problem is that operators constructed directly from the process description do not have these properties. In general these operators annihilate the halted state. If information-erasing steps are present, there are additional problems. These problems are illustrated in this paper by consideration of operators for two simple one-step processes and two simple Turing machines. In general the operators are not unitary and, if erasing steps are present, they are not even contraction operators. Various methods of extension or dilation to unitary operators are discussed. Here unitary power dilations are considered as a solution to these problems. It is seen that these dilations automatically provide a good solution to the initial- and final-state problems. For processes with erasing steps, recording steps must be included prior to the dilation, but only for the steps that erase information. Hamiltonians for these processes are also discussed. It is noted that {ital H}, described by exp({minus}{ital iH}{Delta})={ital U}{sup {ital T}}, where {ital U}{sup {ital T}} is a unitary step operator for the process and {Delta} a time interval, has complexity problems. These problems and those noted above are avoided here by the use of the Feynman approach to constructing Hamiltonians directly from the unitary power dilations of the model operators. It is seen that the Hamiltonians so constructed have some interesting properties.
Classical systems can be contextual too: Analogue of the Mermin-Peres square
Pawel Blasiak
2015-02-25T23:59:59.000Z
Contextuality lays at the heart of quantum mechanics. In the prevailing opinion it is considered as a signature of 'quantumness' that classical theories lack. However, this assertion is only partially justified. Although contextuality is certainly true of quantum mechanics, it cannot be taken by itself as discriminating against classical theories. Here we consider a representative example of contextual behaviour, the so-called Mermin-Peres square, and present a discrete toy model of a bipartite system which reproduces the pattern of quantum predictions that leads to contradiction with the assumption of non-contextuality. This illustrates that quantum-like contextual effects have their analogues within classical models with epistemic constraints such as limited information gain and measurement disturbance.
On the justification of applying quantum strategies to the Prisoners' Dilemma and mechanism design
Haoyang Wu
2010-07-08T23:59:59.000Z
The Prisoners' Dilemma is perhaps the most famous model in the field of game theory. Consequently, it is natural to investigate its quantum version when one considers to apply quantum strategies to game theory. There are two main results in this paper: 1) The well-known Prisoners' Dilemma can be categorized into three types and only the third type is adaptable for quantum strategies. 2) As a reverse problem of game theory, mechanism design provides a better circumstance for quantum strategies than game theory does.
Supporting Kibble-Zurek Mechanism in Quantum Ising Model through a Trapped Ion
Jin-Ming Cui; Yun-Feng Huang; Zhao Wang; Dong-Yang Cao; Jian Wang; Wei-Min Lv; Yong Lu; Le Luo; Adolfo del Campo; Yong-Jian Han; Chuan-Feng Li; Guang-Can Guo
2015-05-21T23:59:59.000Z
Progress in quantum simulation has fostered the research on far-from-equilibrium dynamics. The Kibble-Zurek mechanism is the paradigmatic framework to account for the non adiabatic critical dynamics of a system driven across a phase transition in a finite time. Its study in the quantum regime is hindered by the requisite of ground state cooling. We report the experimental quantum simulation of critical dynamics in the transverse-field Ising model by a set of non-equilibrium processes in the pseudo-momentum space, that can be probed with high accuracy using a single trapped ion. Our results support the validity of the Kibble-Zurek mechanism in the quantum regime and advance the quantum simulation of critical systems far-away from equilibrium.
A Non-Local Reality: Is there a Phase Uncertainty in Quantum Mechanics?
Elizabeth S. Gould; Niayesh Afshordi
2014-07-15T23:59:59.000Z
A century after the advent of Quantum Mechanics and General Relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable, conflicts. Motivations for violations of the notion of relativistic locality include the Bell's inequalities for hidden variable theories, the cosmological horizon problem, and Lorentz-violating approaches to quantum geometrodynamics, such as Horava-Lifshitz gravity. Here, we explore a recent proposal for a "real ensemble" non-local description of quantum mechanics, in which "particles" can copy each others' observable values AND phases, independent of their spatial separation. We first specify the exact theory, ensuring that it is consistent and has (ordinary) quantum mechanics as a fixed point, where all particles with the same values for a given observable have the same phases. We then study the stability of this fixed point numerically, and analytically, for simple models. We provide evidence that most systems (in our study) are locally stable to small deviations from quantum mechanics, and furthermore, the phase variance per value of the observable, as well as systematic deviations from quantum mechanics, decay as $\\sim$ (Energy$\\times$Time)$^{-2n}$, where $n \\geq 1$. Interestingly, this convergence is controlled by the absolute value of energy (and not energy difference), suggesting a possible connection to gravitational physics. Finally, we discuss different issues related to this theory, as well as potential novel applications for the spectrum of primordial cosmological perturbations and the cosmological constant problem.
Li, Jun; Guo, Hua, E-mail: zhangdh@dicp.ac.cn, E-mail: hguo@unm.edu [Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131 (United States)] [Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131 (United States); Chen, Jun; Zhang, Dong H., E-mail: zhangdh@dicp.ac.cn, E-mail: hguo@unm.edu [State key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023 (China)
2014-01-28T23:59:59.000Z
A permutationally invariant global potential energy surface for the HOCO system is reported by fitting a larger number of high-level ab initio points using the newly proposed permutation invariant polynomial-neural network method. The small fitting error (?5 meV) indicates a faithful representation of the potential energy surface over a large configuration space. Full-dimensional quantum and quasi-classical trajectory studies of the title reaction were performed on this potential energy surface. While the results suggest that the differences between this and an earlier neural network fits are small, discrepancies with state-to-state experimental data remain significant.
Gherib, Rami; Izmaylov, Artur F
2015-01-01T23:59:59.000Z
Adequate simulation of non-adiabatic dynamics through conical intersection requires account for a non-trivial geometric phase (GP) emerging in electronic and nuclear wave-functions in the adiabatic representation. Popular mixed quantum-classical (MQC) methods, surface hopping and Ehrenfest, do not carry a nuclear wave-function to be able to incorporate the GP into nuclear dynamics. Surprisingly, the MQC methods reproduce ultra-fast interstate crossing dynamics generated with the exact quantum propagation so well as if they contained information about the GP. Using two-dimensional linear vibronic coupling models we unravel how the MQC methods can effectively mimic the most significant dynamical GP effects: 1) compensation for repulsive diagonal second order non-adiabatic couplings and 2) transfer enhancement for a fully cylindrically symmetric component of a nuclear distribution.
Thygesen, Kristian
systems.11Â15 When the size of a plasmonic structure reaches the nanoscale, quantum effects begin to play of the electron system that are found in solids, at extended surfaces, and at the surface of confined metal and photovoltaics.6 Applications of plasmons in next generation nanoelectronics7 and quantum information technology8
A note on the Landauer principle in quantum statistical mechanics
Vojkan Jaksic; Claude-Alain Pillet
2014-05-30T23:59:59.000Z
The Landauer principle asserts that the energy cost of erasure of one bit of information by the action of a thermal reservoir in equilibrium at temperature T is never less than $kTlog 2$. We discuss Landauer's principle for quantum statistical models describing a finite level quantum system S coupled to an infinitely extended thermal reservoir R. Using Araki's perturbation theory of KMS states and the Avron-Elgart adiabatic theorem we prove, under a natural ergodicity assumption on the joint system S+R, that Landauer's bound saturates for adiabatically switched interactions. The recent work of Reeb and Wolf on the subject is discussed and compared.
n the microcosmos of quantum mechanics, phenomena abound that
Nielsen, Steven O.
, can appear to behave as a water wave in one instance and as a discrete particle in another. Both. These waves interfere, producing a series of light and dark fringes when projected onto a screen [see point or another.) 86 SCIENTIFIC AMERICAN December 1994 The Duality in Matter and Light In quantum
States in the Hilbert space formulation and in the phase space formulation of quantum mechanics
Tosiek, J., E-mail: tosiek@p.lodz.pl; Brzykcy, P., E-mail: 800289@edu.p.lodz.pl
2013-05-15T23:59:59.000Z
We consider the problem of testing whether a given matrix in the Hilbert space formulation of quantum mechanics or a function considered in the phase space formulation of quantum theory represents a quantum state. We propose several practical criteria for recognising states in these two versions of quantum physics. After minor modifications, they can be applied to check positivity of any operators acting in a Hilbert space or positivity of any functions from an algebra with a ?-product of Weyl type. -- Highlights: ? Methods of testing whether a given matrix represents a quantum state. ? The Stratonovich–Weyl correspondence on an arbitrary symplectic manifold. ? Criteria for checking whether a function on a symplectic space is a Wigner function.
Non-classical paths in interference experiments
Rahul Sawant; Joseph Samuel; Aninda Sinha; Supurna Sinha; Urbasi Sinha
2014-08-09T23:59:59.000Z
In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well known text books in quantum mechanics implicitly and/or explicitly use this assumption which is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from non-classical paths in quantum interference experiments which provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these non-classical paths is hard. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.
Cosmological Perturbations of Quantum-Mechanical Origin and Anisotropy of the Microwave Background
L. P. Grishchuk
1993-04-01T23:59:59.000Z
Cosmological perturbations generated quantum-mechanically (as a particular case, during inflation) possess statistical properties of squeezed quantum states. The power spectra of the perturbations are modulated and the angular distribution of the produced temperature fluctuations of the CMBR is quite specific. An exact formula is derived for the angular correlation function of the temperature fluctuations caused by squeezed gravitational waves. The predicted angular pattern can, in principle, be revealed by the COBE-type observations.
How to check quantum mechanics independently (Reply to arXiv:1505.04293)
Yuri I. Ozhigov
2015-06-17T23:59:59.000Z
This is the reply to the paper of Andrei Khrennikov arXiv:1505.04293 in which he expresses dissatisfaction with that the rough data in quantum experiments is not easily available and compares it with the open rough data in genetics. I try to explain why quantum experiments rough data is closed and why it differs radically from the biological. I also tried to answer the more thorny issue: is it possible to check quantum mechanics independently of other humans, e.g. trusting nobody.
Discrete Phase Space: Quantum mechanics and non-singular potential functions
Das, Anadijiban
2015-01-01T23:59:59.000Z
The three-dimensional potential equation, motivated by representations of quantum mechanics, is investigated in four different scenarios: (i) In the usual Euclidean space $\\mathbb{E}_{3}$ where the potential is singular but invariant under the continuous inhomogeneous orthogonal group $\\mathcal{I}O(3)$. The invariance under the translation subgroup is compared to the corresponding unitary transformation in the Schr\\"{o}dinger representation of quantum mechanics. This scenario is well known but serves as a reference point for the other scenarios. (ii) Next, the discrete potential equation as a partial difference equation in a three-dimensional lattice space is studied. In this arena the potential is non-singular but invariance under $\\mathcal{I}O(3)$ is broken. This is the usual picture of lattice theories and numerical approximations. (iii) Next we study the six-dimensional continuous phase space. Here a phase space representation of quantum mechanics is utilized. The resulting potential is singular but posse...
