QUANTUM CHAOS, CLASSICAL RANDOMNESS, AND BOHMIAN MECHANICS
Goldstein, Sheldon
QUANTUM CHAOS, CLASSICAL RANDOMNESS, AND BOHMIAN MECHANICS Detlef DË? urr* ,+ , Sheldon Goldstein of quantum theory, Bohmian mechanics, in which ``quantum chaos'' also arises solely from the dynamical law. Moreover, this occurs in a manner far simpler than in the classical case. KEY WORDS: Quantum chaos; quantum
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.
A Quantum Approach to Classical Statistical Mechanics
Rolando D. Somma; Cristian D. Batista; Gerardo Ortiz
2006-10-11T23:59:59.000Z
We present a new approach to study the thermodynamic properties of $d$-dimensional classical systems by reducing the problem to the computation of ground state properties of a $d$-dimensional quantum model. This classical-to-quantum mapping allows us to deal with standard optimization methods, such as simulated and quantum annealing, on an equal basis. Consequently, we extend the quantum annealing method to simulate classical systems at finite temperatures. Using the adiabatic theorem of quantum mechanics, we derive the rates to assure convergence to the optimal thermodynamic state. For simulated and quantum annealing, we obtain the asymptotic rates of $T(t) \\approx (p N) /(k_B \\log t)$ and $\\gamma(t) \\approx (Nt)^{-\\bar{c}/N}$, for the temperature and magnetic field, respectively. Other annealing strategies, as well as their potential speed-up, are also discussed.
Aalok Pandya
2008-09-08T23:59:59.000Z
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert space has been discussed for the chosen Quantum states. Since the theory of classical gravity is basically geometric in nature and Quantum Mechanics is in no way devoid of geometry, the explorations pertaining to more and more geometry in Quantum Mechanics could prove to be valuable for larger objectives such as understanding of gravity.
Aalok Pandya
2009-01-19T23:59:59.000Z
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of probability in Quantum Mechanics and its interpretations. We give yet another interpretation to the notion of Faraday lines and loops as the locus of probability flow. Also, the possibilities of visualization of spectra of area operators by means of classical geometric forms and conventional Quantum Mechanics are explored.
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.
The Born Rule in Quantum and Classical Mechanics
Paul Brumer; Jiangbin Gong
2006-04-24T23:59:59.000Z
Considerable effort has been devoted to deriving the Born rule (e.g. that $|\\psi(x)|^2 dx$ is the probability of finding a system, described by $\\psi$, between $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert space formulation of {\\it classical} mechanics as well. These results provide new insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.
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.
General classical and quantum-mechanical description of magnetic resonance
Alexander J. Silenko
2015-08-04T23:59:59.000Z
A general theoretical description of the magnetic resonance is given. General formulas describing a behavior of all components of the polarization vector at the magnetic resonance are derived in the case of an arbitrary initial polarization. The equations obtained are exact on condition that the nonresonance rotating field is neglected. The spin dynamics is also calculated at frequencies far from resonance without neglecting the above-mentioned field. A quantum-mechanical analysis of the spin evolution at the magnetic resonance is fulfilled and the full agreement between the classical and quantum-mechanical approaches is proven. Distinguishing features of magnetic and quasimagnetic resonances for nuclei and particles moving in accelerators and storage rings which include resonances caused by the electric dipole moment are considered.
General classical and quantum-mechanical description of magnetic resonance
Silenko, Alexander J
2015-01-01T23:59:59.000Z
A general theoretical description of the magnetic resonance is given. General formulas describing a behavior of all components of the polarization vector at the magnetic resonance are derived in the case of an arbitrary initial polarization. The equations obtained are exact on condition that the nonresonance rotating field is neglected. The spin dynamics is also calculated at frequencies far from resonance without neglecting the above-mentioned field. A quantum-mechanical analysis of the spin evolution at the magnetic resonance is fulfilled and the full agreement between the classical and quantum-mechanical approaches is proven. Distinguishing features of magnetic and quasimagnetic resonances for nuclei and particles moving in accelerators and storage rings which include resonances caused by the electric dipole moment are considered.
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.
Fractional Classical Mechanics
Nick Laskin
2013-02-03T23:59:59.000Z
Fractional classical mechanics has been introduced and developed as a classical counterpart of the fractional quantum mechanics. Lagrange, Hamilton and Hamilton-Jacobi frameworks have been implemented for the fractional classical mechanics. The Lagrangian of fractional classical mechanics has been introduced, and equation of motion has been obtained. Fractional oscillator model has been launched and solved in 1D case. A new equation for the period of oscillations of fractional classical oscillator has been found. The interplay between the energy dependency of the period of classical oscillations and the non-equidistant distribution of the energy levels for fractional quantum oscillator has been discussed. We discuss as well, the relationships between new equations of fractional classical mechanics and the well-known fundamental equations of classical mechanics.
Adrian Faigon
2007-11-01T23:59:59.000Z
Mechanics can be founded on a principle relating the uncertainty delta-q in the trajectory of an observable particle to its motion relative to the observer. From this principle, p.delta-q=const., p being the q-conjugated momentum, mechanical laws are derived and the meaning of the Lagrangian and Hamiltonian functions are discussed. The connection between the presented principle and Hamilton's Least Action Principle is examined. Wave mechanics and Schrodinger equation appear without additional assumptions by choosing the representation for delta-q in the case the motion is not trajectory describable. The Cramer-Rao inequality serves that purpose. For a particle hidden from direct observation, the position uncertainty determined by the enclosing boundaries leads to thermodynamics in a straightforward extension of the presented formalism. The introduction of uncertainty in classical mechanics formulation enables the translation of mechanical laws into the wide ranging conceptual framework of information theory. The boundaries between classical mechanics, thermodynamics and quantum mechanics are defined in terms of informational changes associated with the system evolution. As a direct application of the proposed formulation upper bounds for the rate of information transfer are derived.
Quantum-mechanical aspects of classically chaotic driven systems
Milonni, P.W.; Ackerhalt, J.R.; Goggin, M.E.
1987-01-01T23:59:59.000Z
This paper treats atoms and molecules in laser fields as periodically driven quantum systems. The paper concludes by determining that stochastic excitation is possible in quantum systems with quasiperiodic driving. 17 refs. (JDH)
O. Chavoya-Aceves
2004-09-25T23:59:59.000Z
The Hamilton-Jacobi method is generalized, both, in classical and relativistic mechanics. The implications in quantum mechanics are considered in the case of Klein-Gordon equation. We find that the wave functions of Klein-Gordon theory can be considered as describing the motion of an ensemble of particles that move under the action of the electromagnetic field alone, without quantum potentials, hidden uninterpreted variables, or zero point fields. The number of particles is not locally conserved.
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.
Quantum Chaos and Statistical Mechanics
Mark Srednicki
1994-06-14T23:59:59.000Z
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
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
On the Mean-Field and Classical Limits of Quantum Mechanics
François Golse; Clément Mouhot; Thierry Paul
2015-08-10T23:59:59.000Z
The main result in this paper is a new inequality bearing on solutions of the $N$-body linear Schr\\"{o}dinger equation and of the mean field Hartree equation. This inequality implies that the mean field limit of the quantum mechanics of $N$ identical particles is uniform in the classical limit and provides a quantitative estimate of the quality of the approximation. This result applies to the case of $C^{1,1}$ interaction potentials. The quantity measuring the approximation of the $N$-body quantum dynamics by its mean field limit is analogous to the Monge-Kantorovich (or Wasserstein) distance with exponent $2$. The inequality satisfied by this quantity is reminiscent of the work of Dobrushin on the mean field limit in classical mechanics [Func. Anal. Appl. 13 (1979), 115-123]. Our approach of this problem is based on a direct analysis of the $N$-particle Liouville equation, and avoids using techniques based on the BBGKY hierarchy or on second quantization.
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.
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.
QUICK QUANTUM MECHANICS ---Introduction ---
Jackson, Andrew D.
QUICK QUANTUM MECHANICS --- Introduction --- The following notes are intended to be a supplement to your study of Liboff's ``Introductory Quantum Mechanics.'' They are not an alternative! My purpose here of Classical Mechanics After Newton found his equations of motion, physicists knew they would have to wait
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.
C. L. Herzenberg
2007-01-13T23:59:59.000Z
This article provides a popular, largely non-technical explanation of how large objects can behave classically while smaller objects behave quantum mechanically, based on the effect of the presence of cosmic expansion velocities in extended objects. This article is intended to provide a more accessible presentation of concepts introduced in earlier papers that address this long-standing enigma in physics.
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.
Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula
Michel Vittot
2004-06-07T23:59:59.000Z
We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of observables. We give a bound for the perturbation in order to solve this inversion. And apply this result to a particular case of the control theory, as a first example, and to the ``quantum adiabatic transformation'', as another example.
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.
The Quantum-Classical Transition in Nonlinear Dynamical Systems
Salman Habib; Kurt Jacobs; Hideo Mabuchi; Robert Ryne; Kosuke Shizume; Bala Sundaram
2000-10-26T23:59:59.000Z
Viewed as approximations to quantum mechanics, classical evolutions can violate the positive-semidefiniteness of the density matrix. The nature of this violation suggests a classification of dynamical systems based on classical-quantum correspondence; we show that this can be used to identify when environmental interaction (decoherence) will be unsuccessful in inducing the quantum-classical transition. In particular, the late-time Wigner function can become positive without any corresponding approach to classical dynamics. In the light of these results, we emphasize key issues relevant for experiments studying the quantum-classical transition.
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.
Classical and quantum chaos in atomic systems
Delande, D.; Buchleitner, A. [Universite Pierre et Marie Curie, Paris (France)
1994-12-31T23:59:59.000Z
Atomic systems played a major role in the birth and growth of quantum mechanics. One central idea was to relate the well-known classical motion of the electron of a hydrogen atom--an ellipsis around the nucleus--to the experimentally observed quantization of the energy levels. This is the aim of the Bohr and Bohr-Sommerfeld models. These simple semiclassical models were unable to make any reliable prediction on the energy spectrum of the next simplest atom, helium. Because of the great success of quantum mechanics, the problem of correspondence between the classical and the quantal dynamics has not received much attention in the last 60 years. The fundamental question is (Gutzwiller, 1990). How can classical mechanics be understood as a limiting case within quantum mechanics? For systems with time-independent one-dimensional dynamics like the harmonic oscillator and the hydrogen atom, the correspondence is well understood. The restriction to such simple cases creates the erroneous impression that the classical behavior of simple systems is entirely comprehensible and easily described. During the last 20 years it has been recognized that this in not true and that a complex behavior can be obtained from simple equations of motion. This usually happens when the motion is chaotic, that is, unpredictable on a long time scale although perfectly deterministic (Henon, 1983). A major problem is that of understanding how the regular or chaotic behavior of the classical system is manifest in its quantum properties, especially in the semiclassical limit. 53 refs., 15 figs., 1 tab.
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.
Physicalism versus quantum mechanics
Stapp, Henry P; Theoretical Physics Group; Physics Division
2009-01-01T23:59:59.000Z
Foundations of Quantum Mechanics. (Princeton UniversityMind, Matter, and Quantum Mechanics, (Springer, Berlin & NewMindful Universe: Quantum Mechanics and the Participating
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.
"Classical-ish": Negotiating the boundary between classical and quantum particles
Dreyfus, Benjamin W; Gupta, Ayush; Elby, Andrew
2015-01-01T23:59:59.000Z
Quantum mechanics can seem like a departure from everyday experience of the physical world, but constructivist theories assert that learners build new ideas from their existing ones. To explore how students can navigate this tension, we examine video of a focus group completing a tutorial about the "particle in a box." In reasoning about the properties of a quantum particle, the students bring in elements of a classical particle ontology, evidenced by students' language and gestures. This reasoning, however, is modulated by metacognitive moments when the group explicitly considers whether classical intuitions apply to the quantum system. The students find some cases where they can usefully apply classical ideas to quantum physics, and others where they explicitly contrast classical and quantum mechanics. Negotiating this boundary with metacognitive awareness is part of the process of building quantum intuitions. Our data suggest that (some) students bring productive intellectual resources to this negotiation.
"Classical-ish": Negotiating the boundary between classical and quantum particles
Benjamin W. Dreyfus; Erin Ronayne Sohr; Ayush Gupta; Andrew Elby
2015-07-02T23:59:59.000Z
Quantum mechanics can seem like a departure from everyday experience of the physical world, but constructivist theories assert that learners build new ideas from their existing ones. To explore how students can navigate this tension, we examine video of a focus group completing a tutorial about the "particle in a box." In reasoning about the properties of a quantum particle, the students bring in elements of a classical particle ontology, evidenced by students' language and gestures. This reasoning, however, is modulated by metacognitive moments when the group explicitly considers whether classical intuitions apply to the quantum system. The students find some cases where they can usefully apply classical ideas to quantum physics, and others where they explicitly contrast classical and quantum mechanics. Negotiating this boundary with metacognitive awareness is part of the process of building quantum intuitions. Our data suggest that (some) students bring productive intellectual resources to this negotiation.
Classical and quantum flux energy conditions
Martin-Moruno, Prado
2013-01-01T23:59:59.000Z
The classical energy conditions are known to not be fundamental physics -- they are typically violated by semiclassical quantum effects. Consequently, some effort has gone into finding possible semiclassical replacements for the classical energy conditions -- the most well developed being the Ford-Roman quantum inequalities. In the current article we shall instead develop classical and quantum versions of a "flux energy condition" (FEC and QFEC) based on the notion of constraining the possible fluxes measured by timelike observers. The classical FEC will be seen to be satisfied by some quantum states, while its quantum analogue (the QFEC) is satisfied under a rather wide range of conditions.
QUANTUM MECHANICS WITHOUT STATISTICAL POSTULATES
G. GEIGER; ET AL
2000-11-01T23:59:59.000Z
The Bohmian formulation of quantum mechanics describes the measurement process in an intuitive way without a reduction postulate. Due to the chaotic motion of the hidden classical particle all statistical features of quantum mechanics during a sequence of repeated measurements can be derived in the framework of a deterministic single system theory.
Physicalism versus quantum mechanics
Henry P. Stapp
2008-03-11T23:59:59.000Z
In the context of theories of the connection between mind and brain, physicalism is the demand that all is basically purely physical. But the concept of "physical" embodied in this demand is characterized essentially by the properties of the physical that hold in classical physical theories. Certain of these properties contradict the character of the physical in quantum mechanics, which provides a better, more comprehensive, and more fundamental account of phenomena. It is argued that the difficulties that have plaged physicalists for half a century, and that continue to do so, dissolve when the classical idea of the physical is replaced by its quantum successor. The argument is concretized in a way that makes it accessible to non-physicists by exploiting the recent evidence connecting our conscious experiences to macroscopic measurable synchronous oscillations occurring in well-separated parts of the brain. A specific new model of the mind-brain connection that is fundamentally quantum mechanical but that ties conscious experiences to these macroscopic synchronous oscillations is used to illustrate the essential disparities between the classical and quantum notions of the physical, and in particular to demonstrate the failure in the quantum world of the principle of the causal closure of the physical, a failure that goes beyond what is entailed by the randomness in the outcomes of observations, and that accommodates the efficacy in the brain of conscious intent.
Quantum-classical correspondence in response theory
Kryvohuz, Maksym
2008-01-01T23:59:59.000Z
In this thesis, theoretical analysis of correspondence between classical and quantum dynamics is studied in the context of response theory. Thesis discusses the mathematical origin of time-divergence of classical response ...
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.
Generic emergence of classical features in quantum Darwinism
Fernando G. S. L. Brandao; Marco Piani; Pawel Horodecki
2015-08-26T23:59:59.000Z
Quantum Darwinism explains the emergence of classical reality from the underlying quantum reality by the fact that a quantum system is observed indirectly, by looking at parts of its environment, so that only specific information about the system that is redundantly proliferated to many parts of the environment becomes accessible and objective. However it is not clear under what conditions this mechanism holds true. Here we rigorously prove that the emergence of classicality is a general feature of any quantum dynamics: observers who acquire information about a quantum system indirectly have access at most to classical information about one and the same measurement of the quantum system; moreover, if such information is available to many observers, they necessarily agree. Remarkably, our analysis goes beyond the system-environment categorization. We also provide a full characterization of the so-called quantum discord in terms of local redistribution of correlations.
Course Syllabus PHYS 331 Advanced Classical Mechanics
Vollmayr-Lee, Ben
Course Syllabus PHYS 331 Advanced Classical Mechanics Fall 2011 Instructor: Ben Vollmayr-Lee, Olin 168, ben.vollmayr-lee@bucknell.edu, x73106 Textbook: John Taylor, Classical Mechanics Office Hours://www.eg.bucknell.edu/bvollmay/phys331 Course Description Classical mechanics is where it all started. Newton demonstrated that the same
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.
Quantum Mechanics and Multiply Connected Spaces
B. G. Sidharth
2006-05-16T23:59:59.000Z
t is well known that the difference between Quantum Mechanics and Classical Theory appears most crucially in the non Classical spin half of the former theory and the Wilson-Sommerfelt quantization rule. We argue that this is symptomatic of the fact that Quantum Theory is actually a theory in multiply connected space while Classical Theory operates in simply connected space.
Holographic position uncertainty and the quantum-classical transition
C. L. Herzenberg
2010-04-16T23:59:59.000Z
Arguments based on general principles of quantum mechanics have suggested that a minimum length associated with Planck-scale unification may in the context of the holographic principle entail a new kind of observable uncertainty in the transverse position of macroscopically separated objects. Here, we address potential implications of such a position uncertainty for establishing an additional threshold between quantum and classical behavior.
Classical Mechanics (Prof. P. L. Read)
Read, Peter L.
Classical Mechanics (Prof. P. L. Read) Lecture 1 Photograph © Andrew Dunn, 5 November 2004. #12;What is Classical Mechanics? · .. rational mechanics will be the science of motion resulting from any Mechanics? · System of mathematical physics developed since the time of Galileo, Newton & Kepler · Concerned
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.
Quantum Chaos Versus Classical Chaos: Why is Quantum Chaos Weaker?
H. Kroger; J. F. Laprise; G. Melkonyan; R. Zomorrodi
2006-03-09T23:59:59.000Z
We discuss the questions: How to compare quantitatively classical chaos with quantum chaos? Which one is stronger? What are the underlying physical reasons?
Bohmian mechanics contradicts quantum mechanics
Neumaier, Arnold
Bohmian mechanics contradicts quantum mechanics Arnold Neumaier Institut fur Mathematik, Universit://solon.cma.univie.ac.at/#24;neum/ Abstract. It is shown that, for a harmonic oscillator in the ground state, Bohmian mechanics and quantum mechanics predict values of opposite sign for certain time correlations. The discrepancy can
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
Andrew C. Doherty; Salman Habib; Kurt Jacobs; Hideo Mabuchi; Sze M. Tan
2000-03-09T23:59:59.000Z
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.
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.
Quantum Mechanics Dung-Hai Lee
Murayama, Hitoshi
Quantum Mechanics Dung-Hai Lee Summer 2000 #12;Contents 1 A brief reminder of linear Algebra 3 1 mechanics as Feynman path inte- grals in imaginary time . . . . . . . . . . . . . . . . . . . 47 3.14 From classical to quantum mechanics . . . . . . . . . . . 47 3.14.1 Route I
Introduction to Quantum Mechanics
Eduardo J. S. Villaseñor
2008-04-23T23:59:59.000Z
The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.
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.
Time Fractional Formalism: Classical and Quantum Phenomena
Hosein Nasrolahpour
2012-03-18T23:59:59.000Z
In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can provide a deeper understanding of the physical interpretations of fractional derivative.
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.
2T Physics and Quantum Mechanics
W. Chagas-Filho
2008-02-20T23:59:59.000Z
We use a local scale invariance of a classical Hamiltonian and describe how to construct six different formulations of quantum mechanics in spaces with two time-like dimensions. All these six formulations have the same classical limit described by the same Hamiltonian. One of these formulations is used as a basis for a complementation of the usual quantum mechanics when in the presence of gravity.
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.
Quantum chaos and order based on classically moving reference frames
Hai Wenhua [Department of Physics, Hunan Normal University, Changsha 410081 (China); Department of Physics, Jishou University, Jishou 416000, Hunan (China); Xie Qiongtao; Fang Jianshu [Department of Physics, Hunan Normal University, Changsha 410081 (China)
2005-07-15T23:59:59.000Z
We develop a mathematically consistent approach for treating the quantum systems based on moving classical reference frames. The classical and quantum exact solutions show excellently classical-quantum correspondence, in which the quantum chaotic coherent states correspond to the classically chaotic motions. Applying the approach to the periodically driven linear and nonlinear oscillators, the regular and chaotic quantum states and quantum levels, and the quantum chaotic regions are evidenced. The results indicate that chaos may cause the collapse of matter wave packets and suppress the quantum effect of energy.
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.
Artscience (AS) in Classical and Quantum Physics: Paper I
S. L. Weinberg
2005-09-22T23:59:59.000Z
A general methodology and specific formalism are used to restrict the Copenhagen interpretation of quantum mechanics. A natural psi-collapse to reality is developed in an equation with terms independent of the measuring equipment. The theory requires one of three experiments for the ensemble average of position, momentum, or energy, or a probability-experiment. Both classically and quantum mechanically, we define Artscience (AS) as Logic-Epistemology in Physics, where epistemology is treated as phenomenology. AS (logic phenomenology) is thus shown to be related to Physics (formalism-data) .
Towards the topological quantization of classical mechanics
Francisco Nettel; Hernando Quevedo; Moices Rodriguez
2008-01-16T23:59:59.000Z
We consider the method of topological quantization for conservative systems with a finite number of degrees of freedom. Maupertuis' formalism for classical mechanics provides an appropriate scenario which permit us to adapt the method of topological quantization, originally formulated for gravitational field configurations. We show that any conservative system in classical mechanics can be associated with a principal fiber bundle. As an application of topological quantization we derive expressions for the topological spectra of some simple mechanical systems and show that they reproduce the discrete behavior of the corresponding canonical spectra.
Driven Morse oscillator: Classical chaos, quantum theory, and photodissociation
Goggin, M.E.; Milonni, P.W.
1988-02-01T23:59:59.000Z
We compare the classical and quantum theories of a Morse oscillator driven by a sinusoidal field, focusing attention on multiple-photon excitation and dissociation. In both the classical and quantum theories the threshold field strength for dissociation may be estimated fairly accurately on the basis of classical resonance overlap, and the classical and quantum results for the threshold are in good agreement except near higher-order classical resonances and quantum multiphoton resonances. We discuss the possibility of ''quantum chaos'' in such driven molecular systems and use the Morse oscillator to test the manifestations of classical resonance overlap suggested semiclassically.