Testing Born's Rule in Quantum Mechanics with a Triple Slit Experiment
Urbasi Sinha; Christophe Couteau; Zachari Medendorp; Immo Söllner; Raymond Laflamme; Rafael Sorkin; Gregor Weihs
2008-11-13T23:59:59.000Z
In Mod. Phys. Lett. A 9, 3119 (1994), one of us (R.D.S) investigated a formulation of quantum mechanics as a generalized measure theory. Quantum mechanics computes probabilities from the absolute squares of complex amplitudes, and the resulting interference violates the (Kolmogorov) sum rule expressing the additivity of probabilities of mutually exclusive events. However, there is a higher order sum rule that quantum mechanics does obey, involving the probabilities of three mutually exclusive possibilities. We could imagine a yet more general theory by assuming that it violates the next higher sum rule. In this paper, we report results from an ongoing experiment that sets out to test the validity of this second sum rule by measuring the interference patterns produced by three slits and all the possible combinations of those slits being open or closed. We use attenuated laser light combined with single photon counting to confirm the particle character of the measured light.
Quantum Mechanical Corrections to Simulated Shock Hugoniot Temperatures
Goldman, N; Reed, E; Fried, L E
2009-07-17T23:59:59.000Z
The authors present a straightforward method for the inclusion of quantum nuclear vibrational effects in molecular dynamics calculations of shock Hugoniot temperatures. Using a grueneisen equation of state and a quasi-harmonic approximation to the vibrational energies, they derive a simple, post-processing method for calculation of the quantum corrected Hugoniot temperatures. They have used our novel technique on ab initio simulations of both shock compressed water and methane. Our results indicate significantly closer agreement with all available experimental temperature data for these two systems. Our formalism and technique can be easily applied to a number of different shock compressed molecular liquids or covalent solids, and has the potential to decrease the large uncertainties inherent in many experimental Hugoniot temperature measurements of these systems.
Qualitative insights on fundamental mechanics
G. N. Mardari
2006-11-10T23:59:59.000Z
The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We show that the main parameters of any fundamental model must be theory-independent. They cannot be predicted, because they cannot have internal causes. However, it is possible to describe them in the language of classical mechanics. We invoke philosophical reasons in favor of a specific model, which treats particles as sources of real waves. Experimental considerations for gravitational, electromagnetic, and quantum phenomena are outlined.
Fractal energy carpets in non-Hermitian Hofstadter quantum mechanics
Chernodub, M N
2015-01-01T23:59:59.000Z
We study the non-Hermitian Hofstadter dynamics of a quantum particle with biased motion on a square lattice in the background of a magnetic field. We show that in quasi-momentum space the energy spectrum is an overlap of infinitely many inequivalent fractals. The energy levels in each fractal are space-filling curves with Hausdorff dimension 2. The band structure of the spectrum is similar to a fractal spider net in contrast to the Hofstadter butterfly for unbiased motion.
Generalized contexts and consistent histories in quantum mechanics
Losada, Marcelo [Instituto de Física Rosario, Pellegrini 250, 2000 Rosario (Argentina); Laura, Roberto, E-mail: rlaura@fceia.unr.edu.ar [Facultad de Ciencias Exactas, Ingeniería y Agrimensura, Pellegrini 250, 2000 Rosario (Argentina); Instituto de Física Rosario, Pellegrini 250, 2000 Rosario (Argentina)
2014-05-15T23:59:59.000Z
We analyze a restriction of the theory of consistent histories by imposing that a valid description of a physical system must include quantum histories which satisfy the consistency conditions for all states. We prove that these conditions are equivalent to imposing the compatibility conditions of our formalism of generalized contexts. Moreover, we show that the theory of consistent histories with the consistency conditions for all states and the formalism of generalized context are equally useful representing expressions which involve properties at different times.
A closed formula for the barrier transmission coefficient in quaternionic quantum mechanics
De Leo, Stefano; Leonardi, Vinicius; Pereira, Kenia [Department of Applied Mathematics, State University of Campinas, SP 13083-970, Campinas (Brazil); Ducati, Gisele [CMCC, Federal University of ABC, SP 09210-170, Santo Andre (Brazil)
2010-11-15T23:59:59.000Z
In this paper, we analyze, by using a matrix approach, the dynamics of a nonrelativistic particle in presence of a quaternionic potential barrier. The matrix method used to solve the quaternionic Schroedinger equation allows us to obtain a closed formula for the transmission coefficient. Up to now, in quaternionic quantum mechanics, almost every discussion on the dynamics of nonrelativistic particle was motivated by or evolved from numerical studies. A closed formula for the transmission coefficient stimulates an analysis of qualitative differences between complex and quaternionic quantum mechanics and by using the stationary phase method, gives the possibility to discuss transmission times.
Andrei P. Kirilyuk
2014-05-14T23:59:59.000Z
The universal symmetry, or conservation, of complexity underlies any law or principle of system dynamics and describes the unceasing transformation of dynamic information into dynamic entropy as the unique way to conserve their sum, the total dynamic complexity. Here we describe the real world structure emergence and dynamics as manifestation of the universal symmetry of complexity of initially homogeneous interaction between two protofields. It provides the unified complex-dynamic, causally complete origin of physically real, 3D space, time, elementary particles, their properties (mass, charge, spin, etc.), quantum, relativistic, and classical behaviour, as well as fundamental interaction forces, including naturally quantized gravitation. The old and new cosmological problems (including "dark" mass and energy) are basically solved for this explicitly emerging, self-tuning world structure characterised by strictly positive (and large) energy-complexity. A general relation is obtained between the numbers of world dimensions and fundamental forces, excluding plausible existence of hidden dimensions. The unified, causally explained quantum, classical, and relativistic properties (and types of behaviour) are generalised to all higher levels of complex world dynamics. The real world structure, dynamics, and evolution are exactly reproduced by the probabilistic dynamical fractal, which is obtained as the truly complete general solution of a problem and the unique structure of the new mathematics of complexity. We outline particular, problem-solving applications of always exact, but irregularly structured symmetry of unreduced dynamic complexity to microworld dynamics, including particle physics, genuine quantum chaos, real nanobiotechnology, and reliable genomics.
Castagnoli, Giuseppe [Via San Bernardo 9/A, I-16030 Pieve Ligure (Genova) (Italy)
2010-11-15T23:59:59.000Z
In classical problem solving, there is, of course, correlation between the selection of the problem on the part of Bob (the problem setter) and that of the solution on the part of Alice (the problem solver). In quantum problem solving, this correlation becomes quantum. This means that Alice contributes to selecting 50% of the information that specifies the problem. As the solution is a function of the problem, this gives to Alice advanced knowledge of 50% of the information that specifies the solution. Both the quadratic and exponential speed-ups are explained by the fact that quantum algorithms start from this advanced knowledge.
Miller, William H.
A novel discrete variable representation for quantum mechanical reactive scattering via the S. Phys. 88, 6233 ( 1988) ] for quantum reactive scattering. (It can also be readily used for quantum. INTRODUCTION The last three to four years have seen a "great leap for- ward" in the ability to carry out
Quantum entanglement in the multiverse
Salvador Robles-Perez; Pedro F. Gonzalez-Diaz
2012-07-26T23:59:59.000Z
In this paper it is shown that the quantum state of a multiverse made up of classically disconnected regions of the space-time, whose dynamical evolution is dominated by a homogeneous and isotropic fluid, is given by a squeezed state. These are typical quantum states that have no classical counterpart and, therefore, they allow us to analyze the violation of classical inequalities as well as the EPR argument in the context of the quantum multiverse. The thermodynamical properties of entanglement are calculated for a composite quantum state of two universes whose states are quantum mechanically correlated. The energy of entanglement between the positive and negative modes of a scalar field, which correspond to the expanding and contracting branches of a phantom universe, respectively, are also computed.
Quantum Mechanics with a Momentum-Space Artificial Magnetic Field
Hannah M. Price; Tomoki Ozawa; Iacopo Carusotto
2014-11-19T23:59:59.000Z
The Berry curvature is a geometrical property of an energy band which acts as a momentum space magnetic field in the effective Hamiltonian describing single-particle quantum dynamics. We show how this perspective may be exploited to study systems directly relevant to ultracold gases and photonics. Given the exchanged roles of momentum and position, we demonstrate that the global topology of momentum space is crucially important. We propose an experiment to study the Harper-Hofstadter Hamiltonian with a harmonic trap that will illustrate the advantages of this approach and that will also constitute the first realization of magnetism on a torus.
Generalized space and linear momentum operators in quantum mechanics
Costa, Bruno G. da, E-mail: bruno.costa@ifsertao-pe.edu.br [Instituto Federal de Educação, Ciência e Tecnologia do Sertão Pernambucano, Campus Petrolina, BR 407, km 08, 56314-520 Petrolina, Pernambuco (Brazil); Instituto de Física, Universidade Federal da Bahia, R. Barão de Jeremoabo s/n, 40170-115 Salvador, Bahia (Brazil); Borges, Ernesto P., E-mail: ernesto@ufba.br [Instituto de Física, Universidade Federal da Bahia, R. Barão de Jeremoabo s/n, 40170-115 Salvador, Bahia (Brazil)
2014-06-15T23:59:59.000Z
We propose a modification of a recently introduced generalized translation operator, by including a q-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator p{sup ^}{sub q}, and its canonically conjugate deformed position operator x{sup ^}{sub q}. A canonical transformation leads the Hamiltonian of a position-dependent mass particle to another Hamiltonian of a particle with constant mass in a conservative force field of a deformed phase space. The equation of motion for the classical phase space may be expressed in terms of the generalized dual q-derivative. A position-dependent mass confined in an infinite square potential well is shown as an instance. Uncertainty and correspondence principles are analyzed.
Liu, Yong-Chun; Luan, Xingsheng; Wong, Chee Wei
2015-01-01T23:59:59.000Z
Ground state cooling of massive mechanical objects remains a difficult task restricted by the unresolved mechanical sidebands. We propose an optomechanically-induced-transparency cooling scheme to achieve ground state cooling of mechanical motion without the resolved sideband condition in a pure optomechanical system with two mechanical modes coupled to the same optical cavity mode. We show that ground state cooling is achievable for sideband resolution $\\omega_{m}/\\kappa$ as low as 0.003. This provides a new route for quantum manipulation of massive macroscopic devices and high-precision measurements.
Mingsheng Ying; Yuan Feng
2007-01-04T23:59:59.000Z
Loop is a powerful program construct in classical computation, but its power is still not exploited fully in quantum computation. The exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop programs. In this paper, we introduce a general scheme of quantum loops and describe its computational process. The notions of termination and almost termination are proposed for quantum loops, and the function computed by a quantum loop is defined. To show their expressive power, quantum loops are applied in describing quantum walks. Necessary and sufficient conditions for termination and almost termination of a general quantum loop on any mixed input state are presented. A quantum loop is said to be (almost) terminating if it (almost) terminates on any input state. We show that a quantum loop is almost terminating if and only if it is uniformly almost terminating. It is observed that a small disturbance either on the unitary transformation in the loop body or on the measurement in the loop guard can make any quantum loop (almost) terminating. Moreover, a representation of the function computed by a quantum loop is given in terms of finite summations of matrices. To illustrate the notions and results obtained in this paper, two simplest classes of quantum loop programs, one qubit quantum loops, and two qubit quantum loops defined by controlled gates, are carefully examined.