Unifying classical and quantum key distillation
Matthias Christandl; Artur Ekert; Michal Horodecki; Pawel Horodecki; Jonathan Oppenheim; Renato Renner
2007-02-28T23:59:59.000Z
Assume that two distant parties, Alice and Bob, as well as an adversary, Eve, have access to (quantum) systems prepared jointly according to a tripartite state. In addition, Alice and Bob can use local operations and authenticated public classical communication. Their goal is to establish a key which is unknown to Eve. We initiate the study of this scenario as a unification of two standard scenarios: (i) key distillation (agreement) from classical correlations and (ii) key distillation from pure tripartite quantum states. Firstly, we obtain generalisations of fundamental results related to scenarios (i) and (ii), including upper bounds on the key rate. Moreover, based on an embedding of classical distributions into quantum states, we are able to find new connections between protocols and quantities in the standard scenarios (i) and (ii). Secondly, we study specific properties of key distillation protocols. In particular, we show that every protocol that makes use of pre-shared key can be transformed into an equally efficient protocol which needs no pre-shared key. This result is of practical significance as it applies to quantum key distribution (QKD) protocols, but it also implies that the key rate cannot be locked with information on Eve's side. Finally, we exhibit an arbitrarily large separation between the key rate in the standard setting where Eve is equipped with quantum memory and the key rate in a setting where Eve is only given classical memory. This shows that assumptions on the nature of Eve's memory are important in order to determine the correct security threshold in QKD.
Classical and Quantum Chaos and Control of Heat Flow
Giulio Casati; Carlos Mejia-Monasterio
2006-10-10T23:59:59.000Z
We discuss the problem of heat conduction in classical and quantum low dimensional systems from a microscopic point of view. At the classical level we provide convincing numerical evidence for the validity of Fourier law of heat conduction in linear mixing systems, i.e. in systems without exponential instability. At the quantum level, where motion is characterized by the lack of exponential dynamical instability, we show that the validity of Fourier law is in direct relation with the onset of quantum chaos. We then study the phenomenon of thermal rectification and briefly discuss the different types of microscopic mechanisms that lead to the rectification of heat flow. The control of heat conduction by nonlinearity opens the possibility to propose new devices such as a thermal rectifier.
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.
Quantum wave packets in space and time and an improved criterion for classical behavior
C. L. Herzenberg
2009-04-28T23:59:59.000Z
An improved criterion for distinguishing conditions in which classical or quantum behavior occurs is developed by comparing classical and quantum mechanical measures of size while incorporating spatial and temporal restrictions on wave packet formation associated with limitations on spatial extent and duration.
Quantum cosmological perfect fluid model and its classical analogue
A. B. Batista; J. C. Fabris; S. V. B. Goncalves; Joel Tossa
2001-08-22T23:59:59.000Z
The quantization of gravity coupled to a perfect fluid model leads to a Schr\\"odinger-like equation, where the matter variable plays the role of time. The wave function can be determined, in the flat case, for an arbitrary barotropic equation of state $p = \\alpha\\rho$; solutions can also be found for the radiative non-flat case. The wave packets are constructed, from which the expectation value for the scale factor is determined. The quantum scenarios reveal a bouncing Universe, free from singularity. We show that such quantum cosmological perfect fluid models admit a universal classical analogue, represented by the addition, to the ordinary classical model, of a repulsive stiff matter fluid. The meaning of the existence of this universal classical analogue is discussed. The quantum cosmological perfect fluid model is, for a flat spatial section, formally equivalent to a free particle in ordinary quantum mechanics, for any value of $\\alpha$, while the radiative non-flat case is equivalent to the harmonic oscillator. The repulsive fluid needed to reproduce the quantum results is the same in both cases.
Geometrization of Quantum Mechanics
J. F. Carinena; J. Clemente-Gallardo; G. Marmo
2007-03-23T23:59:59.000Z
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.
Classical Coordination Mechanisms in the Chemical Model
Fradet, Pascal
great souvenir! Abstract Originally, the chemical model of computation has been proposed as a sim- pleClassical Coordination Mechanisms in the Chemical Model J.-P. Ban^atre P. Fradet Y. Radenac-Pierre Ban^atre) had with Gilles on topics related with programming in general and chemical programming
Becoming classical: A possible influence on the quantum-to-classical transition
C. L. Herzenberg
2006-02-23T23:59:59.000Z
Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world. Calculations suggest that the minute recessional velocities associated with regions encompassed by extended bodies may have a role in creating the distinction between quantum and classical behavior. Using an uncertainty in position estimated from the spread in velocities associated with its size, the criterion that the uncertainty in position should be smaller than the extension of the object leads to a threshold size that could provide a fundamental limit distinguishing the realm of objects governed by classical laws from those governed by quantum mechanics.
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.
Emergence of classical behavior from the quantum spin
M. Radonjic; S. Prvanovic; N. Buric
2012-02-09T23:59:59.000Z
Classical Hamiltonian system of a point moving on a sphere of fixed radius is shown to emerge from the constrained evolution of quantum spin. The constrained quantum evolution corresponds to an appropriate coarse-graining of the quantum states into equivalence classes, and forces the equivalence classes to evolve as single units representing the classical states. The coarse-grained quantum spin with the constrained evolution in the limit of the large spin becomes indistinguishable from the classical system.
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.
Evolution Law of Quantum Observables from Classical Hamiltonian in Non-Commutative Phase Space
Daniela Dragoman
2006-04-11T23:59:59.000Z
The evolution equations of quantum observables are derived from the classical Hamiltonian equations of motion with the only additional assumption that the phase space is non-commutative. The demonstration of the quantum evolution laws is quite general; it does not rely on any assumption on the operator nature of x and p and is independent of the quantum mechanical formalism.
Quantum Mechanics and Black Holes
Jose N. Pecina-Cruz
2005-11-27T23:59:59.000Z
This paper discusses the existence of black holes from the foundations of quantum mechanics. It is found that quantum mechanics rule out a possible gravitational collapse.
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...
Quantum Mechanics Without Observers
W. H. Sulis
2013-03-03T23:59:59.000Z
The measurement problem and the role of observers have plagued quantum mechanics since its conception. Attempts to resolve these have introduced anthropomorphic or non-realist notions into physics. A shift of perspective based upon process theory and utilizing methods from combinatorial games, interpolation theory and complex systems theory results in a novel realist version of quantum mechanics incorporating quasi-local, nondeterministic hidden variables that are compatible with the no-hidden variable theorems and relativistic invariance, and reproduce the standard results of quantum mechanics to a high degree of accuracy without invoking observers.
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
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.
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.
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.
Quantum mechanics: last stop for reductionism
Gabriele Carcassi
2012-03-16T23:59:59.000Z
The state space of a homogeneous body is derived under two different assumptions: infinitesimal reducibility and irreducibility. The first assumption leads to a real vector space, used in classical mechanics, while the second one leads to a complex vector space, used in quantum mechanics.
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,.
Quantum Mechanical Pressure Frank Rioux
Rioux, Frank
Quantum Mechanical Pressure Frank Rioux CSB|SJU Quantum mechanics is based on the concept of wave it to its quantum mechanical equivalent. 2 2 2 2 2 p h KE m m = = Because objects with wave-like properties" character of quantum mechanical kinetic energy is the ultimate basis for the stability of matter. It also
QUANTUM MECHANICS II Physics 342
Rosner, Jonathan L.
QUANTUM MECHANICS II Physics 342 KPTC 103 9:00 10:20 a.m. 1 Tues., Thurs. Winter Quarter 2011 quantum mechanics at the graduate level. The text for Quantum Mechanics II will be J. J. Sakurai and Jim Napolitano, Modern Quantum Mechanics, Second Edition (Addison-Wesley, San Francisco, 2011). For supplemental
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.
Quantum phenomena modelled by interactions between many classical worlds
Michael J. W. Hall; D. -A. Deckert; Howard M. Wiseman
2014-10-26T23:59:59.000Z
We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical 'worlds', and quantum effects arise solely from a universal interaction between these worlds, without reference to any wave function. Here a `world' means an entire universe with well-defined properties, determined by the classical configuration of its particles and fields. In our approach each world evolves deterministically; probabilities arise due to ignorance as to which world a given observer occupies; and we argue that in the limit of infinitely many worlds the wave function can be recovered (as a secondary object) from the motion of these worlds. We introduce a simple model of such a 'many interacting worlds' approach and show that it can reproduce some generic quantum phenomena---such as Ehrenfest's theorem, wavepacket spreading, barrier tunneling and zero point energy---as a direct consequence of mutual repulsion between worlds. Finally, we perform numerical simulations using our approach. We demonstrate, first, that it can be used to calculate quantum ground states, and second, that it is capable of reproducing, at least qualitatively, the double-slit interference phenomenon.
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.
How do black holes move, as quantum objects or as classical objects?
C. L. Herzenberg
2007-09-12T23:59:59.000Z
Results of a recent study of the transition between quantum and classical behavior are applied to black holes. The study led to a criterion separating quantum from classical behavior on the basis of mass or size, dependent on local effects of cosmic expansion. Application of this criterion to black holes indicates that the motion of smaller black holes will be characteristically quantum mechanical, while the motion of larger black holes must be classical, with a threshold distinguishing these behaviors at a Schwartzschild radius of roughly the size of a nucleon.
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.
MATHEMATICS 428/609D Mathematical Classical Mechanics
Fournier, John J.F.
MATHEMATICS 428/609D Mathematical Classical Mechanics This course is intended to complement physics department classical mechanics courses in the sense that the physical background will be developed experience with rigorous mathematics (like Math 320 and 321) and with classical mechanics (like Physics 206
CLASSICAL MECHANICS: THE THREE-BODY PROBLEM ZI CHONG KAO
May, J. Peter
CLASSICAL MECHANICS: THE THREE-BODY PROBLEM ZI CHONG KAO Abstract. The Three-Body Problem is one of the oldest unsolved problems of classical mechanics. It arose as a natural extension of the Two-Body Prob of numerous techniques in classical mechan- ics as well as dynamical systems. Understanding the Three
Kinematics of trajectories in classical mechanics
Rajibul Shaikh; Sayan Kar; Anirvan DasGupta
2014-05-21T23:59:59.000Z
In this paper, we show how the study of kinematics of a family of trajectories of a classical mechanical system may be unified within the framework of analysis of geodesic flows in Riemannian geometry and Relativity. After setting up the general formalism, we explore it through studies on various one and two dimensional systems. Quantities like expansion, shear and rotation (ESR), which are more familiar to the relativist, now re-appear while studying such families of trajectories in configuration space, in very simple mechanical systems. The convergence/divergence of a family of trajectories during the course of time evolution, the shear and twist of the area enclosing the family, and the focusing/defocusing of the trajectories within a finite time are investigated analytically for these systems. The understanding of the configuration space developed through such investigations is elaborated upon, and possible future avenues are pointed out.
Separation of variables for the classical and quantum Neumann model
O. Babelon; M. Talon
1992-01-16T23:59:59.000Z
The method of separation of variables is shown to apply to both the classical and quantum Neumann model. In the classical case this nicely yields the linearization of the flow on the Jacobian of the spectral curve. In the quantum case the Schr\\"odinger equation separates into one--dimensional equations belonging to the class of generalized Lam\\'e differential equations.
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.
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.
A geometric approach to quantum control in a classical-like framework
Davide Pastorello
2015-08-28T23:59:59.000Z
A quantum theory in a finite-dimensional Hilbert space can be formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework where quantum dynamics is represented by a Hamiltonian flow in the phase space given by Hilbert projective space. This paper is devoted to investigate how the notion of accessibility algebra from classical control theory can be applied within geometric classical-like formulation of Quanum Mechanics to study controllability of a quantum system in order to state the following conjecture: Under certain conditions, classical control theory provides a machinery which can be directly applied in quantum control within the geometric Hamiltonian picture.
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.
Classical and quantum chaos in a circular billiard with a straight cut
Ree, S.; Reichl, L.E. [Center for Studies in Statistical Mechanics and Complex Systems, The University of Texas at Austin, Austin, Texas 78712 (United States)] [Center for Studies in Statistical Mechanics and Complex Systems, The University of Texas at Austin, Austin, Texas 78712 (United States)
1999-08-01T23:59:59.000Z
We study classical and quantum dynamics of a particle in a circular billiard with a straight cut. Classically, this system can be integrable, nonintegrable with {ital soft chaos}, or nonintegrable with {ital hard chaos} as we vary the size of the cut. We plot Poincar{acute e} surfaces of section to study chaos. Quantum mechanically, we look at Husimi plots, and also use the quantum web, the technique primarily used in spin systems so far, to try to see differences in quantum manifestations of soft and hard chaos. {copyright} {ital 1999} {ital The American Physical Society}
Chapin, Kimberly R.
1997-01-01T23:59:59.000Z
TIME IN QUANTUM MECHANICS A Thesis by KIMBERLY R. CHAPIN Submitted to Texas A8M University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Approved as to style and content by: Marian O. Scully (Chair... of Committee) Edward S. Fry (Member) aan Laane (Member) Thomas W. Adair, III (Head of Department) August 1997 Major Subject: Physics TIME IN QIJANTUM MECHANICS A Thesis by KIMBERLY R. CHAPIN Submitted to the Oflice of Graduate Studies of Texas A...
Argyris Nicolaidis
2012-11-09T23:59:59.000Z
We suggest that the inner syntax of Quantum Mechanics is relational logic, a form of logic developed by C. S. Peirce during the years 1870 - 1880. The Peircean logic has the structure of category theory, with relation serving as an arrow (or morphism). At the core of the relational logical system is the law of composition of relations. This law leads to the fundamental quantum rule of probability as the square of an amplitude. Our study of a simple discrete model, extended to the continuum, indicates that a finite number of degrees of freedom can live in phase space. This "granularity" of phase space is determined by Planck's constant h. We indicate also the broader philosophical ramifications of a relational quantum mechanics.
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.
A new introductory quantum mechanics curriculum
Kohnle, Antje; Browne, Dan; Everitt, Mark; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth
2013-01-01T23:59:59.000Z
The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of interpretive aspects of quantum mechanics and quantum information theory. This article gives an overview of the resources available at the IOP website. The core text is presented as around 80 articles co-authored by leading experts that are arranged in themes and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is part of the resource. Solutions to activities are available ...
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
On Randomness in Quantum Mechanics
Alberto C. de la Torre
2007-07-19T23:59:59.000Z
The quantum mechanical probability densities are compared with the probability densities treated by the theory of random variables. The relevance of their difference for the interpretation of quantum mechanics is commented.
Three Pictures of Quantum Mechanics
Olszewski Jr., Edward A.
Three Pictures of Quantum Mechanics Thomas R. Shafer April 17, 2009 #12;Outline of the Talk · Brief review of (or introduction to) quantum mechanics. · 3 different viewpoints on calculation. · Schrödinger the Stage: Quantum Mechanics in Five Minutes #12;The Wave Function · A particle or system is described
Some topics in thermodynamics and quantum mechanics
Robert Carroll
2012-11-17T23:59:59.000Z
We sketch some connecting relations involving fractional and quantum calculi, fractal structure, thermodynamics, and quantum mechanics.
Characterization of a noisy quantum process by complementary classical operations
Holger F. Hofmann; Ryo Okamoto; Shigeki Takeuchi
2006-10-31T23:59:59.000Z
One of the challenges in quantum information is the demonstration of quantum coherence in the operations of experimental devices. While full quantum process tomography can do the job, it is both cumbersome and unintuitive. In this presentation, we show that a surprisingly detailed and intuitively accessible characterization of errors is possible by measuring the error statistics of only two complementary classical operations of a quantum gate.
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.
(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
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.
Interpretation of cosmological expansion effects on the quantum-classical transition
C. L. Herzenberg
2006-06-07T23:59:59.000Z
Recently, what appears to be a fundamental limit associated with the size of an object that separates the quantum behavior characterizing small objects from the classical behavior characterizing large objects has been derived from the Hubble velocity spread in an extended object. This threshold is now examined further and interpreted in terms of diffusion processes in stochastic quantum mechanics. This limiting size that separates quantum behavior from classical behavior is shown to correspond approximately to the diffusion distance of the object over the Hubble time.
Fayer, Michael D.
Does Quantum Mechanics Make Sense?Does Quantum Mechanics Make Sense? Some relatively simple Classical Mechanics Quantum Mechanics Relative Absolute What does relative vs. absolute size mean?What does relative vs. absolute size mean? Why does it matter?Why does it matter? #12;Classical Mechanics
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.
QUANTUM/CLASSICAL INTERFACE: A GEOMETRIC APPROACH FROM THE
alge- bras, in particular the algebra of physical space (APS), provide the lu- bricant for smoothQUANTUM/CLASSICAL INTERFACE: A GEOMETRIC APPROACH FROM THE CLASSICAL SIDE William E. Baylis Physics relativistic physics in Clifford's geometric algebra has a spino- rial formulation that is closely related
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.
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.
Classical foundations of many-particle quantum chaos
Boris Gutkin; Vladimir Osipov
2015-03-09T23:59:59.000Z
In the framework of semiclassical theory the universal properties of quantum systems with classically chaotic dynamics can be accounted for through correlations between partner periodic orbits with small action differences. So far, however, the scope of this approach has been mainly limited to systems of a few particles with low-dimensional phase spaces. In the present work we consider N-particle chaotic systems with local homogeneous interactions, where N is not necessarily small. Based on a model of coupled cat maps we demonstrate emergence of a new mechanism for correlation between periodic orbit actions. In particular, we show the existence of partner orbits which are specific to many-particle systems. For a sufficiently large N these new partners dominate the spectrum of correlating periodic orbits and seem to be necessary for construction of a consistent many-particle semiclassical theory.
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.
Efficient Classical Simulation of Continuous Variable Quantum Information Processes
Stephen D. Bartlett; Barry C. Sanders; Samuel L. Braunstein; Kae Nemoto
2002-02-18T23:59:59.000Z
We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum information. For a collection of harmonic oscillators, any quantum process that begins with unentangled Gaussian states, performs only transformations generated by Hamiltonians that are quadratic in the canonical operators, and involves only measurements of canonical operators (including finite losses) and suitable operations conditioned on these measurements can be simulated efficiently on a classical computer.
Quantum signature in classical electrodynamics of the free radiation field
Michele Marrocco
2015-05-20T23:59:59.000Z
Quantum optics is a field of research based on the quantum theory of light. Here, we show that the classical theory of light can be equally effective in explaining a cornerstone of quantum optics: the quantization of the free radiation field. The quantization lies at the heart of quantum optics and has never been obtained classically. Instead, we find it by taking into account the degeneracy of the spherical harmonics that appear in multipole terms of the ordinary Maxwell theory of the free electromagnetic field. In this context, the number of energy quanta is determined by a finite countable set of spherical harmonics of higher order than the fundamental (monopole). This one plays, instead, the role of the electromagnetic vacuum that, contrary to the common view, has its place in the classical theory of light.
Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics
Gerhard Groessing
2013-04-12T23:59:59.000Z
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder's group on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schr\\"odinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level. It is further demonstrated both analytically and with the aid of computer simulations that our model provides explanations for various quantum effects such as double-slit or n-slit interference. We show the averaged trajectories emerging from our model to be identical to Bohmian trajectories, albeit without the need to invoke complex wave functions or any other quantum mechanical tool. Finally, the model provides new insights into the origins of entanglement, and, in particular, into the phenomenon of a "systemic" nonlocality.
129 Lecture Notes Relativistic Quantum Mechanics
Murayama, Hitoshi
129 Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics's equation of motion in mechanics. The initial condtions to solve the Newton's equation of motion
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.
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.
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
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.
Classical and Quantum Dynamics of Free Electromagnetic Laser Pulses
S. Goto; R. W. Tucker; T. J. Walton
2015-02-09T23:59:59.000Z
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 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.
Invariance in adelic quantum mechanics
Branko Dragovich
2006-12-07T23:59:59.000Z
Adelic quantum mechanics is form invariant under an interchange of real and p-adic number fields as well as rings of p-adic integers. We also show that in adelic quantum mechanics Feynman's path integrals for quadratic actions with rational coefficients are invariant under changes of their entries within nonzero rational numbers.
Quantum Discrete Fourier Transform with Classical Output for Signal Processing
Chao-Yang Pang; Ben-Qiong Hu
2007-06-17T23:59:59.000Z
Discrete Fourier transform (DFT) is the base of modern signal or information processing. 1-Dimensional fast Fourier transform (1D FFT) and 2D FFT have time complexity O(NlogN) and O(N^2logN) respectively. Quantum 1D and 2D DFT algorithms with classical output (1D QDFT and 2D QDFT) are presented in this paper. And quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, QDFT has two advantages at least. One of advantages is that 1D and 2D QDFT has time complexity O(sqrt(N)) and O(N) respectively. The other advantage is that QDFT can process very long signal sequence at a time. QDFT and quantum convolution demonstrate that quantum signal processing with classical output is possible.
On a New Form of Quantum Mechanics
N. N. Gorobey; A. S. Lukyanenko
2008-07-22T23:59:59.000Z
We propose a new form of nonrelativistic quantum mechanics which is based on a quantum version of the action principle.
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.
Quantum-classical transition and quantum activation of ratchet currents in the parameter space
M. W. Beims; M. Schlesinger; C. Manchein; A. Celestino; A. Pernice; W. T. Strunz
2015-05-14T23:59:59.000Z
The quantum ratchet current is studied in the parameter space of the dissipative kicked rotor model coupled to a zero temperature quantum environment. We show that vacuum fluctuations blur the generic isoperiodic stable structures found in the classical case. Such structures tend to survive when a measure of statistical dependence between the quantum and classical currents are displayed in the parameter space. In addition, we show that quantum fluctuations can be used to overcome transport barriers in the phase space. Related quantum ratchet current activation regions are spotted in the parameter space. Results are discussed {based on quantum, semiclassical and classical calculations. While the semiclassical dynamics involves vacuum fluctuations, the classical map is driven by thermal noise.
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.
Quantum Mechanics 1 for graduate students
Course 606 Quantum Mechanics 1 for graduate students Fall 2010 Instructor Valery Pokrovsky 1 electromagnetic field. Gauge invariance. Landau levels. 7. Semiclassical approximation. 8. Quantum mechanics. Scattering. The main textbook is E. Merzbacher, Quantum Mechanics, third edition, Wiley. Additional
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.
Completely positive classical structures and sequentializable quantum protocols
Chris Heunen; Sergio Boixo
2012-10-02T23:59:59.000Z
We study classical structures in various categories of completely positive morphisms: on sets and relations, on cobordisms, on a free dagger compact category, and on Hilbert spaces. As an application, we prove that quantum maps with commuting Kraus operators can be sequentialized. Hence such protocols are precisely as robust under general dephasing noise when entangled as when sequential.
Classical and quantum dynamics of optical frequency conversion
White, Andrew G.
to the quantitative and qualitative agreement between experiment and theory, and the experimental reliabilityClassical and quantum dynamics of optical frequency conversion By Andrew G. White A THESIS encouraged me to find out about dinosaurs #12;#12;Declaration This thesis is an account of research
The Quantum-Classical Transition and Wave Packet Dispersion
C. L. Herzenberg
2007-06-11T23:59:59.000Z
Two recent studies have presented new information relevant to the transition from quantum behavior to classical behavior, and related this to parameters characterizing the universe as a whole. The present study based on a separate approach has developed similar results that appear to substantiate aspects of earlier work and also to introduce further new ideas.