Introduction Classical Field Theory
Baer, Christian
Introduction Classical Field Theory Locally Covariant Quantum Field Theory Renormalization Time evolution Conclusions and outlook Locality and Algebraic Structures in Field Theory Klaus Fredenhagen IIÂ¨utsch and Pedro Lauridsen Ribeiro) Klaus Fredenhagen Locality and Algebraic Structures in Field Theory #12
The Radical Pair Mechanism and the Avian Chemical Compass: Quantum Coherence and Entanglement
Zhang, Yiteng; Kais, Sabre
2015-01-01T23:59:59.000Z
We review the spin radical pair mechanism which is a promising explanation of avian navigation. This mechanism is based on the dependence of product yields on (1) the hyperfine interaction involving electron spins and neighboring nuclear spins and (2) the intensity and orientation of the geomagnetic field. One surprising result is that even at ambient conditions quantum entanglement of electron spins can play an important role in avian magnetoreception. This review describes the general scheme of chemical reactions involving radical pairs generated from singlet and triplet precursors; the spin dynamics of the radical pairs; and the magnetic field dependence of product yields caused by the radical pair mechanism. The main part of the review includes a description of the chemical compass in birds. We review: the general properties of the avian compass; the basic scheme of the radical pair mechanism; the reaction kinetics in cryptochrome; quantum coherence and entanglement in the avian compass; and the effects o...
Developing and Researching PhET simulations for Teaching Quantum Mechanics S. B. McKagan,1
Colorado at Boulder, University of
(PhET) Project, known for its interactive computer simulations for teaching and learning physics, now includes 18 simulations on quantum mechanics designed to improve learning of this difficult subject. OurDeveloping and Researching PhET simulations for Teaching Quantum Mechanics S. B. McKagan,1 K. K
Si, Wei
2015-01-01T23:59:59.000Z
We explore an instantaneous decoherence correction (IDC) approach for the decoherence and energy relaxation in the quantum-classical dynamics of charge transport in organic semiconducting crystals. These effects, originating from environmental fluctuations, are essential ingredients of the carrier dynamics. The IDC is carried out by measurement-like operations in the adiabatic representation. While decoherence is inherent in the IDC, energy relaxation is taken into account by considering the detailed balance through the introduction of energy-dependent reweighing factors, which could be either Boltzmann (IDC-BM) or Miller-Abrahams (IDC-MA) type. For a non-diagonal electron-phonon coupling model, it is shown that the IDC tends to enhance diffusion while energy relaxation weakens this enhancement. As expected, both the IDC-BM and IDC-MA achieve a near-equilibrium distribution at finite temperatures in the diffusion process, while the Ehrenfest dynamics renders system tending to infinite temperature limit. The r...
Chemical dynamics in the gas phase: Time-dependent quantum mechanics of chemical reactions
Gray, S.K. [Argonne National Laboratory, IL (United States)
1993-12-01T23:59:59.000Z
A major goal of this research is to obtain an understanding of the molecular reaction dynamics of three and four atom chemical reactions using numerically accurate quantum dynamics. This work involves: (i) the development and/or improvement of accurate quantum mechanical methods for the calculation and analysis of the properties of chemical reactions (e.g., rate constants and product distributions), and (ii) the determination of accurate dynamical results for selected chemical systems, which allow one to compare directly with experiment, determine the reliability of the underlying potential energy surfaces, and test the validity of approximate theories. This research emphasizes the use of recently developed time-dependent quantum mechanical methods, i.e. wave packet methods.
Branch dependence in the "consistent histories" approach to quantum mechanics
Thomas Müller
2006-11-12T23:59:59.000Z
In the consistent histories formalism one specifies a family of histories as an exhaustive set of pairwise exclusive descriptions of the dynamics of a quantum system. We define branching families of histories, which strike a middle ground between the two available mathematically precise definitions of families of histories, viz., product families and Isham's history projector operator formalism. The former are too narrow for applications, and the latter's generality comes at a certain cost, barring an intuitive reading of the ``histories''. Branching families retain the intuitiveness of product families, they allow for the interpretation of a history's weight as a probability, and they allow one to distinguish two kinds of coarse-graining, leading to reconsidering the motivation for the consistency condition.
Philosophy of mind and the problem of free will in the light of quantum mechanics
Henry P. Stapp
2008-05-01T23:59:59.000Z
Defects occasioned by the advent of quantum mechanics are described in detail of recent arguments by John Searle and by Jaegwon Kim pertaining to the question of the complete reducibility to the physical of the apparent capacity of a person's conscious thoughts to affect the behaviour of that person's physically described brain.
Mechanism of tungsten-dependent acetylene hydratase from quantum chemical calculations
Liao, Rongzhen
Mechanism of tungsten-dependent acetylene hydratase from quantum chemical calculations Rong hydratase is a tungsten-dependent enzyme that cata- lyzes the nonredox hydration of acetylene metalloenzyme cluster approach Tungsten is the heaviest metal in biology and plays prominent roles in carbon
Philosophy of Mind and the Problem of FreeWill in the Light of Quantum Mechanics.
Stapp, Henry; Stapp, Henry P
2008-04-01T23:59:59.000Z
Arguments pertaining to the mind-brain connection and to the physical effectiveness of our conscious choices have been presented in two recent books, one by John Searle, the other by Jaegwon Kim. These arguments are examined, and it is argued that the difficulties encountered arise from a defective understanding and application of a pertinent part of contemporary science, namely quantum mechanics.
Kadmensky, S. G., E-mail: kadmensky@phys.vsu.ru; Titova, L. V.; Pen'kov, N. V. [Voronezh State University (Russian Federation)
2006-08-15T23:59:59.000Z
In the framework of quantum-mechanical fission theory, the method of calculation for partial fission width amplitudes and asymptotic behavior of the fissile nucleus wave function with strong channel coupling taken into account has been suggested. The method allows one to solve the calculation problem of angular and energy distribution countation for binary and ternary fission.
WKB and MAF Quantization Rules for Spatially Confined Quantum Mechanical Systems
A. Sinha; R. Roychoudhury
1999-10-15T23:59:59.000Z
A formalism is developed to obtain the energy eigenvalues of spatially confined quantum mechanical systems in the framework of The usual WKB and MAF methods. The technique is applied to three different cases,viz one dimensional Harmonic Oscillators,Quartic Oscillators and a boxed-in charged particle in electric field.
Paul M. Alsing
2015-02-04T23:59:59.000Z
In this paper we extend the investigation of Adami and Ver Steeg [Class. Quantum Grav. \\textbf{31}, 075015 (2014)] to treat the process of black hole particle emission effectively as the analogous quantum optical process of parametric down conversion (PDC) with a dynamical (depleted vs. non-depleted) `pump' source mode which models the evaporating black hole (BH) energy degree of freedom. We investigate both the short time (non-depleted pump) and long time (depleted pump) regimes of the quantum state and its impact on the Holevo channel capacity for communicating information from the far past to the far future in the presence of Hawking radiation. The new feature introduced in this work is the coupling of the emitted Hawking radiation modes through the common black hole `source pump' mode which phenomenologically represents a quantized energy degree of freedom of the gravitational field. This (zero-dimensional) model serves as a simplified arena to explore BH particle production/evaporation and back-action effects under an explicitly unitary evolution which enforces quantized energy/particle conservation. Within our analogous quantum optical model we examine the entanglement between two emitted particle/anti-particle and anti-particle/particle pairs coupled via the black hole (BH) evaporating `pump' source. We also analytically and dynamically verify the `Page information time' for our model which refers to the conventionally held belief that the information in the BH radiation becomes significant after the black hole has evaporated half its initial energy into the outgoing radiation. Lastly, we investigate the effect of BH particle production/evaporation on two modes in the exterior region of the BH event horizon that are initially maximally entangled, when one mode falls inward and interacts with the black hole, and the other remains forever outside and non-interacting.
Bidirectional coherent classical communication
Aram W. Harrow; Debbie W. Leung
2005-05-12T23:59:59.000Z
A unitary interaction coupling two parties enables quantum communication in both the forward and backward directions. Each communication capacity can be thought of as a tradeoff between the achievable rates of specific types of forward and backward communication. Our first result shows that for any bipartite unitary gate, coherent classical communication is no more difficult than classical communication -- they have the same achievable rate regions. Previously this result was known only for the unidirectional capacities (i.e., the boundaries of the tradeoff). We then relate the tradeoff curve for two-way coherent communication to the tradeoff for two-way quantum communication and the tradeoff for coherent communiation in one direction and quantum communication in the other.
Superradiant Quantum Heat Engine
Ali Ü. C. Hardal; Özgür E. Müstecapl?oglu
2015-03-12T23:59:59.000Z
Quantum physics has revolutionized the classical disciplines of mechanics, statistical physics, and electrodynamics. It modernized our society with many advances such as lasers and transistors. One branch of scientific knowledge however seems untouched: thermodynamics. Major motivation behind thermodynamics is to develop efficient heat engines. Technology has a trend to miniaturize engines, reaching to the quantum regimes. Inevitably, development of quantum heat engines (QHEs) requires investigations of thermodynamical principles from quantum mechanical perspective, and motivates the emerging field of quantum thermodynamics. Studies of QHEs debate on whether quantum coherence can be used as a resource. We explore an alternative that quantum coherence can be a catalyst. We propose a QHE which consists of a photon gas inside an optical cavity as the working fluid and quantum coherent atomic clusters as the fuel. Utilizing the superradiance, where a cluster can radiate quadratically faster than a single atom, we show that the work capability of the QHE becomes proportional to the square of the number of the atoms. In addition to practical value of cranking up a QHE, our results reveal a fundamental difference of a quantum fuel from its classical counterpart.
Thomas Durt
2010-03-14T23:59:59.000Z
According to the so-called Quantum Darwinist approach, the emergence of "classical islands" from a quantum background is assumed to obey a (selection) principle of maximal information. We illustrate this idea by considering the coupling of two oscillators (modes). As our approach suggests that the classical limit could have emerged throughout a long and progressive Evolution mechanism, it is likely that primitive living organisms behave in a "more quantum", "less classical" way than more evolved ones. This brings us to seriously consider the possibility to measure departures from classicality exhibited by biological systems. We describe an experimental proposal the aimed at revealing the presence of entanglement in the biophotonic radiation emitted by biological sources.
Three approaches to classical thermal field theory
Gozzi, E., E-mail: gozzi@ts.infn.it [Department of Physics, University of Trieste, Strada Costiera 11, Miramare - Grignano, 34151 Trieste (Italy); INFN, Sezione di Trieste (Italy); Penco, R., E-mail: rpenco@syr.edu [Department of Physics, Syracuse University, Syracuse, NY 13244-1130 (United States)
2011-04-15T23:59:59.000Z
Research Highlights: > Classical thermal field theory admits three equivalent path integral formulations. > Classical Feynman rules can be derived for all three formulations. > Quantum Feynman rules reduce to classical ones at high temperatures. > Classical Feynman rules become much simpler when superfields are introduced. - Abstract: In this paper we study three different functional approaches to classical thermal field theory, which turn out to be the classical counterparts of three well-known different formulations of quantum thermal field theory: the closed-time path (CTP) formalism, the thermofield dynamics (TFD) and the Matsubara approach.