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.
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.
Implementation of Quantum and Classical Discrete Fractional Fourier Transforms
Steffen Weimann; Armando Perez-Leija; Maxime Lebugle; Robert Keil; Malte Tichy; Markus Gräfe; Rene Heilmann; Stefan Nolte; Hector Moya-Cessa; Gregor Weihs; Demetrios N. Christodoulides; Alexander Szameit
2015-07-31T23:59:59.000Z
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the integrated configuration used in our experiments, the order of the transform is mapped onto the longitudinal coordinate, thus opening up the prospect of simultaneously observing all Transformation orders. In the context of classical optics, we implement discrete fractional Fourier transforms, both integer and fractional, of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to transform separable and highly entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools, such as quantum chemistry and biology, physics and mathematics.
The classical mechanics of autonomous microscopic engines
Lukas Gilz; Eike P. Thesing; James R. Anglin
2015-09-08T23:59:59.000Z
Even microscopic engines have hitherto been defined to require macroscopic elements such as heat reservoirs, but here we observe that what makes engines useful is energy transfer across a large ratio of dynamical time scales ("downconversion"), and that small, closed dynamical systems which could perform steady downconversion ("Hamiltonian daemons") would fulfill the practical requirements of autonomous microscopic engines. We show that such daemons are possible, and obey mechanical constraints comparable to, but different from, the laws of thermodynamics.
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.
Hyper-Hamiltonian quantum mechanics
Vladimir Trifonov
2006-03-02T23:59:59.000Z
We present a modification of quantum mechanics with a *possible worlds* semantics. It is shown that `gauge' degrees of freedom along possible worlds can be used to encode gravitational information.
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.
Geometry and symmetry of quantum and classical-quantum variational principles
Esther Bonet Luz; Cesare Tronci
2015-01-28T23:59:59.000Z
This paper presents the geometric setting of quantum variational principles and extends it to comprise the interaction between classical and quantum degrees of freedom. Euler-Poincar\\'e reduction theory is applied to the Schr\\"odinger, Heisenberg and Wigner-Moyal dynamics of pure states. This construction leads to new variational principles for the description of mixed quantum states. The corresponding momentum map properties are presented as they arise from the underlying unitary symmetries. Finally, certain semidirect-product group structures are shown to produce new variational principles for Dirac's interaction picture and the equations of hybrid classical-quantum dynamics.
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 and Quantum Chaos in the Diamond Shaped Billiard
Salazar, R; Jaramillo, D; González, D L
2012-01-01T23:59:59.000Z
We analyse the classical and quantum behaviour of a particle trapped in a diamond shaped billiard. We defined this billiard as a half stadium connected with a triangular billiard. A parameter $\\xi$ which gradually change the shape of the billiard from a regular equilateral triangle ($\\xi=1$) to a diamond ($\\xi=0$) was used to control the transition between the regular and chaotic regimes. The classical behaviour is regular when the control parameter $\\xi$ is one; in contrast, the system is chaotic when $\\xi \
Alternative linear structures for classical and quantum systems
E. Ercolessi; A. Ibort; G. Marmo; G. Morandi
2007-06-12T23:59:59.000Z
The possibility of deforming the (associative or Lie) product to obtain alternative descriptions for a given classical or quantum system has been considered in many papers. Here we discuss the possibility of obtaining some novel alternative descriptions by changing the linear structure instead. In particular we show how it is possible to construct alternative linear structures on the tangent bundle TQ of some classical configuration space Q that can be considered as "adapted" to the given dynamical system. This fact opens the possibility to use the Weyl scheme to quantize the system in different non equivalent ways, "evading", so to speak, the von Neumann uniqueness theorem.
QUANTUM MECHANICS AND REAL Department of Mathematics
Penrose, Oliver
QUANTUM MECHANICS AND REAL EVENTS O.Penrose Department of Mathematics Heriot-Watt University into the evolution of a quantum-mechanical system, without altering the usual laws of quantum mechanics in any way Although quantum mechanics is wonderfully successful for predicting the results of experiments done
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.
Quantum chaos in the nuclear collective model: I. Classical-quantum correspondence
Pavel Stransky; Petr Hruska; Pavel Cejnar
2009-02-23T23:59:59.000Z
Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic classical features with energy and control parameters. Corresponding signatures are now verified also on the quantum level for different schemes of quantization and with a variable classicality constant.
Contexts, Systems and Modalities: a new ontology for quantum mechanics
Alexia Auffèves; Philippe Grangier
2015-01-23T23:59:59.000Z
In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any particular observer's perception, and obeying universal and intelligible rules. Rather than elaborating on the quantum formalism itself, we propose to modify the quantum ontology, by requiring that physical properties are attributed jointly to the system, and to the context in which it is embedded. In combination with a quantization principle, this non-classical definition of physical reality sheds new light on counter-intuitive features of quantum mechanics such as the origin of probabilities, non-locality, and the quantum-classical boundary.
Robust quantum spatial coherence near a classical environment
Zhou, Shuyu; Keil, Mark; Japha, Yonathan; Folman, Ron
2015-01-01T23:59:59.000Z
In quantum physics spatial coherence allows a massive object to be present in two locations at the same time. Such spatial coherence is easily lost in the presence of a classical environment, making it unobservable in our day-to-day experience. Here we report the persistence of spatial coherence for ultra-cold atoms held only 5$\\,\\mu$m from a room temperature surface, reducing substantially the distance previously achieved between trapped atoms exhibiting spatial coherence and their classical environment. At this distance, the environment would normally destroy spatial coherence over any length greater than a few micrometers, but we nevertheless observe coherence over a length of 30$\\,\\mu$m. We show that no observable dephasing is taking place, even on a time scale on the order of one second. From a technological point of view, this may enable quantum devices based on atomic circuits.
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.
What quantum computers may tell us about quantum mechanics
Monroe, Christopher
17 What quantum computers may tell us about quantum mechanics Christopher R. Monroe University of Michigan, Ann Arbor Quantum mechanics occupies a unique position in the history of science. It has sur successes of quantum mechanics, its foundations are often questioned, owing to the glaring difficulties
Quantum mechanics of a generalised rigid body
Ben Gripaios; Dave Sutherland
2015-04-06T23:59:59.000Z
We consider the quantum version of Arnold's generalisation of a rigid body in classical mechanics. Thus, we quantise the motion on an arbitrary Lie group manifold of a particle whose classical trajectories correspond to the geodesics of any one-sided-invariant metric. We show how the derivation of the spectrum of energy eigenstates can be simplified by making use of automorphisms of the Lie algebra and (for groups of Type I) by methods of harmonic analysis. As examples, we consider all connected and simply-connected Lie groups up to dimension 3. This includes the universal cover of the archetypical rigid body, along with a number of new exactly-solvable models. We also discuss a possible application to the topical problem of quantising a perfect fluid.
221B Lecture Notes Relativistic Quantum Mechanics
Murayama, Hitoshi
221B Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics We's equation of motion in mechanics. The initial condtions to solve the Newton's equation of motion
221B Lecture Notes Relativistic Quantum Mechanics
Murayama, Hitoshi
221B Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics We, similarly to the Newton's equation of motion in mechanics. The initial condtions to solve the Newton
Is Holographic Entropy and Gravity the result of Quantum Mechanics?
Joakim Munkhammar
2010-03-09T23:59:59.000Z
In this paper we suggest a connection between quantum mechanics and Verlinde's recently proposed entropic force theory for the laws of Newton. We propose an entropy based on the quantum mechanical probability density distribution. With the assumption that the holographic principle holds we propose that our suggested quantum entropy generalizes the Bekenstein entropy used by Verlinde in his approach. Based on this assumption we suggest that Verlinde's entropic theory of gravity has a quantum mechanical origin. We establish a reformulation of the Newtonian potential for gravity based on this quantum mechanical entropy. We also discuss the notion of observation and the correspondence to classical physics. Finally we give a discussion, a number of open problems and some concluding remarks.
PLANCK'S FORMULA IN CLASSICAL MECHANICS Andrea CARATI, Luigi GALGANI
.e. by considering processes involving continuous variations of energy. A particular effort in this direction), the expected energy distribution is apparently frozen about the initial one, with the addition of a ``thermal of classical mechanics. We prove that the expected energy distribution of the oscillators obeys Planck
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
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.
Bohmian Trajectories as the Foundation of Quantum Mechanics
Sheldon Goldstein; Roderich Tumulka; Nino Zanghi
2009-12-14T23:59:59.000Z
Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schroedinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for: to serve as the foundation of quantum mechanics, i.e., to explain quantum mechanics in terms of a theory that is free of paradoxes and allows an understanding that is as clear as that of classical mechanics. Indeed, they succeed in serving that purpose in the context of a theory known as Bohmian mechanics, to which this article is an introduction.
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.
Creation mechanism of quantum accelerator modes
Summy, G. S.
We investigate the creation mechanism of quantum accelerator modes which are attributed to the existence of the stability islands in an underlying pseudoclassical phase space of the quantum delta-kicked accelerator. Quantum ...
Chen, Yiling
Chapter 3 Computational Mechanism Design The classic mechanism design literature largely ignores possible outcomes (the revelation principle), and that the mechanism can solve an optimization problem to select the best outcome (e.g. the Groves mechanisms). It is useful to take a ``markets
Chen, Yiling
Chapter 3 Computational Mechanism Design The classic mechanism design literature largely ignores possible outcomes the revelation principle, and that the mechanism can solve an optimization problem to select the best outcome e.g. the Groves mechanisms. It is useful to take a markets-as-computation" view
Chen, Yiling
Chapter 2 Classic Mechanism Design Mechanism design is the subÂfield of microeconomics and gameÂtheoretic approach to mechanism design, and presents important possibility and impossibility results of computational mechanism design, and also surveys the economic literature on limÂ ited communication and agent
Quantum mechanics emerges from information theory applied to causal horizons
Jae-Weon Lee
2011-02-28T23:59:59.000Z
It is suggested that quantum mechanics is not fundamental but emerges from classical information theory applied to causal horizons. The path integral quantization and quantum randomness can be derived by considering information loss of fields or particles crossing Rindler horizons for accelerating observers. This implies that information is one of the fundamental roots of all physical phenomena. The connection between this theory and Verlinde's entropic gravity theory is also investigated.
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.
A possible cosmological effect on the quantum-to-classical transition
C. L. Herzenberg
2006-03-16T23:59:59.000Z
Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, these extraordinarily small effects may in fact have a real and significant influence on our world. A calculation suggests that the minute recessional velocities associated with regions encompassed by extended bodies may have a role in creating the distinction between quantum and classical behavior. Using the criterion that the uncertainty in position should be smaller than the size of an object together with estimates based on the range of Hubble velocities extending through the object lead to a threshold size that could provide a fundamental limit distinguishing the realm of objects governed by classical laws from those governed by quantum mechanics.
Testing spontaneous wave-function collapse models on classical mechanical oscillators
Lajos Diósi
2014-11-17T23:59:59.000Z
We show that the heating effect of spontaneous wave-function collapse models implies an experimentally significant increment $\\Delta T$ of equilibrium temperature in a mechanical oscillator. The obtained form $\\Delta T$ is linear in the oscillator's relaxation time $\\tau$ and independent of the mass. The oscillator can be in a classical thermal state, the effect $\\Delta T$ is classical for a wide range of frequencies and quality factors. We note that the test of $\\Delta T$ does not necessitate quantum state monitoring but tomography. In both gravity-related (DP) and continuous spontaneous localization (CSL) models the strong-effect edge of their parameter range can be challenged in existing experiments on classical oscillators. For the CSL theory, the conjectured highest collapse rate parameter values become immediately constrained by evidences from current experiments on extreme slow-ring-down oscillators.