Aerts, Diederik
Published as: Aerts, D., 1998, "The entity and modern physics: the creation-discovery view of reality", in Interpreting Bodies: Classical and Quantum Objects in Modern Physics, ed. Castellani, E., Princeton University Press, Princeton. The entity and modern physics: the creation-discovery- view
Chaos, Fractal and Quantum Poincare Recurrences in Diamagnetic Kepler Problem
A. Ugulava; L. Chotorlishvili; T. Kereselidze; V. Skrinnikov
2006-08-01T23:59:59.000Z
The statistics of quantum Poincare recurrences in Hilbert space for diamagnetic hydrogen atom in strong magnetic field has been investigated. It has been shown that quantities characterizing classical chaos are in a good agreement with the ones that are used to describe quantum chaos. The equality of classical and quantum Poincare recurrences has been shown. It has been proved that one of the signs of the emergence of quantum chaos is the irreversible transition from a pure quantum mechanical state to the mixed one.
Quantum mechanics in phase space: First order comparison between the Wigner and the Fermi function
G. Benenti; G. Strini
2009-09-08T23:59:59.000Z
The Fermi g_F(x,p) function provides a phase space description of quantum mechanics conceptually different from that based on the the Wigner function W(x,p). In this paper, we show that for a peaked wave packet the g_F(x,p)=0 curve approximately corresponds to a phase space contour level of the Wigner function and provides a satisfactory description of the wave packet's size and shape. Our results show that the Fermi function is an interesting tool to investigate quantum fluctuations in the semiclassical regime.
Graphs whose normalized Laplacian matrices are separable as density matrices in quantum mechanics
Chai Wah Wu
2014-07-23T23:59:59.000Z
Recently normalized Laplacian matrices of graphs are studied as density matrices in quantum mechanics. Separability and entanglement of density matrices are important properties as they determine the nonclassical behavior in quantum systems. In this note we look at the graphs whose normalized Laplacian matrices are separable or entangled. In particular, we show that the number of such graphs is related to the number of 0-1 matrices that are line sum symmetric and to the number of graphs with at least one vertex of degree 1.
Fast Quantum Methods for Optimization
Sergio Boixo; Gerardo Ortiz; Rolando Somma
2014-09-08T23:59:59.000Z
Discrete combinatorial optimization consists in finding the optimal configuration that minimizes a given discrete objective function. An interpretation of such a function as the energy of a classical system allows us to reduce the optimization problem into the preparation of a low-temperature thermal state of the system. Motivated by the quantum annealing method, we present three strategies to prepare the low-temperature state that exploit quantum mechanics in remarkable ways. We focus on implementations without uncontrolled errors induced by the environment. This allows us to rigorously prove a quantum advantage. The first strategy uses a classical-to-quantum mapping, where the equilibrium properties of a classical system in $d$ spatial dimensions can be determined from the ground state properties of a quantum system also in $d$ spatial dimensions. We show how such a ground state can be prepared by means of quantum annealing, including quantum adiabatic evolutions. This mapping also allows us to unveil some fundamental relations between simulated and quantum annealing. The second strategy builds upon the first one and introduces a technique called spectral gap amplification to reduce the time required to prepare the same quantum state adiabatically. If implemented on a quantum device that exploits quantum coherence, this strategy leads to a quadratic improvement in complexity over the well-known bound of the classical simulated annealing method. The third strategy is not purely adiabatic; instead, it exploits diabatic processes between the low-energy states of the corresponding quantum system. For some problems it results in an exponential speedup (in the oracle model) over the best classical algorithms.
Conditional quantum distinguishability and pure quantum communication
Tian-Hai Zeng
2005-09-14T23:59:59.000Z
I design a simple way of distinguishing non-orthogonal quantum states with perfect reliability using only quantum control-not gates in one condition. In this way, we can implement pure quantum communication in directly sending classical information, Ekert quantum cryptography and quantum teleportation without the help of classical communications channel.
Agarwal, Animesh
2015-01-01T23:59:59.000Z
Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however computationally this technique is very demanding. The abovementioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One possible solution to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this ...
The Radical Pair Mechanism and the Avian Chemical Compass: Quantum Coherence and Entanglement
Yiteng Zhang; Gennady P. Berman; Sabre Kais
2015-03-23T23:59:59.000Z
We review the spin radical pair mechanism which is a promising explanation of avian navigation. This mechanism is based on the dependence of product yields on (1) the hyperfine interaction involving electron spins and neighboring nuclear spins and (2) the intensity and orientation of the geomagnetic field. One surprising result is that even at ambient conditions quantum entanglement of electron spins can play an important role in avian magnetoreception. This review describes the general scheme of chemical reactions involving radical pairs generated from singlet and triplet precursors; the spin dynamics of the radical pairs; and the magnetic field dependence of product yields caused by the radical pair mechanism. The main part of the review includes a description of the chemical compass in birds. We review: the general properties of the avian compass; the basic scheme of the radical pair mechanism; the reaction kinetics in cryptochrome; quantum coherence and entanglement in the avian compass; and the effects of noise. We believe that the "quantum avian compass" can play an important role in avian navigation and can also provide the foundation for a new generation of sensitive and selective magnetic-sensing nano-devices.
Vacuum fluctuations the clue for a realistic interpretation of quantum mechanics
Emilio Santos
2012-08-22T23:59:59.000Z
Arguments are gived for the plausibility that quantum mechanics is a stochastic theory and that many quantum phenomena derive from the existence of a real noise consisting of vacuum fluctuations of all fundamental fields existing in nature. Planck's constant appears as the parameter fixing the scale of the fluctuations. Hints for an intuitive explanation are offered for some typical quantum features, like the uncertainty principle or the particle behaviour of fields. It is proposed that the recent discovery of dark energy in the universe is an argument for the reality of the vacuum fluctuations. A study is made of the compatibility of the model with the results of performed tests of Bell\\'{}s inequalities.
Orthogonal-state-based cryptography in quantum mechanics and local post-quantum theories
S. Aravinda; Anindita Banerjee; Anirban Pathak; R. Srikanth
2015-03-16T23:59:59.000Z
We introduce the concept of cryptographic reduction, in analogy with a similar concept in computational complexity theory. In this framework, class $A$ of crypto-protocols reduces to protocol class $B$ in a scenario $X$, if for every instance $a$ of $A$, there is an instance $b$ of $B$ and a secure transformation $X$ that reproduces $a$ given $b$, such that the security of $b$ guarantees the security of $a$. Here we employ this reductive framework to study the relationship between security in quantum key distribution (QKD) and quantum secure direct communication (QSDC). We show that replacing the streaming of independent qubits in a QKD scheme by block encoding and transmission (permuting the order of particles block by block) of qubits, we can construct a QSDC scheme. This forms the basis for the \\textit{block reduction} from a QSDC class of protocols to a QKD class of protocols, whereby if the latter is secure, then so is the former. Conversely, given a secure QSDC protocol, we can of course construct a secure QKD scheme by transmitting a random key as the direct message. Then the QKD class of protocols is secure, assuming the security of the QSDC class which it is built from. We refer to this method of deduction of security for this class of QKD protocols, as \\textit{key reduction}. Finally, we propose an orthogonal-state-based deterministic key distribution (KD) protocol which is secure in some local post-quantum theories. Its security arises neither from geographic splitting of a code state nor from Heisenberg uncertainty, but from post-measurement disturbance.
Process, System, Causality, and Quantum Mechanics, A Psychoanalysis of Animal Faith
H. Pierre Noyes; Tom Etter
1998-08-06T23:59:59.000Z
We shall argue in this paper that a central piece of modern physics does not really belong to physics at all but to elementary probability theory. Given a joint probability distribution J on a set of random variables containing x and y, define a link between x and y to be the condition x=y on J. Define the {\\it state} D of a link x=y as the joint probability distribution matrix on x and y without the link. The two core laws of quantum mechanics are the Born probability rule, and the unitary dynamical law whose best known form is the Schrodinger's equation. Von Neumann formulated these two laws in the language of Hilbert space as prob(P) = trace(PD) and D'T = TD respectively, where P is a projection, D and D' are (von Neumann) density matrices, and T is a unitary transformation. We'll see that if we regard link states as density matrices, the algebraic forms of these two core laws occur as completely general theorems about links. When we extend probability theory by allowing cases to count negatively, we find that the Hilbert space framework of quantum mechanics proper emerges from the assumption that all D's are symmetrical in rows and columns. On the other hand, Markovian systems emerge when we assume that one of every linked variable pair has a uniform probability distribution. By representing quantum and Markovian structure in this way, we see clearly both how they differ, and also how they can coexist in natural harmony with each other, as they must in quantum measurement, which we'll examine in some detail. Looking beyond quantum mechanics, we see how both structures have their special places in a much larger continuum of formal systems that we have yet to look for in nature.
Effective quantum equations for the semiclassical description of the Hydrogen atom
Guillermo Chacón-Acosta; Héctor H. Hernández
2012-03-22T23:59:59.000Z
We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of the system as a system of infinite many classical equations for expectation values of configuration variables, their moments and quantum dispersions. It also provides a semiclassical description of the orbits and the evolution of observables and spreadings and their back-reaction on the evolution.
An algebraic theory of infinite classical lattices II: Axiomatic theory
Don Ridgeway
2005-10-08T23:59:59.000Z
We apply the algebraic theory of infinite classical lattices from Part I to write an axiomatic theory of measurements, based on Mackey's axioms for quantum mechanics. The axioms give a complete theory of measurements in the sense of Haag and Kastler, taking the traditional form of a logic of propositions provided with a classical spectral theorem. The results are expressed in terms of probability distributions of individual measurements. As applications, we give a separation theorem for states by the set of observables and discuss its relationship to the equivalence of ensembles in the thermodynamic-limit program. We also introduce a weak equivalence of states based on the theory.
M. Heller; W. Sasin
2000-01-24T23:59:59.000Z
The groupoid approach to noncommutative unification of general relativity with quantum mechanics is compared with the canonical gravity quantization. It is shown that by restricting the corresponding noncommutative algebra to its (commutative) subalgebra, which determines the space-time slicing, an algebraic counterpart of superspace (space of 3-metrics) can be obtained. It turns out that when this space-time slicing emerges the universe is already in its commutative regime. We explore the consequences of this result.
A quantum mechanical scheme to reduce radiation damage in electron microscopy
Okamoto, Hiroshi; Fink, Hans-Werner
2015-01-01T23:59:59.000Z
We show that radiation damage to unstained biological specimens is not an intractable problem in electron microscopy. When a structural hypothesis of a specimen is available, quantum mechanical principles allow us to verify the hypothesis with a very low electron dose. Realization of such a concept requires precise control of the electron wave front. Based on a diffractive electron optical implementation, we demonstrate the feasibility of this new method by both experimental and numerical investigations.
A quantum mechanical scheme to reduce radiation damage in electron microscopy
Hiroshi Okamoto; Tatiana Latychevskaia; Hans-Werner Fink
2015-06-24T23:59:59.000Z
We show that radiation damage to unstained biological specimens is not an intractable problem in electron microscopy. When a structural hypothesis of a specimen is available, quantum mechanical principles allow us to verify the hypothesis with a very low electron dose. Realization of such a concept requires precise control of the electron wave front. Based on a diffractive electron optical implementation, we demonstrate the feasibility of this new method by both experimental and numerical investigations.