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.
Star Products for Relativistic Quantum Mechanics
P. Henselder
2007-05-24T23:59:59.000Z
The star product formalism has proved to be an alternative formulation for nonrelativistic quantum mechanics. We want introduce here a covariant star product in order to extend the star product formalism to relativistic quantum mechanics in the proper time formulation.
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.
The extension problem for partial Boolean structures in Quantum Mechanics
Costantino Budroni; Giovanni Morchio
2011-01-13T23:59:59.000Z
Alternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the equivalence of the approaches going back to Bell and Kochen-Specker. An algebraic approach is presented, allowing for a discussion of partial classical extension, amounting to reduction of the number of contexts, classical representability arising as a special case. As a result, known techniques are generalized and some of the associated computational difficulties overcome. The implications on the discussion of Boole-Bell inequalities are indicated.
The extension problem for partial Boolean structures in Quantum Mechanics
Budroni, Costantino
2010-01-01T23:59:59.000Z
Alternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the equivalence of the approaches going back to Bell and Kochen-Specker. An algebraic approach is presented, allowing for a discussion of partial classical extension, amounting to reduction of the number of contexts, classical representability arising as a special case. As a result, known techniques are generalized and some of the associated computational difficulties overcome. The implications on the discussion of Boole-Bell inequalities are indicated.
The Universal Arrow of Time II: Quantum mechanics case
Oleg Kupervasser
2013-05-23T23:59:59.000Z
This paper is a natural continuation of our previous paper arXiv:1011.4173 . We illustrated earlier that in classical Hamilton mechanics, for overwhelming majority of real chaotic macroscopic systems, alignment of their thermodynamic time arrows occurs because of their low interaction. This fact and impossibility to observe entropy decrease at introspection explain the second law of thermodynamics. The situation in quantum mechanics is even a little bit easier: all closed systems of finite volume are periodic or nearly periodic. The proof in quantum mechanics is in many respects similar to the proof in classical Hamilton mechanics - it also uses small interaction between subsystems and impossibility to observe entropy decrease at introspection. However, there are special cases which were not found in the classical mechanics. In these cases one microstate corresponds to a set of possible macrostates (more precisely, their quantum superposition). Consideration of this property with use of decoherence theory and taking into account thermodynamic time arrows will introduce new outcomes in quantum mechanics. It allows to resolve basic paradoxes of quantum mechanics: (a) to explain the paradox of wave packet reduction at measurements when an observer is included in the system (introspection) (paradox of the Schrodinger cat); (b) to explain unobservability of superposition of macroscopic states by an external observer in real experiments (paradox of Wigner's friend); (c) to prove full equivalence of multi-world and Copenhagen interpretations of quantum mechanics; (d) to explain deviations from the exponential law at decay of particles and pass from one energy level to another (paradox of a kettle which will never begin to boil).
Quantum Mechanics: Structures, Axioms and Paradoxes
Aerts, Diederik
Quantum Mechanics: Structures, Axioms and Paradoxes Diederik Aerts Center Leo Apostel, Brussels present an analysis of quantum mechanics and its problems and para- doxes taking into account the results a genuine incomplete- ness of standard quantum mechanics, however not an incompleteness that means
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.
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.
A Signed Particle Formulation of Non-Relativistic Quantum Mechanics
Sellier, Jean Michel
2015-01-01T23:59:59.000Z
A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as field-less classical objects which carry a negative or positive sign and interact with an external potential by means of creation and annihilation events only. This approach is shown to be a generalization of the signed particle Wigner Monte Carlo method which reconstructs the time-dependent Wigner quasi-distribution function of a system and, therefore, the corresponding Schroedinger time-dependent wave-function. Its classical limit is discussed and a physical interpretation, based on experimental evidences coming from quantum tomography, is suggested. Moreover, in order to show the advantages brought by this novel formulation, a straightforward extension to relativistic effects is discussed. To conclude, quantum tunnelling numerical experiments are performed to show the val...
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.
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.
Buryak, Ilya [Chemistry Department, Lomonosov Moscow State University, GSP-1, Vorobievy Gory, Moscow 119991 (Russian Federation) [Chemistry Department, Lomonosov Moscow State University, GSP-1, Vorobievy Gory, Moscow 119991 (Russian Federation); Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 3 Pyzhevsky per., 119017 Moscow (Russian Federation); Frommhold, Lothar [Physics Department, University of Texas at Austin, Austin, Texas 78712-1081 (United States)] [Physics Department, University of Texas at Austin, Austin, Texas 78712-1081 (United States); Vigasin, Andrey A., E-mail: vigasin@ifaran.ru [Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 3 Pyzhevsky per., 119017 Moscow (Russian Federation)
2014-04-21T23:59:59.000Z
We compare calculations of the translational collision-induced spectra and their integrated intensities of both He–Ar and Ne–Ar collisional complexes, using the quantum mechanical and a semiclassical formalism. Advanced potential energy and induced dipole functions are used for the calculations. The quantum method used is as described previously [L. Frommhold, Collision-induced Absorption in Gases (Cambridge University Press, 1993 and 2006)]. The semiclassical method is based on repeated classical atom-atom scattering calculations to simulate an ensemble average; subsequent Fourier transform then renders the binary absorption coefficient as a function of frequency. The problem of classical calculations is the violation of the principle of detailed balance, which may be introduced only artificially in classical calculations. Nevertheless, it is shown that the use of classical trajectories permits a fairly accurate reproduction of the experimental spectra, comparable to the quantum mechanical results at not too low temperatures and for collisional pairs of not too small reduced mass. Inexpensive classical calculations may thus be promising to compute spectra also of molecular pairs, or even of polyatomic collisional pairs with anisotropic intermolecular interactions, for which the quantum approach is still inefficient or impractical.
Physical properties as modal operators in the topos approach to quantum mechanics
Hector Freytes; Graciela Domenech; Christian de Ronde
2014-12-21T23:59:59.000Z
In the framework of the topos approach to quantum mechanics we give a representation of physical properties in terms of modal operators on Heyting algebras. It allows us to introduce a classical type study of the mentioned properties.
Bohmian Mechanics with Complex Action: A New Trajectory-Based Formulation of Quantum Mechanics
Yair Goldfarb; Ilan Degani; David J. Tannor
2006-04-20T23:59:59.000Z
In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared -- it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification -- a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wavepacket dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10^{-7} calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.
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.
Hidden Symmetries of Dynamics in Classical and Quantum Physics
Marco Cariglia
2014-11-05T23:59:59.000Z
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description of physical systems as varied as non-relativistic, relativistic, with or without gravity, classical or quantum, and are related to the existence of conserved quantities of the dynamics and integrability. In recent years their study has grown intensively, due to the discovery of non-trivial examples that apply to different types of theories and different numbers of dimensions. Applications encompass the study of integrable systems such as spinning tops, the Calogero model, systems described by the Lax equation, the physics of higher dimensional black holes, the Dirac equation, supergravity with and without fluxes, providing a tool to probe the dynamics of non-linear systems.
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.
Quantum Mechanics Joachim Burgdorfer and Stefan Rotter
Rotter, Stefan
1 1 Quantum Mechanics Joachim Burgd¨orfer and Stefan Rotter 1.1 Introduction 3 1.2 Particle and Quantization 8 1.5 Angular Momentum in Quantum Mechanics 9 1.6 Formalism of Quantum Mechanics 12 1.7 Solution 29 1.8.3 Resonances 30 1.9 Semiclassical Mechanics 31 1.9.1 The WKB Approximation 31 1.9.2 The EBK
Converting Classical Theories to Quantum Theories by Solutions of the Hamilton-Jacobi Equation
Zhi-Qiang Guo; Ivan Schmidt
2012-08-03T23:59:59.000Z
By employing special solutions of the Hamilton-Jacobi equation and tools from lattice theories, we suggest an approach to convert classical theories to quantum theories for mechanics and field theories. Some nontrivial results are obtained for a gauge field and a fermion field. For a topologically massive gauge theory, we can obtain a first order Lagrangian with mass term. For the fermion field, in order to make our approach feasible, we supplement the conventional Lagrangian with a surface term. This surface term can also produce the massive term for the fermion.
Conjugates, Filters and Quantum Mechanics
Alexander Wilce
2014-11-18T23:59:59.000Z
The Jordan structure of finite-dimensional quantum theory is derived, in a conspicuously easy way, from a few simple postulates concerning abstract probabilistic models (each defined by a set of basic measurements and a convex set of states). A key assumption is that each system $A$ can be paired with an isomorphic conjugate system, $\\bar{A}$, by means of a non-signaling bipartite state $\\eta_A$ perfectly and uniformly correlating each basic measurement on $A$ with its counterpart on $\\bar{A}$. In the case of a quantum-mechanical system associated with a complex Hilbert space ${\\mathbf H}$, the conjugate system is that associated with the conjugate Hilbert space $\\bar{\\mathbf H}$, and $\\eta_A$ corresponds to the standard maximally entangled EPR state on ${\\mathbf H} \\otimes \\bar{\\mathbf H}$.
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.
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.
Errors and paradoxes in quantum mechanics
D. Rohrlich
2007-08-28T23:59:59.000Z
Errors and paradoxes in quantum mechanics, entry in the Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, ed. F. Weinert, K. Hentschel, D. Greenberger and B. Falkenburg (Springer), to appear
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.
Chaos and low-order corrections to classical mechanics or geometrical optics
Sundaram, B. (Department of Physics and Center for Theoretical Physics, Texas A M University, College Station, Texas 77843-4242 (United States)); Milonni, P.W. (Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States))
1995-03-01T23:59:59.000Z
Based on simple first-order quantum corrections to classical equations of motion, which we show to be closely related to Gaussian wave-packet dynamics (GWD) and a time-dependent variational principle (TDVP), we deduce that quantum corrections to classical dynamics should typically become most pronounced when the classical system becomes chaotic. The time duration over which classical dynamics, GWD, or TDVP may provide good approximations is much shorter when the classical dynamics are chaotic. However, for certain situations involving very short laser pulses, these approximations can be very accurate. The same concepts are applicable to paraxial wave optics, which may offer simpler experimental studies of quantum chaos'': the distinction between classical and quantum'' chaos is in large part the distinction between ray versus wave behavior.
An extended phase space for Quantum Mechanics
C. Lopez
2015-09-23T23:59:59.000Z
The standard formulation of Quantum Mechanics violates locality of interactions and the action reaction principle. An alternative formulation in an extended phase space could preserve both principles, but Bell's theorems show that a distribution of probability in a space of local variables can not reproduce the quantum correlations. An extended phase space is defined in an alternative formulation of Quantum Mechanics. Quantum states are represented by a complex va\\-lued distribution of amplitude, so that Bell's theorems do not apply.
Intrinsic decoherence dynamics in smooth Hamiltonian systems: Quantum-classical correspondence
Gong, Jiangbin; Brumer, Paul [Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Canada M5S 3H6 (Canada)
2003-08-01T23:59:59.000Z
A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences between the classical and quantum decoherence dynamics of an initial quantum state are exposed using both analytical and computational results. In particular, the classicality of early-time intrinsic decoherence dynamics is explored analytically using a second-order perturbative treatment, and an interesting connection between decoherence rates and the stability nature of classical trajectories is revealed in a simple approximate classical theory of intrinsic decoherence dynamics. The results offer deeper insights into decoherence, dynamics of quantum entanglement, and quantum chaos.