Quantum corrected non-thermal radiation spectrum from the tunnelling mechanism
Subenoy Chakraborty; Subhajit Saha; Christian Corda
2015-05-28T23:59:59.000Z
Tunnelling mechanism is today considered a popular and widely used method in describing Hawking radiation. However, in relation to black hole (BH) emission, this mechanism is mostly used to obtain the Hawking temperature by comparing the probability of emission of an outgoing particle with the Boltzmann factor. On the other hand, Banerjee and Majhi reformulated the tunnelling framework deriving a black body spectrum through the density matrix for the outgoing modes for both the Bose-Einstein distribution and the Fermi-Dirac distribution. In contrast, Parikh and Wilczek introduced a correction term performing an exact calculation of the action for a tunnelling spherically symmetric particle and, as a result, the probability of emission of an outgoing particle corresponds to a non-strictly thermal radiation spectrum. Recently, one of us (C. Corda) introduced a BH effective state and was able to obtain a non-strictly black body spectrum from the tunnelling mechanism corresponding to the probability of emission of an outgoing particle found by Parikh and Wilczek. The present work introduces the quantum corrected effective temperature and the corresponding quantum corrected effective metric is written using Hawking's periodicity arguments. Thus, we obtain further corrections to the non-strictly thermal BH radiation spectrum as the final distributions take into account both the BH dynamical geometry during the emission of the particle and the quantum corrections to the semiclassical Hawking temperature.
Axel Friedenauer; Hector Schmitz; Jan Tibor Glückert; Diego Porras; Tobias Schätz
2008-02-27T23:59:59.000Z
To gain deeper insight into the dynamics of complex quantum systems we need a quantum leap in computer simulations. We can not translate quantum behaviour arising with superposition states or entanglement efficiently into the classical language of conventional computers. The final solution to this problem is a universal quantum computer [1], suggested in 1982 and envisioned to become functional within the next decade(s); a shortcut was proposed via simulating the quantum behaviour of interest in a different quantum system, where all parameters and interactions can be controlled and the outcome detected sufficiently well. Here we study the feasibility of a quantum simulator based on trapped ions [2]. We experimentally simulate the adiabatic evolution of the smallest non-trivial spin system from the paramagnetic into the (anti-)ferromagnetic order with a quantum magnetisation for two spins of 98%, controlling and manipulating all relevant parameters of the Hamiltonian independently via electromagnetic fields. We prove that the observed transition is not driven by thermal fluctuations, but of quantum mechanical origin, the source of quantum fluctuations in quantum phase transitions [3]. We observe a final superposition state of the two degenerate spin configurations for the ferromagnetic and the antiferromagnetic order, respectively. These correspond to deterministically entangled states achieved with a fidelity up to 88%. Our work demonstrates a building block for simulating quantum spin-Hamiltonians with trapped ions. The method has potential for scaling to a higher number of coupled spins [2].
Suzuki, Yasumitsu; Maitra, Neepa T; Gross, E K U
2015-01-01T23:59:59.000Z
We study the exact nuclear time-dependent potential energy surface (TDPES) for laser-induced electron localization with a view to eventually developing a mixed quantum-classical dynamics method for strong-field processes. The TDPES is defined within the framework of the exact factorization [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] and contains the exact effect of the couplings to the electronic subsystem and to any external fields within a scalar potential. We compare its features with those of the quasistatic potential energy surfaces (QSPES) often used to analyse strong-field processes. We show that the gauge-independent component of the TDPES has a mean-field-like character very close to the density-weighted average of the QSPESs. Oscillations in this component are smoothened out by the gauge-dependent component, and both components are needed to yield the correct force on the nuclei. Once the localization begins to set in, the gradient of the exact TDPES tracks one ...
Emission mechanisms of bulk GaN and InGaN quantum wells prepared by lateral epitaxial overgrowth
Bowers, John
Emission mechanisms of bulk GaN and InGaN quantum wells prepared by lateral epitaxial overgrowth S for publication 5 January 1999 The emission mechanisms of bulk GaN and InGaN quantum wells QWs were studied suggest that TDs simply reduce the net volume of light-emitting area. This effect is less pronounced in InGaN
Quantum realism and quantum surrealism
Mateus Araújo
2014-08-29T23:59:59.000Z
In this thesis we explore the questions of what should be considered a "classical" theory, and which aspects of quantum theory cannot be captured by any theory that respects our intuition of classicality. This exploration is divided in two parts: in the first we review classical results of the literature, such as the Kochen-Specker theorem, von Neumann's theorem, Gleason's theorem, as well as more recent ideas, such as the distinction between $\\psi$-ontic and $\\psi$-epistemic ontological models, Spekkens' definition of contextuality, Hardy's ontological excess baggage theorem and the PBR theorem. The second part is concerned with pinning down what should be the "correct" definition of contextuality. We settle down on the definition advocated by Abramsky and Branderburger, motivated by the Fine theorem, and show the connection of this definition with the work of George Boole. This definition allows us to unify the notions of locality and noncontextuality, and use largely the same tools to characterize how quantum mechanics violates these notions of classicality. Exploring this formalism, we find a new family of noncontextuality inequalities. We conclude by reviewing the notion of state-independent contextuality.
Real-Time Transport in Open Quantum Systems From $\\mathcal{PT}$-Symmetric Quantum Mechanics
Justin E. Elenewski; Hanning Chen
2014-08-07T23:59:59.000Z
Nanoscale electronic transport is of intense technological interest, with applications ranging from semiconducting devices and molecular junctions to charge migration in biological systems. Most explicit theoretical approaches treat transport using a combination of density functional theory (DFT) and non-equilibrium Green's functions. This is a static formalism, with dynamic response properties accommodated only through complicated extensions. To circumvent this limitation, the carrier density may be propagated using real-time time-dependent DFT (RT-TDDFT), with boundary conditions corresponding to an open quantum system. Complex absorbing potentials can emulate outgoing particles at the simulation boundary, although these do not account for introduction of charge density. It is demonstrated that the desired positive particle flux is afforded by a class of $\\mathcal{PT}$-symmetric generating potentials that are characterized by anisotropic transmission resonances. These potentials add density every time a particle traverses the cell boundary, and may be used to engineer a continuous pulse train for incident packets. This is a first step toward developing a complete transport formalism unique to RT-TDDFT.
Nikolai N. Bogolubov, Jr.; Anatoliy K. Prykarpatsky
2008-10-21T23:59:59.000Z
The main fundamental principles characterizing the vacuum field structure are formulated and the modeling of the related vacuum medium and charged point particle dynamics by means of devised field theoretic tools are analyzed. The work is devoted to studying the vacuum structure, special relativity, electrodynamics of interacting charged point particles and quantum mechanics, and is a continuation of \\cite{BPT,BRT1}. Based on the vacuum field theory no-geometry approach, the Lagrangian and Hamiltonian reformulation of some alternative classical electrodynamics models is devised. The Dirac type quantization procedure, based on the canonical Hamiltonian formulation, is developed for some alternative electrodynamics models. Within an approach developed a possibility of the combined description both of electrodynamics and gravity is analyzed.
Zurek, Wojciech H [Los Alamos National Laboratory
2008-01-01T23:59:59.000Z
Quantum Darwinism - proliferation, in the environment, of multiple records of selected states of the system (its information-theoretic progeny) - explains how quantum fragility of individual state can lead to classical robustness of their multitude.
Semenov, Alexander; Babikov, Dmitri, E-mail: dmitri.babikov@mu.edu [Chemistry Department, Wehr Chemistry Building, Marquette University, Milwaukee, Wisconsin 53201-1881 (United States)] [Chemistry Department, Wehr Chemistry Building, Marquette University, Milwaukee, Wisconsin 53201-1881 (United States)
2014-01-28T23:59:59.000Z
The mixed quantum/classical theory (MQCT) for rotationally inelastic scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is benchmarked against the full quantum calculations for two molecular systems: He + H{sub 2} and Na + N{sub 2}. This allows testing new method in the cases of light and reasonably heavy reduced masses, for small and large rotational quanta, in a broad range of collision energies and rotational excitations. The resultant collision cross sections vary through ten-orders of magnitude range of values. Both inelastic and elastic channels are considered, as well as differential (over scattering angle) cross sections. In many cases results of the mixed quantum/classical method are hard to distinguish from the full quantum results. In less favorable cases (light masses, larger quanta, and small collision energies) some deviations are observed but, even in the worst cases, they are within 25% or so. The method is computationally cheap and particularly accurate at higher energies, heavier masses, and larger densities of states. At these conditions MQCT represents a useful alternative to the standard full-quantum scattering theory.
O. Arcizet; P. -F. Cohadon; T. Briant; M. Pinard; A. Heidmann; J. -M. Mackowski; C. Michel; L. Pinard; O. Francais; L. Rousseau
2006-05-19T23:59:59.000Z
We experimentally demonstrate the high-sensitivity optical monitoring of a micro-mechanical resonator and its cooling by active control. Coating a low-loss mirror upon the resonator, we have built an optomechanical sensor based on a very high-finesse cavity (30000). We have measured the thermal noise of the resonator with a quantum-limited sensitivity at the 10^-19 m/rootHz level, and cooled the resonator down to 5K by a cold-damping technique. Applications of our setup range from quantum optics experiments to the experimental demonstration of the quantum ground state of a macroscopic mechanical resonator.
Computer simulations of local anesthetic mechanisms: Quantum chemical investigation of procaine
Smith, Jeremy C [ORNL; Bondar, A.N. [University of California, Irvine; Suhai, Sandor [German Cancer Research Center, Heidelberg; Frangopol, P.T. [Institute of Atomic Physics, Bucharest Roumania
2007-02-01T23:59:59.000Z
A description at the atomic level of detail of the interaction between local anesthetics, lipid membranes and membrane proteins, is essential for understanding the mechanism of local anesthesia. The importance of performing computer simulations to decipher the mechanism of local anesthesia is discussed here in the context of the current status of understanding of the local anesthetics action. As a first step towards accurate simulations of the interaction between local anesthetics, proteins, lipid and water molecules, here we use quantum mechanical methods to assess the charge distribution and structural properties of procaine in the presence and in the absence of water molecules. The calculations indicate that, in the absence of hydrogen-bonding water molecules, protonated procaine strongly prefers a compact structure enabled by intramolecular hydrogen bonding. In the presence of water molecules the torsional energy pro?le of procaine is modified, and hydrogen bonding to water molecules is favored relative to intra-molecular hydrogen bonding.
Non-commutative Quantum Mechanics in Three Dimensions and Rotational Symmetry
Debabrata Sinha; Biswajit Chakraborty; Frederik G Scholtz
2011-08-12T23:59:59.000Z
We generalize the formulation of non-commutative quantum mechanics to three dimensional non-commutative space. Particular attention is paid to the identification of the quantum Hilbert space in which the physical states of the system are to be represented, the construction of the representation of the rotation group on this space, the deformation of the Leibnitz rule accompanying this representation and the implied necessity of deforming the co-product to restore the rotation symmetry automorphism. This also implies the breaking of rotational invariance on the level of the Schroedinger action and equation as well as the Hamiltonian, even for rotational invariant potentials. For rotational invariant potentials the symmetry breaking results purely from the deformation in the sense that the commutator of the Hamiltonian and angular momentum is proportional to the deformation.
On the Irreps of the N-Extended Supersymmetric Quantum Mechanics and Their Fusion Graphs
Francesco Toppan
2006-12-27T23:59:59.000Z
In this talk we review the classification of the irreducible representations of the algebra of the N-extended one-dimensional supersymmetric quantum mechanics presented in hep-th/0511274. We answer some issues raised in hep-th/0611060, proving the agreement of the results here contained with those in hep-th/0511274. We further show that the fusion algebra of the 1D N-extended supersymmetric vacua introduced in hep-th/0511274 admits a graphical presentation. The N=2 graphs are here explicitly presented for the first time.
Quantum mechanics forbids an initial or final singularity in a closed FRW universe
T. R. Mongan
1999-03-07T23:59:59.000Z
The existence of singularities in a closed FRW universe depends on the assumption that general relativity is valid for distances less than the Planck length. However, stationary state wave functions of the Schrodinger equation for a closed radiation-dominated FRW universe derived by Elbaz et al (General Relativity and Gravitation 29, 481, 1997) are zero at zero radius of curvature. Thus, even if general relativity is assumed valid at distances less than the Planck length, quantum mechanics seems to forbid singularities in a closed FRW universe.
Sunandan Gangopadhyay; Anirban Saha; Swarup Saha
2014-09-11T23:59:59.000Z
The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized following the prescription in \\cite{ncgw1}. Standard algebraic techniques are then employed to solve the Hamiltonian of the system. The solutions, in both cases, show signatures of the coordinate noncommutativity. In the harmonic oscillator case, this signature plays a key role in altering the resonance point and the oscillation frequency of the system.
Quantum Structures of the Hydrogen Atom
J. Jeknic-Dugic; M. Dugic; A. Francom; M. Arsenijevic
2014-05-28T23:59:59.000Z
Modern quantum theory introduces quantum structures (decompositions into subsystems) as a new discourse that is not fully comparable with the classical-physics counterpart. To this end, so-called Entanglement Relativity appears as a corollary of the universally valid quantum mechanics that can provide for a deeper and more elaborate description of the composite quantum systems. In this paper we employ this new concept to describe the hydrogen atom. We offer a consistent picture of the hydrogen atom as an open quantum system that naturally answers the following important questions: (a) how do the so called "quantum jumps" in atomic excitation and de-excitation occur? and (b) why does the classically and seemingly artificial "center-of-mass + relative degrees of freedom" structure appear as the primarily operable form in most of the experimental reality of atoms?
Quantum Computing Computer Scientists
Yanofsky, Noson S.
of Vector Spaces 3 The Leap From Classical to Quantum 3.1 Classical Deterministic Systems 3.2 ClassicalQuantum Computing for Computer Scientists Noson S. Yanofsky and Mirco A. Mannucci #12;© May 2007 Noson S. Yanofsky Mirco A. Mannucci #12;Quantum Computing for Computer Scientists Noson S. Yanofsky
Statistical mechanics of Coulomb gases as quantum theory on Riemann surfaces
Gulden, T.; Janas, M.; Koroteev, P.; Kamenev, A., E-mail: kamenev@physics.umn.edu [University of Minnesota, Department of Physics (United States)
2013-09-15T23:59:59.000Z
Statistical mechanics of a 1D multivalent Coulomb gas can be mapped onto non-Hermitian quantum mechanics. We use this example to develop the instanton calculus on Riemann surfaces. Borrowing from the formalism developed in the context of the Seiberg-Witten duality, we treat momentum and coordinate as complex variables. Constant-energy manifolds are given by Riemann surfaces of genus g {>=} 1. The actions along principal cycles on these surfaces obey the ordinary differential equation in the moduli space of the Riemann surface known as the Picard-Fuchs equation. We derive and solve the Picard-Fuchs equations for Coulomb gases of various charge content. Analysis of monodromies of these solutions around their singular points yields semiclassical spectra as well as instanton effects such as the Bloch bandwidth. Both are shown to be in perfect agreement with numerical simulations.
Diederik Aerts; Massimiliano Sassoli de Bianchi
2015-04-19T23:59:59.000Z
The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states, explaining the interference effects, and the entanglement correlations, in terms of the different orientations that a state-vector can take within the generalized Bloch sphere. We also introduce a tensorial determination of the generators of SU(N), particularly suitable to describe multipartite systems, from the viewpoint of the sub-entities. We then use it to show that non-product states admit a general description in which the sub-entities can always remain in well-defined states, even when they are entangled. Therefore, the completed version of quantum mechanics provided by the extended Bloch representation, in which the density operators are also representative of pure states, allows to solve not only the well-known measurement problem, but also the lesser-known entanglement problem. This because we no longer need to give up the general physical principle saying that a composite entity exists, and therefore is in a pure state, if and only if its components also exist, and therefore are in well-defined pure states.
Vacuum Fluctuation (1): the Same Basis of the Relativity and the Quantum Mechanics
Xing-Hao Ye
2007-11-09T23:59:59.000Z
The aim of this paper is to reveal the deep relationship between matter and vacuum, and to seek for the same physical basis of the relativity and the quantum mechanics. In doing this, three postulates of vacuum fluctuation are proposed first, the basic premises of the relativity and the quantum mechanics including the velocity limit, the energy-frequency relation and the de Broglie wavelength expression of any matter particles are deduced then. As applications, the idea is used to analyze the Compton effect and the electron-positron annihilation. It is found that the calculation becomes simple, and the physical meaning gets clear. The simplicity comes from the power of the three postulates. To illustrate this, the basic conclusions of the special theory of relativity such as the relations of mass-velocity, mass-energy, energy-momentum, time dilation and length contraction are further deduced. In addition, the significance of the investigation of vacuum fluctuation in the unification of the physical theories is pointed out.
Ha, Taekjip
gases, this behavior is perplexing. But, a simple classical statistical mechanics model of a chain for given N and M. Call the result (N,M). (b) Using Stirling's approximation in the form ln(N!) N ln(N) - N and extent R, in the regime Na >> R. Write down the expression for the free energy of the chain (in
Quantum correlations; quantum probability approach
W. A. Majewski
2015-05-21T23:59:59.000Z
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical and quantum), mathematical structures, and their consequences. These include the canonical form of classical correlation functionals, general definitions of separable (entangled) states, definition and analysis of quantumness of correlations, description of entanglement of formation, and PPT states. This work is intended both for physicists interested not only in collection of results but also in the mathematical methods justifying them, and mathematicians looking for an application of quantum probability to concrete new problems of quantum theory.
G. Manfredi
2005-05-01T23:59:59.000Z
Traditional plasma physics has mainly focused on regimes characterized by high temperatures and low densities, for which quantum-mechanical effects have virtually no impact. However, recent technological advances (particularly on miniaturized semiconductor devices and nanoscale objects) have made it possible to envisage practical applications of plasma physics where the quantum nature of the particles plays a crucial role. Here, I shall review different approaches to the modeling of quantum effects in electrostatic collisionless plasmas. The full kinetic model is provided by the Wigner equation, which is the quantum analog of the Vlasov equation. The Wigner formalism is particularly attractive, as it recasts quantum mechanics in the familiar classical phase space, although this comes at the cost of dealing with negative distribution functions. Equivalently, the Wigner model can be expressed in terms of $N$ one-particle Schr{\\"o}dinger equations, coupled by Poisson's equation: this is the Hartree formalism, which is related to the `multi-stream' approach of classical plasma physics. In order to reduce the complexity of the above approaches, it is possible to develop a quantum fluid model by taking velocity-space moments of the Wigner equation. Finally, certain regimes at large excitation energies can be described by semiclassical kinetic models (Vlasov-Poisson), provided that the initial ground-state equilibrium is treated quantum-mechanically. The above models are validated and compared both in the linear and nonlinear regimes.
P. Falsaperla; G. Fonte; G. Salesi
2007-01-16T23:59:59.000Z
We show that it is possible to associate univocally with each given solution of the time-dependent Schroedinger equation a particular phase flow ("quantum flow") of a non-autonomous dynamical system. This fact allows us to introduce a definition of chaos in quantum dynamics (quantum chaos), which is based on the classical theory of chaos in dynamical systems. In such a way we can introduce quantities which may be appelled "Quantum Lyapunov Exponents". Our approach applies to a non-relativistic quantum-mechanical system of n charged particles; in the present work numerical calculations are performed only for the hydrogen atom. In the computation of the trajectories we first neglect the spin contribution to chaos, then we consider the spin effects in quantum chaos. We show how the quantum Lyapunov exponents can be evaluated and give several numerical results which describe some properties found in the present approach. Although the system is very simple and the classical counterpart is regular, the most non-stationary solutions of the corresponding Schroeodinger equation are "chaotic" according to our definition.
Molecular Quantum Mechanics 2010: From Methylene to DNA and Beyond Conference Support
None
2013-05-15T23:59:59.000Z
This grant was $12500 for partial support of an international conference, Molecular Quantum Mechanics 2010, which was held on the campus of the University of California, Berkeley, from 24 to 29 May 2010. The conference involved more than 250 participants. The conference schedule ran from as early as 8:00 AM to as late as 10:30 PM at night, in order to accommodate six historical lectures, 16 plenary lectures, 42 invited talks and two very strong poster sessions containing 143 contributed posters. Since 1989, the Molecular Quantum Mechanics (MQM) series of international conferences has show- cased the frontiers of research in quantum chemistry with a strong focus on basic theory and algorithms, as well as highlights of topical applications. Both were strongly in evidence at MQM 2010. At the same time as embracing the future, the MQM conferences also honour the lifetime contributions of some of the most prominent scientists in the field of theoretical and computational quantum chemistry. MQM 2010 recognised the work of Prof. Henry F. ‘Fritz’ Schaefer of the Center for Computational Chemistry at the University of Georgia, who was previously on the faculty at Berkeley The travel of invited speakers was partially covered by sponsorships from Dell Computer, Hewlett-Packard, Journal of Chemical Theory and Computation, Virginia Tech College of Science, Molecular Physics, Q-Chem Inc and the American Institute of Physics. By contrast, the conference grant from the Department of Energy was used to provide fellowships and scholarships to enable graduate students and postdoctoral fellows to attend the meeting, and thereby broaden the participation of young scientists at a meeting where in the past most of the attendees have been more senior faculty researchers. We believe that we were very successful in this regard: 118 students and postdocs attended out of the total of 256 participants. In detail, the DOE sponsorship money was partially used for dormitory scholarships that covered the cost of shared accommodation for students and postdocs at Berkeley dormitories. This covered the $200-$305 cost of a shared room for the 5-day duration of the conference. The only condition of these scholarships was that the awardee must present a poster at the meeting. Approximately $7565 was spent for these dormitory scholarships. The remaining expenditures of $4800 was used for 12 merit scholarships which were awarded to students whose poster presentations were judged the best at the conference. This amount covered a significant part of their travel and registration fees.
Quantum thermodynamic cooling cycle
Jose P. Palao; Ronnie Kosloff; Jeffrey M. Gordon
2001-06-08T23:59:59.000Z
The quantum-mechanical and thermodynamic properties of a 3-level molecular cooling cycle are derived. An inadequacy of earlier models is rectified in accounting for the spontaneous emission and absorption associated with the coupling to the coherent driving field via an environmental reservoir. This additional coupling need not be dissipative, and can provide a thermal driving force - the quantum analog of classical absorption chillers. The dependence of the maximum attainable cooling rate on temperature, at ultra-low temperatures, is determined and shown to respect the recently-established fundamental bound based on the second and third laws of thermodynamics.