Gennady P. Berman; Fausto Borgonovi; Diego A. R. Dalvit
2008-01-29T23:59:59.000Z
We review our results on a mathematical dynamical theory for observables for open many-body quantum nonlinear bosonic systems for a very general class of Hamiltonians. We show that non-quadratic (nonlinear) terms in a Hamiltonian provide a singular "quantum" perturbation for observables in some "mesoscopic" region of parameters. In particular, quantum effects result in secular terms in the dynamical evolution, that grow in time. We argue that even for open quantum nonlinear systems in the deep quasi-classical region, these quantum effects can survive after decoherence and relaxation processes take place. We demonstrate that these quantum effects in open quantum systems can be observed, for example, in the frequency Fourier spectrum of the dynamical observables, or in the corresponding spectral density of noise. Estimates are presented for Bose-Einstein condensates, low temperature mechanical resonators, and nonlinear optical systems prepared in large amplitude coherent states. In particular, we show that for Bose-Einstein condensate systems the characteristic time of deviation of quantum dynamics for observables from the corresponding classical dynamics coincides with the characteristic time-scale of the well-known quantum nonlinear effect of phase diffusion.
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.
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.
Bohmian particle trajectories contradict quantum mechanics
Michael Zirpel
2009-03-23T23:59:59.000Z
The Bohmian interpretation of quantum mechanics adds particle trajectories to the wave function and ensures that the probability distribution of the particle positions agrees with quantum mechanics at any time. This is not sufficient to avoid contradictions with quantum mechanics. There are correlations between particle positions at different times which cannot be reproduced with real particle trajectories. A simple rearrangement of an experimental test of the Bell-CHSH inequality demonstrates this.
Quantum Mechanics and Closed Timelike Curves
Florin Moldoveanu
2007-04-23T23:59:59.000Z
General relativity allows solutions exhibiting closed timelike curves. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. The implications of self-consistent interactions on acausal region of space-time are investigated. If the correspondence principle is true, then all generalizations of quantum mechanics on acausal manifolds are not renormalizable. Therefore quantum mechanics can only be defined on global hyperbolic manifolds and all general relativity solutions exhibiting time travel are unphysical.
Quantum mechanics as a complete physical theory
D. A. Slavnov
2002-11-10T23:59:59.000Z
We show that the principles of a ''complete physical theory'' and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that allow constructing a renewed mathematical scheme of quantum mechanics. This scheme involves the standard mathematical formalism of quantum mechanics. Simultaneously, it contains a mathematical object that adequately describes a single experiment. We give an example of the application of the proposed scheme.
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.
Deformed Geometric Algebra and Supersymmetric Quantum Mechanics
Peter Henselder
2006-09-09T23:59:59.000Z
Deforming the algebraic structure of geometric algebra on the phase space with a Moyal product leads naturally to supersymmetric quantum mechanics in the star product formalism.
The Hamilton-Jacobi Theory, Quantum Mechanics and General Relativity
B. G. Sidharth
2005-10-12T23:59:59.000Z
The Hamilton-Jacobi theory of Classical Mechanics can be extended in a novel manner to systems which are fuzzy in the sense that they can be represented by wave functions. A constructive interference of the phases of the wave functions then gives us back Classical systems. In a suitable description this includes both Quantum Theory and General Relativity in the well known superspace formulation. However, there are several nuances which provide insight into these latter systems. All this is considered in this paper together with suitable generalization, to cascades of super universes.
Thermalization and possible quantum relaxation times in "classical" fluids: theory and experiment
Z. Nussinov; F. Nogueira; M. Blodgett; K. F. Kelton
2015-09-07T23:59:59.000Z
Quantum effects in material systems are often pronounced at low energies and become insignificant at high temperatures. We find that, perhaps counterintuitively, certain quantum effects may follow the opposite route and become sharp when extrapolated to high temperature within a "classical" liquid phase. In the current work, we suggest basic quantum bounds on relaxation (and thermalization) times, examine kinetic theory by taking into account such possible fundamental quantum time scales, find new general equalities connecting semi-classical dynamics and thermodynamics to Planck's constant, and compute current correlation functions. Our analysis suggests that, on average, the extrapolated high temperature dynamical viscosity of general liquids may tend to a value set by the product of the particle number density ${\\sf n}$ and Planck's constant $h$. We compare this theoretical result with experimental measurements of an ensemble of 23 metallic fluids where this seems to indeed be the case. The extrapolated high temperature viscosity of each of these liquids $\\eta$ divided (for each respective fluid by its value of ${\\sf n} h$) veers towards a Gaussian with an ensemble average value that is close to unity up to an error of size $0.6 \\%$. Inspired by the Eigenstate Thermalization Hypothesis, we suggest a relation between the lowest equilibration temperature to the melting or liquidus temperature and discuss a possible corollary concerning the absence of finite temperature "ideal glass" transitions. We suggest a general quantum mechanical derivation for the viscosity of glasses at general temperatures. We invoke similar ideas to discuss other transport properties and demonstrate how simple behaviors including resistivity saturation and linear $T$ resistivity may appear very naturally. Our approach suggests that minimal time lags may be present in fluid dynamics.
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.
Iyengar, Srinivasan S.
Quantum Mechanics Course Number: C668 C668: Special topics in physical chemistry: Advanced Quantum Mechanics Instructor: Srinivasan S. Iyengar Office Hours Wednesday, Friday 10:30AM-12PM (Chemistry C202B@gmail.com Chemistry, Indiana University i c 2014, Srinivasan S. Iyengar (instructor) #12;Quantum Mechanics Course
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.
Mechanical quantum resonators A. N. Cleland
Geller, Michael R.
Mechanical quantum resonators A. N. Cleland and M. R. Geller Department of Physics, University based on the integration of GHz-frequency mechanical resonators with Josephson phase qubits, which have
Quantum mechanics without potential function
A. D. Alhaidari; M. E. H. Ismail
2015-06-26T23:59:59.000Z
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\\"odinger equation, which is solved for the wave function, bound states energy spectrum and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which is written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states and resonances. This formulation enables one to handle not only the well-known quantum systems but also previously untreated ones. Illustrative examples are given for two- and there-parameter systems.
Quaternionic Formulation of Supersymmetric Quantum Mechanics
Seema Rawat; O. P. S. Negi
2007-03-18T23:59:59.000Z
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions. Supercharges, superpartner Hamiltonians and energy eigenvalues are discussed and it has been shown that the results are consistent with the results of quantum mechanics.
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.
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).
An entropic picture of emergent quantum mechanics
D. Acosta; P. Fernandez de Cordoba; J. M. Isidro; J. L. G. Santander
2011-09-20T23:59:59.000Z
Quantum mechanics emerges a la Verlinde from a foliation of space by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantised in units of Boltzmann's constant k. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on space. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant h from Boltzmann's constant k.
Trading classical communication, quantum communication, and entanglement in quantum Shannon theory
Min-Hsiu Hsieh; Mark M. Wilde
2010-04-09T23:59:59.000Z
We give trade-offs between classical communication, quantum communication, and entanglement for processing information in the Shannon-theoretic setting. We first prove a unit-resource capacity theorem that applies to the scenario where only the above three noiseless resources are available for consumption or generation. The optimal strategy mixes the three fundamental protocols of teleportation, super-dense coding, and entanglement distribution. We then provide an achievable rate region and a matching multi-letter converse for the direct static capacity theorem. This theorem applies to the scenario where a large number of copies of a noisy bipartite state are available (in addition to consumption or generation of the above three noiseless resources). Our coding strategy involves a protocol that we name the classically-assisted state redistribution protocol and the three fundamental protocols. We finally provide an achievable rate region and a matching mutli-letter converse for the direct dynamic capacity theorem. This theorem applies to the scenario where a large number of uses of a noisy quantum channel are available in addition to the consumption or generation of the three noiseless resources. Our coding strategy combines the classically-enhanced father protocol with the three fundamental unit protocols.
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
Particle and Wave: Developing the Quantum Wave Accompanying a Classical Particle
C. L. Herzenberg
2008-12-04T23:59:59.000Z
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of reference of a moving particle is expressed in terms of the coordinates in the laboratory frame of reference in order to provide an initial spatiotemporal function to work from in initiating the development of a quantum wave. When temporal periodicity is ascribed to the particle, a provisional spatiotemporal function for a particle travelling at constant velocity manifests itself as an running wave characterized by parameters associated with the moving particle. A wave description for bidirectional motion is generated based on an average time coordinate for a combination of oppositely directed elementary running waves, and the resulting spatiotemporal function exhibits wave behavior characteristic of a standing wave. Ascribing directional orientation to the intrinsic periodicity of the particle introduces directional sub-states; variations in the relative number of sub-states as a function of angle in combined states lead to spatially varying magnitudes for the associated waves. Further analysis leads to full mathematical expression for all waves representing free particle motion. A generalization for particles subject to force fields enables us to develop a governing differential equation identical in form to the Schroedinger equation.
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.
Trading classical communication, quantum communication, and entanglement in quantum Shannon theory
Hsieh, Min-Hsiu
2009-01-01T23:59:59.000Z
We give optimal trade-offs between classical communication, quantum communication, and entanglement for processing information in the Shannon-theoretic setting. We first prove a "unit-resource" capacity theorem that applies to the scenario where only the above three noiseless resources are available for consumption or generation. The optimal strategy mixes the three fundamental protocols of teleportation, super-dense coding, and entanglement distribution. Furthermore, no protocol other than these three fundamental ones is necessary to generate the unit resource capacity region. We then prove the "direct static" capacity theorem that applies to the scenario where a large number of copies of a noisy bipartite state are available (in addition to consumption or generation of the above three noiseless resources). The result is that a coding strategy involving the classically-assisted mother protocol and the three fundamental protocols is optimal. We finally prove the "direct dynamic" capacity theorem. This theorem...
David Brizuela
2014-11-03T23:59:59.000Z
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences between the classical and quantum dynamics. In particular, there are two different sources of quantum effects. Distributional effects, which are also present in the classical evolution of an extended distribution, are due to the fact that all moments can not be vanishing because of the Heisenberg uncertainty principle. In addition, the non-commutativity of the basic quantum operators add some terms to the quantum equations of motion that explicitly depend on the Planck constant and are not present in the classical setting. These are thus purely-quantum effects. Some particular Hamiltonians are analyzed that have very special properties regarding the evolution they generate in the classical and quantum sector. In addition, a large class of inequalities obeyed by high-order statistical moments, and in particular uncertainty relations that bound the information that is possible to obtain from a quantum system, are derived.
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.
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
Dynamics of quantum-classical hybrid systems: Effect of matter-wave pressure
Shen, J. [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Huang, X. L. [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); School of Physics and Electronic Technology, Liaoning Normal University, Dalian 116029 (China); Yi, X. X. [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Centre for Quantum Technologies and Department of Physics, National University of Singapore, Singapore 117543 (Singapore); Wu Chunfeng; Oh, C. H. [Centre for Quantum Technologies and Department of Physics, National University of Singapore, Singapore 117543 (Singapore)
2010-12-15T23:59:59.000Z
Radiation pressure affects the kinetics of a system exposed to radiation and it constitutes the basis of laser cooling. In this article, we study matter-wave pressure through examining the dynamics of a quantum-classical hybrid system. The quantum and classical subsystems are affected mutually via a changing boundary condition. Two systems, that is, an atom and a Bose-Einstein condensate (BEC), are considered as the quantum subsystems, while an oscillating wall is taken as the classical subsystem. We show that the classical subsystem would experience a force proportional to Q{sup -3} from the quantum atom, where Q denotes the distance between the two walls, whereas it acquires an additional force proportional to Q{sup -2} from the BEC due to the atom-atom interaction in the BEC. These forces can be understood as the matter-wave pressure.