Quantum thermodynamic cooling cycle
Palao, J P; Gordon, J M; Palao, Jose P.; Kosloff, Ronnie; Gordon, Jeffrey M.
2001-01-01T23:59:59.000Z
The quantum-mechanical and thermodynamic properties of a 3-level molecular cooling cycle are derived. An inadequacy of earlier models is rectified in accounting for the spontaneous emission and absorption associated with the coupling to the coherent driving field via an environmental reservoir. This additional coupling need not be dissipative, and can provide a thermal driving force - the quantum analog of classical absorption chillers. The dependence of the maximum attainable cooling rate on temperature, at ultra-low temperatures, is determined and shown to respect the recently-established fundamental bound based on the second and third laws of thermodynamics.
Roumen Tsekov
2011-04-15T23:59:59.000Z
A new approach to thermo-quantum diffusion is proposed and a nonlinear quantum Smoluchowski equation is derived, which describes classical diffusion in the field of the Bohm quantum potential. A nonlinear thermo-quantum expression for the diffusion front is obtained, being a quantum generalization of the classical Einstein law. The quantum diffusion at zero temperature is also described and a new dependence of the position dispersion on time is derived. A stochastic Bohm-Langevin equation is also proposed.
Cosmology with a Decaying Vacuum Energy Parametrization Derived from Quantum Mechanics
Szydlowski, Marek; Urbanowski, Krzysztof
2015-01-01T23:59:59.000Z
Within the quantum mechanical treatment of the decay problem one finds that at late times $t$ the survival probability of an unstable state cannot have the form of an exponentially decreasing function of time $t$ but it has an inverse power-like form. This is a general property of unstable states following from basic principles of quantum theory. The consequence of this property is that in the case of false vacuum states the cosmological constant becomes dependent on time: $\\Lambda - \\Lambda_{\\text{bare}}\\equiv \\Lambda(t) -\\Lambda_{\\text{bare}} \\sim 1/t^{2}$. We construct the cosmological model with decaying vacuum energy density and matter for solving the cosmological constant problem and the coincidence problem. We show the equivalence of the proposed decaying false vacuum cosmology with the $\\Lambda(t)$ cosmologies (the $\\Lambda(t)$CDM models). The cosmological implications of the model of decaying vacuum energy (dark energy) are discussed. We constrain the parameters of the model with decaying vacuum usin...
Numerical investigations of Supersymmetric Yang-Mills Quantum Mechanics with 4 supercharges
Zbigniew Ambrozinski; Piotr Korcyl
2014-12-01T23:59:59.000Z
We report on our non-perturbative investigations of supersymmetric Yang-Mills quantum mechanics with 4 supercharges. We employ two independent numerical methods. First of them is the cut Fock space method whose numerical implementation was recently generalized to include the SU(N) gauge group. It allowed us to calculate for the first time the spectrum of the model with SU(3) symmetry in all fermionic sectors. Independently, we implemented the Rational Hybrid Monte Carlo algorithm and reproduced the accessible part of the low-energy spectrum of the model with SU(2) gauge symmetry. We argue that by simulating at imaginary chemical potential one can get access to observables defined in sectors of Hilbert space with a given quark number.
Lee, Chien-Wei; Hwu, Jenn-Gwo [Graduate Institute of Electronics Engineering/ Department of Electrical Engineering, National Taiwan University, Taipei, 10617, Taiwan (China)] [Graduate Institute of Electronics Engineering/ Department of Electrical Engineering, National Taiwan University, Taipei, 10617, Taiwan (China)
2013-10-15T23:59:59.000Z
We derive a statistical physics model of two-dimensional electron gas (2DEG) and propose an accurate approximation method for calculating the quantum-mechanical effects of metal-oxide-semiconductor (MOS) structure in accumulation and strong inversion regions. We use an exponential surface potential approximation in solving the quantization energy levels and derive the function of density of states in 2D to 3D transition region by applying uncertainty principle and Schrödinger equation in k-space. The simulation results show that our approximation method and theory of density of states solve the two major problems of previous researches: the non-negligible error caused by the linear potential approximation and the inconsistency of density of states and carrier distribution in 2D to 3D transition region.
Benioff, P.A.
1981-01-01T23:59:59.000Z
Work done before on the construction of quantum mechanical Hamiltonian models of Turing machines and general descrete processes is extended here to include processes which erase their own histories. The models consist of three phases, the forward process phase in which a map T is iterated and a history of iterations is generated, a copy phase which is activated if and only if T reaches a fix point, and an erase phase which erases the iteration history, undoes the iterations of T and recovers the initial state except for the copy system. A ballast system is used to stop the evolution at the desired state. The general model so constructed is applied to Turing machines. The main changes are that the system undergoing the evolution corresponding to T iterations becomes three systems corresponding to the internal machine, the computation tape, and computation head. Also the copy phase becomes more complex since it is desired that this correspond also to a copying Turing machine.
Orbital HP-Clouds for Solving Schr?dinger Equation inQuantum Mechanics
Chen, J; Hu, W; Puso, M
2006-10-19T23:59:59.000Z
Solving Schroedinger equation in quantum mechanics presents a challenging task in numerical methods due to the high order behavior and high dimension characteristics in the wave functions, in addition to the highly coupled nature between wave functions. This work introduces orbital and polynomial enrichment functions to the partition of unity for solution of Schroedinger equation under the framework of HP-Clouds. An intrinsic enrichment of orbital function and extrinsic enrichment of monomial functions are proposed. Due to the employment of higher order basis functions, a higher order stabilized conforming nodal integration is developed. The proposed methods are implemented using the density functional theory for solution of Schroedinger equation. Analysis of several single and multi-electron/nucleus structures demonstrates the effectiveness of the proposed method.
A quantum mechanical model for the relationship between stock price and stock ownership
Liviu-Adrian Cotfas
2012-09-05T23:59:59.000Z
The trade of a fixed stock can be regarded as the basic process that measures its momentary price. The stock price is exactly known only at the time of sale when the stock is between traders, that is, only in the case when the owner is unknown. We show that the stock price can be better described by a function indicating at any moment of time the probabilities for the possible values of price if a transaction takes place. This more general description contains partial information on the stock price, but it also contains partial information on the stock owner. By following the analogy with quantum mechanics, we assume that the time evolution of the function describing the stock price can be described by a Schrodinger type equation.
A quantitative quantum-chemical analysis tool for the distribution of mechanical force in molecules
Stauch, Tim; Dreuw, Andreas, E-mail: dreuw@uni-heidelberg.de [Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg (Germany)] [Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg (Germany)
2014-04-07T23:59:59.000Z
The promising field of mechanochemistry suffers from a general lack of understanding of the distribution and propagation of force in a stretched molecule, which limits its applicability up to the present day. In this article, we introduce the JEDI (Judgement of Energy DIstribution) analysis, which is the first quantum chemical method that provides a quantitative understanding of the distribution of mechanical stress energy among all degrees of freedom in a molecule. The method is carried out on the basis of static or dynamic calculations under the influence of an external force and makes use of a Hessian matrix in redundant internal coordinates (bond lengths, bond angles, and dihedral angles), so that all relevant degrees of freedom of a molecule are included and mechanochemical processes can be interpreted in a chemically intuitive way. The JEDI method is characterized by its modest computational effort, with the calculation of the Hessian being the rate-determining step, and delivers, except for the harmonic approximation, exact ab initio results. We apply the JEDI analysis to several example molecules in both static quantum chemical calculations and Born-Oppenheimer Molecular Dynamics simulations in which molecules are subject to an external force, thus studying not only the distribution and the propagation of strain in mechanically deformed systems, but also gaining valuable insights into the mechanochemically induced isomerization of trans-3,4-dimethylcyclobutene to trans,trans-2,4-hexadiene. The JEDI analysis can potentially be used in the discussion of sonochemical reactions, molecular motors, mechanophores, and photoswitches as well as in the development of molecular force probes.
Applications of Feedback Control in Quantum Systems
Kurt Jacobs
2006-05-02T23:59:59.000Z
We give an introduction to feedback control in quantum systems, as well as an overview of the variety of applications which have been explored to date. This introductory review is aimed primarily at control theorists unfamiliar with quantum mechanics, but should also be useful to quantum physicists interested in applications of feedback control. We explain how feedback in quantum systems differs from that in traditional classical systems, and how in certain cases the results from modern optimal control theory can be applied directly to quantum systems. In addition to noise reduction and stabilization, an important application of feedback in quantum systems is adaptive measurement, and we discuss the various applications of adaptive measurements. We finish by describing specific examples of the application of feedback control to cooling and state-preparation in nano-electro-mechanical systems and single trapped atoms.
Rossi, Mariana; Paesani, Francesco; Bowman, Joel; Ceriotti, Michele
2014-01-01T23:59:59.000Z
Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer (LMon) model and a mixed quantum-classical (MQC) model as representatives of the first family of methods, and centroid molecular dynamics (CMD) and thermostatted ring polymer molecular dynamics (TRPMD) as examples of the latter. We use as benchmarks D$_2$O doped with HOD and pure H$_2$O at three distinc...
Goddard III, William A.
resistance of "end-contacted" metal electrode-graphene and metal electrode-carbon nanotube (CNT) interfaces for five metals, Ti, Pd, Pt, Cu, and Au, based on the first-principles quantum mechanical (QM) density atoms) is 107 k for Ti, 142 k for Pd, 149 k for Pt, 253 k for Cu, and 187 k for Au. This can be compared
Simons, Jack
Quantum Mechanical Energy-Based Screening of Combinatorially Generated Library of Tautomers. Tau of GdanÂ´sk, 80-952 GdanÂ´sk, Poland, Chemical Sciences Division, Fundamental Sciences Directorate, Pacific of finding low-energy tautomers of a molecule. The procedure consists of (i) combinatorial generation
Hamiltonian Ratchets Holger Schanz,1 Marc-Felix Otto,1 Roland Ketzmerick,1 and Thomas Dittrich2 1 Max. Transport in quantum Hamiltonian ratchets arises by the same mechanism as long as uncertainty allows one of molecular motors, the study of ratchets [1] has widened to a general exploration of "self
Diagrammar in classical scalar field theory
Cattaruzza, E., E-mail: Enrico.Cattaruzza@gmail.com [Department of Physics (Miramare Campus), University of Trieste, Strada Costiera 11, Miramare-Grignano 34014, Trieste (Italy); Gozzi, E., E-mail: gozzi@ts.infn.it [Department of Physics (Miramare Campus), University of Trieste, Strada Costiera 11, Miramare-Grignano 34014, Trieste (Italy); INFN, Sezione di Trieste (Italy); Francisco Neto, A., E-mail: antfrannet@gmail.com [Departamento de Engenharia de Producao, Administracao e Economia, Escola de Minas, Campus Morro do Cruzeiro, UFOP, 35400-000 Ouro Preto MG (Brazil)
2011-09-15T23:59:59.000Z
In this paper we analyze perturbatively a g{phi}{sup 4}classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost 'identical' formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem. - Highlights: > We provide the Feynman diagrams of perturbation theory for a classical field theory. > We give a super-formalism which links the quantum diagrams to the classical ones. > We check perturbatively the fluctuation-dissipation theorem.
Quantum search without entanglement
Lloyd, S
2000-01-01T23:59:59.000Z
Entanglement of quantum variables is usually thought to be a prerequisite for obtaining quantum speed-ups of information processing tasks such as searching databases. This paper presents methods for quantum search that give a speed-up over classical methods, but that do not require entanglement. These methods rely instead on interference to provide a speed-up. Search without entanglement comes at a cost: although they outperform analogous classical devices, the quantum devices that perform the search are not universal quantum computers and require exponentially greater overhead than a quantum computer that operates using entanglement. Quantum search without entanglement is compared to classical search using waves.
Quantum search without entanglement
Seth Lloyd
1999-03-16T23:59:59.000Z
Entanglement of quantum variables is usually thought to be a prerequisite for obtaining quantum speed-ups of information processing tasks such as searching databases. This paper presents methods for quantum search that give a speed-up over classical methods, but that do not require entanglement. These methods rely instead on interference to provide a speed-up. Search without entanglement comes at a cost: although they outperform analogous classical devices, the quantum devices that perform the search are not universal quantum computers and require exponentially greater overhead than a quantum computer that operates using entanglement. Quantum search without entanglement is compared to classical search using waves.
Calculation of the electron two slit experiment using a quantum mechanical variational principle
Harrison, Alan K. [Los Alamos National Laboratory
2012-04-17T23:59:59.000Z
A nonlocal relativistic variational principle (VP) has recently been proposed as an alternative to the Dirac wave equation of standard quantum mechanics. We apply that principle to the electron two-slit experiment. The detection system is modelled as a screen made of atoms, any one of which can be excited by the incident electron, but we avoid restricting the detection mechanism further. The VP is shown to predict that, at the time the electron reaches the screen, its wavefunction will be localized to the neighborhood of a single atom, resulting in a position-type measurement. In an ensemble of such experiments ('identically prepared' except that the initial phase of the wavefunction - the hidden variable in the VP formulation - is sampled over the expected uniform distribution), the distribution of measured positions will reproduce the interference pattern predicted by the Dirac equation. We also demonstrate that with a detection system designed fundamentally to detect the electron's transverse wavelength rather than its position, the VP predicts that one such mode will be detected, that is, a wavelength measurement will result. Finally, it is shown that these results are unchanged in the 'delayed choice' variant of the experiment.
Statistical Mechanical Models and Topological Color Codes
H. Bombin; M. A. Martin-Delgado
2007-11-03T23:59:59.000Z
We find that the overlapping of a topological quantum color code state, representing a quantum memory, with a factorized state of qubits can be written as the partition function of a 3-body classical Ising model on triangular or Union Jack lattices. This mapping allows us to test that different computational capabilities of color codes correspond to qualitatively different universality classes of their associated classical spin models. By generalizing these statistical mechanical models for arbitrary inhomogeneous and complex couplings, it is possible to study a measurement-based quantum computation with a color code state and we find that their classical simulatability remains an open problem. We complement the meaurement-based computation with the construction of a cluster state that yields the topological color code and this also gives the possibility to represent statistical models with external magnetic fields.
R. Tsekov
2012-12-05T23:59:59.000Z
The Brownian motion of a light quantum particle in a heavy classical gas is theoretically described and a new expression for the friction coefficient is obtained for arbitrary temperature. At zero temperature it equals to the de Broglie momentum of the mean free path divided by the mean free path. Alternatively, the corresponding mobility of the quantum particle in the classical gas is equal to the square of the mean free path divided by the Planck constant. The Brownian motion of a quantum particle in a quantum environment is also discussed.
Entanglement purification with two-way classical communication
Alan W. Leung; Peter W. Shor
2007-02-21T23:59:59.000Z
We present an improved protocol for entanglement purification of bipartite mixed states. The protocol requires two-way classical communication and hence implies an improved lower bound on the quantum capacity with two-way classical communication of the quantum depolarizing channel.
Quantum-enhanced deliberation of learning agents using trapped ions
Vedran Dunjko; Nicolai Friis; Hans J. Briegel
2015-01-31T23:59:59.000Z
A scheme that successfully employs quantum mechanics in the design of autonomous learning agents has recently been reported in the context of the projective simulation (PS) model for artificial intelligence. In that approach, the key feature of a PS agent, a specific type of memory which is explored via random walks, was shown to be amenable to quantization. In particular, classical random walks were substituted by Szegedy-type quantum walks, allowing for a speed-up. In this work we propose how such classical and quantum agents can be implemented in systems of trapped ions. We employ a generic construction by which the classical agents are `upgraded' to their quantum counterparts by nested coherent controlization, and we outline how this construction can be realized in ion traps. Our results provide a flexible modular architecture for the design of PS agents. Furthermore, we present numerical simulations of simple PS agents which analyze the robustness of our proposal under certain noise models.
Quantum metrology and its application in biology
Michael A. Taylor; Warwick P. Bowen
2014-09-03T23:59:59.000Z
Quantum metrology provides a route to overcome practical limits in sensing devices. It holds particular relevance in biology, where sensitivity and resolution constraints restrict applications both in fundamental biophysics and in medicine. Here, we review quantum metrology from this biological context. The understanding of quantum mechanics developed over the past century has already enabled important applications in biology, including positron emission tomography (PET) with entangled photons, magnetic resonance imaging (MRI) using nuclear magnetic resonance, and bio-magnetic imaging with superconducting quantum interference devices (SQUIDs). With the birth of quantum information science came the realization that an even greater range of applications arise from the ability to not just understand, but to engineer coherence and correlations in systems at the quantum level. In quantum metrology, quantum coherence and quantum correlations are engineered to enable new approaches to sensing. This review focusses specifically on optical quantum metrology, where states of light that exhibit non-classical photon correlations are used to overcome practical and fundamental constraints, such as the shot-noise and diffraction limits. Recent experiments have demonstrated quantum enhanced sensing of biological systems, and established the potential for quantum metrology in biophysical research. These experiments have achieved capabilities that may be of significant practical benefit, including enhanced sensitivity and resolution, immunity to imaging artifacts, and characterisation of the biological response to light at the single-photon level. New quantum measurement techniques offer even greater promise, raising the prospect for improved multi-photon microscopy and magnetic imaging, among many other possible applications.
Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
Dionysios Mylonas; Peter Schupp; Richard J. Szabo
2014-10-24T23:59:59.000Z
We analyse the symmetries underlying nonassociative deformations of geometry in non-geometric R-flux compactifications which arise via T-duality from closed strings with constant geometric fluxes. Starting from the non-abelian Lie algebra of translations and Bopp shifts in phase space, together with a suitable cochain twist, we construct the quasi-Hopf algebra of symmetries that deforms the algebra of functions and the exterior differential calculus in the phase space description of nonassociative R-space. In this setting nonassociativity is characterised by the associator 3-cocycle which controls non-coassociativity of the quasi-Hopf algebra. We use abelian 2-cocycle twists to construct maps between the dynamical nonassociative star product and a family of associative star products parametrized by constant momentum surfaces in phase space. We define a suitable integration on these nonassociative spaces and find that the usual cyclicity of associative noncommutative deformations is replaced by weaker notions of 2-cyclicity and 3-cyclicity. Using this star product quantization on phase space together with 3-cyclicity, we formulate a consistent version of nonassociative quantum mechanics, in which we calculate the expectation values of area and volume operators, and find coarse-graining of the string background due to the R-flux.
Selective Atomic Heating in Plasmas: Implications for Quantum Theory
Phillips, Jonathan
2008-01-01T23:59:59.000Z
A new model of quantum mechanics, Classical Quantum Mechanics, is based on the (nearly heretical) postulate that electrons are physical objects that obey classical physical laws. Indeed, ionization energies, excitation energies etc. are computed based on picturing electrons as bubbles of charge that symmetrically surround a nucleus. Hence, for example, simple algebraic expressions based on Newtonian force balances are used to predict ionization energies and stable excitation states with remarkable precision. One of the most startling predictions of the model is that there are stable sizes of the hydrogen atom electron (bubble diameter) that are smaller (called hydrinos) than that calculated for the standard ground state. Experimental evidence in support of this novel physical/classical version of quantum is alleged to be found in the existence of super heated hydrogen atoms reported by many teams in a variety of plasmas. It is postulated that the energy required for creating super heated H aoms comes from the...
Richards-Kortum, Rebecca
204 Mechanical Engineering and Materials Science 205 of Architecture. The campus-wide Rice Quantum. Degree Requirements for B.A., B.S.M.E. in Mechanical Engineering or B.A., B.S.M.S. in Materials Science and Engineering The B.A. program in either mechanical engineering or materials science
Generalized quantum secret sharing
Singh, Sudhir Kumar; Srikanth, R. [Department of Electrical Engineering, University of California, Los Angeles, California 90095 (United States); Optics Group, Raman Research Institute, Bangalore-560080 (India)
2005-01-01T23:59:59.000Z
We explore a generalization of quantum secret sharing (QSS) in which classical shares play a complementary role to quantum shares, exploring further consequences of an idea first studied by Nascimento, Mueller-Quade, and Imai [Phys. Rev. A 64, 042311 (2001)]. We examine three ways, termed inflation, compression, and twin thresholding, by which the proportion of classical shares can be augmented. This has the important application that it reduces quantum (information processing) players by replacing them with their classical counterparts, thereby making quantum secret sharing considerably easier and less expensive to implement in a practical setting. In compression, a QSS scheme is turned into an equivalent scheme with fewer quantum players, compensated for by suitable classical shares. In inflation, a QSS scheme is enlarged by adding only classical shares and players. In a twin-threshold scheme, we invoke two separate thresholds for classical and quantum shares based on the idea of information dilution.
Tunnel determinants from spectral zeta functions. Instanton effects in quantum mechanics
Izquierdo, A. Alonso [Departamento de Matematica Aplicada and IUFFyM, Universidad de Salamanca (Spain); Guilarte, J. Mateos [Departamento de Fisica Fundamental and IUFFyM, Universidad de Salamanca (Spain)
2014-07-23T23:59:59.000Z
In this paper we develop an spectral zeta function regularization procedure on the determinants of instanton fluctuation operators that describe the semi-classical order of tunnel effects between degenerate vacua.
A quantum measure of the multiverse
Alexander Vilenkin
2013-12-11T23:59:59.000Z
It has been recently suggested that probabilities of different events in the multiverse are given by the frequencies at which these events are encountered along the worldline of a geodesic observer (the "watcher"). Here I discuss an extension of this probability measure to quantum theory. The proposed extension is gauge-invariant, as is the classical version of this measure. Observations of the watcher are described by a reduced density matrix, and the frequencies of events can be found using the decoherent histories formalism of Quantum Mechanics (adapted to open systems). The quantum watcher measure makes predictions in agreement with the standard Born rule of QM.
A quantum measure of the multiverse
Vilenkin, Alexander
2013-01-01T23:59:59.000Z
It has been recently suggested that probabilities of different events in the multiverse are given by the frequencies at which these events are encountered along the worldline of a geodesic observer (the "watcher"). Here I discuss an extension of this probability measure to quantum theory. The proposed extension is gauge-invariant, as is the classical version of this measure. Observations of the watcher are described by a reduced density matrix, and the frequencies of events can be found using the decoherent histories formalism of Quantum Mechanics (adapted to open systems). The quantum watcher measure makes predictions in agreement with the standard Born rule of QM.