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 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.
Four-dimensional understanding of quantum mechanics
Jarek Duda
2009-10-14T23:59:59.000Z
In this paper I will try to convince that quantum mechanics does not have to lead to indeterminism, but is just a natural consequence of four-dimensional nature of our world - that for example particles shouldn't be imagined as 'moving points' in space, but as their trajectories in the spacetime like in optimizing action formulation of Lagrangian mechanics. There will be analyzed simplified model - Boltzmann distribution among trajectories occurs to give quantum mechanic like behavior - for example electron moving in proton's potential would make some concrete trajectory which average exactly to the probability distribution of the quantum mechanical ground state. We will use this model to build intuition about quantum mechanics and discuss its generalizations to get some effective approximation of physics. We will see that topological excitations of the simplest model obtained this way already creates known from physics particle structure, their decay modes and electromagnetic/gravitational interactions between them.
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.
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.
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...
Description of classical and quantum interference in view of the concept of flow line
M. Davidovic; A. S. Sanz; M. Bozic
2015-08-21T23:59:59.000Z
Bohmian mechanics, a hydrodynamic formulation of quantum mechanics, relies on the concept of trajectory, which evolves in time in compliance with dynamical information conveyed by the wave function. Here this appealing idea is considered to analyze both classical and quantum interference, thus providing an alternative and more intuitive framework to understand the time-evolution of waves, either in terms of the flow of energy (for mechanical waves, sound waves, electromagnetic waves, for instance) or, analogously, the flow of probability (quantum waves), respectively. Furthermore, this procedure also supplies a more robust explanation of interference phenomena, which currently is only based on the superposition principle. That is, while this principle only describes how different waves combine and what effects these combinations may lead to, flow lines provide a more precise explanation on how the energy or probability propagate in space before, during and after the combination of such waves, without dealing with them separately (i.e., the combination or superposition is taken as a whole). In this sense, concepts such as constructive and destructive interference, typically associated with the superposition principle, physically correspond to more or less dense swarms of (energy or probability) flow lines, respectively. A direct consequence of this description is that, when considering the distribution of electromagnetic energy flow lines behind two slits, each one covered by a differently oriented polarizer, it is naturally found that external observers' information on the slit crossed by single photons (understood as energy parcels) is totally irrelevant for the existence of interference fringes, in striking contrast with what is commonly stated and taught.
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.
Quantum Mechanics and the Generalized Uncertainty Principle
Jang Young Bang; Micheal S. Berger
2006-11-30T23:59:59.000Z
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.
Classical analogous of quantum cosmological perfect fluid models
A. B. Batista; J. C. Fabris; S. V. B. Goncalves; J. Tossa
2000-11-28T23:59:59.000Z
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.
The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
Zunaira Babar; Panagiotis Botsinis; Dimitrios Alanis; Soon Xin Ng; Lajos Hanzo
2015-03-09T23:59:59.000Z
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed by exploiting a concatenated code structure, which invokes iterative decoding. Therefore, in this paper we provide an extensive step-by-step tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided concatenated quantum codes based on the underlying quantum-to-classical isomorphism. These design lessons are then exemplified in the context of our proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the outer component of a concatenated quantum code. The proposed QIRCC can be dynamically adapted to match any given inner code using EXIT charts, hence achieving a performance close to the hashing bound. It is demonstrated that our QIRCC-based optimized design is capable of operating within 0.4 dB of the noise limit.
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.
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...
Higher-order semantics for quantum programming languages with classical control
Philip Atzemoglou
2013-11-26T23:59:59.000Z
This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus for dagger compact categories. Our second contribution lifts the expressive power of the dagger lambda calculus, to that of a quantum programming language, by adding classical control in the form of complementary classical structures and dualisers. Finally, our third contribution demonstrates how our lambda calculus can be applied to various well known problems in quantum computation.
On a New Form of Quantum Mechanics (II)
N. Gorobey; A. Lukyanenko; I. Lukyanenko
2009-12-16T23:59:59.000Z
The correspondence of a new form of quantum mechanics based on a quantum version of the action principle, which was proposed earlier [arXiv:0807.3508], with the ordinary quantum mechanics is established. New potentialities of the quantum action principle in the interpretation of quantum mechanics are considered.
CLNS 96/1399 Peculiarities of Quantum Mechanics
CLNS 96/1399 Peculiarities of Quantum Mechanics: Origins and Meaning Yuri F. Orlov Floyd R. Newman, specifically quantum, features of quantum mechanics --- quan tum nonlocality, indeterminism, interference are quantum observables themselves and are represented in quantum mechanics by density matrices of pure states
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.
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.
Similarity between quantum mechanics and thermodynamics: Entropy, temperature, and Carnot cycle
Sumiyoshi Abe; Shinji Okuyama
2011-03-04T23:59:59.000Z
Similarity between quantum mechanics and thermodynamics is discussed. It is found that if the Clausius equality is imposed on the Shannon entropy and the analogue of the heat quantity, then the value of the Shannon entropy comes to formally coincide with that of the von Neumann entropy of the canonical density matrix, and pure-state quantum mechanics apparently transmutes into quantum thermodynamics. The corresponding quantum Carnot cycle of a simple two-state model of a particle confined in a one-dimensional infinite potential well is studied, and its efficiency is shown to be identical to the classical one.
Similarity between quantum mechanics and thermodynamics: Entropy, temperature, and Carnot cycle
Abe, Sumiyoshi
2010-01-01T23:59:59.000Z
Similarity between quantum mechanics and thermodynamics is discussed. It is found that if the Clausius equality is imposed on the Shannon entropy and the analogue of the heat quantity, then the value of the Shannon entropy comes to formally coincide with that of the von Neumann entropy of the canonical density matrix, and pure-state quantum mechanics apparently transmutes into quantum thermodynamics. The corresponding quantum Carnot cycle of a simple two-state model of a particle confined in a one-dimensional infinite potential well is studied, and its efficiency is shown to be identical to the classical one.
Localization of quantum objects in an expanding universe and cosmologically induced classicality
C. L. Herzenberg
2010-11-22T23:59:59.000Z
Independent studies by different authors have proposed that classicality may be induced in quantum objects by cosmological constraints presented by an expanding universe of finite extent in space-time. Cosmological effects on a quantum system can be explored in one approach by considering an object at rest in space with a universal Hubble expansion taking place away from it, and developing a Schroedinger type governing differential equation incorporating an intrinsic expansion speed. Wave function solutions to this governing equation exhibit pronounced central localization. The extent of concentration of probability depends on mass; objects with small masses tend to behave in a delocalized manner as ordinary quantum objects do in a static space, while quantum objects with large masses are concentrated into much smaller regions. To develop a criterion for classicality, we consider that if the size of the localized region of concentrated probability density is larger than the size of the corresponding extended object, then quantum behavior could be expected; whereas if the region of high probability density for the location of the center of mass is smaller than the size of the object, the object would behave in a more classical manner. The resultant size threshold for classicality accords with results of other studies examining these issues based on uncertainty relations and wave packets. This size threshold is informative for the case of compact extended objects and, as the constraint applies to the center of mass of the system, does not lead to inconsistencies for quantum correlations between distant entangled quantum objects. While local decoherence may lead to classicality under a variety of conditions, cosmologically induced classicality would appear to cause fundamental limitations on quantum behavior in our universe.
On the geometry of the energy operator in quantum mechanics
Vitolo, Raffaele
with several contributions from many authors. 1 Introduction One of the problems of quantum mechanical theories
Quantum Mechanics Summary/Review Spring 2009 Compton Lecture Series
Quantum Mechanics Summary/Review Spring 2009 Compton Lecture Series: From Quantum Mechanics one component at a time. · Planck's constant determines the scale at which quantum mechanical effects could get rid of quantum mechanical effects The "wavelength" of particles given by h mv would all
Chen, Yiling
Chapter 2 Classic Mechanism Design Mechanism design is the sub- eld of microeconomics and game-theoretic approach to mechanism design, and presents important possibility and impossibilityresults in the literature and without computational limitations. The next chapter discusses the emerging eld of computational mechanism
Mark D. Lee; Janne Ruostekoski
2014-08-28T23:59:59.000Z
We formulate computationally efficient classical stochastic measurement trajectories for a multimode quantum system under continuous observation. Specifically, we consider the nonlinear dynamics of an atomic Bose-Einstein condensate contained within an optical cavity subject to continuous monitoring of the light leaking out of the cavity. The classical trajectories encode within a classical phase-space representation a continuous quantum measurement process conditioned on a given detection record. We derive a Fokker-Planck equation for the quasi-probability distribution of the combined condensate-cavity system. We unravel the dynamics into stochastic classical trajectories that are conditioned on the quantum measurement process of the continuously monitored system, and that these trajectories faithfully represent measurement records of individual experimental runs. Since the dynamics of a continuously measured observable in a many-atom system can be closely approximated by classical dynamics, the method provides a numerically efficient and accurate approach to calculate the measurement record of a large multimode quantum system. Numerical simulations of the continuously monitored dynamics of a large atom cloud reveal considerably fluctuating phase profiles between different measurement trajectories, while ensemble averages exhibit local spatially varying phase decoherence. Individual measurement trajectories lead to spatial pattern formation and optomechanical motion that solely result from the measurement backaction. The backaction of the continuous quantum measurement process, conditioned on the detection record of the photons, spontaneously breaks the symmetry of the spatial profile of the condensate and can be tailored to selectively excite collective modes.
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.
Lecture Notes in Quantum Mechanics
Doron Cohen
2013-08-27T23:59:59.000Z
These lecture notes cover undergraduate textbook topics (e.g. as in Sakurai), and also additional advanced topics at the same level of presentation. In particular: EPR and Bell; Basic postulates; The probability matrix; Measurement theory; Entanglement; Quantum computation; Wigner-Weyl formalism; The adiabatic picture; Berry phase; Linear response theory; Kubo formula; Modern approach to scattering theory with mesoscopic orientation; Theory of the resolvent and the Green function; Gauge and Galilei Symmetries; Motion in magnetic field; Quantum Hall effect; Quantization of the electromagnetic field; Fock space formalism.
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.
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...
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.
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.
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.
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 ...
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.
Testing the limits of quantum mechanical superpositions
Markus Arndt; Klaus Hornberger
2014-10-01T23:59:59.000Z
Quantum physics has intrigued scientists and philosophers alike, because it challenges our notions of reality and locality--concepts that we have grown to rely on in our macroscopic world. It is an intriguing open question whether the linearity of quantum mechanics extends into the macroscopic domain. Scientific progress over the last decades inspires hope that this debate may be decided by table-top experiments.
Probing quantum-classical boundary with compression software
Hou Shun Poh; Marcin Markiewicz; Pawe? Kurzy?ski; Alessandro Cerè; Dagomir Kaszlikowski; Christian Kurtsiefer
2015-04-13T23:59:59.000Z
We experimentally demonstrate that it is impossible to simulate quantum bipartite correlations with a deterministic universal Turing machine. Our approach is based on the Normalized Information Distance (NID) that allows the comparison of two pieces of data without detailed knowledge about their origin. Using NID, we derive an inequality for output of two local deterministic universal Turing machines with correlated inputs. This inequality is violated by correlations generated by a maximally entangled polarization state of two photons. The violation is shown using a freely available lossless compression program. The presented technique may allow to complement the common statistical interpretation of quantum physics by an algorithmic one.
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.
Emergent Quantum Mechanics and Emergent Symmetries
Gerard 't Hooft
2007-07-31T23:59:59.000Z
Quantum mechanics is 'emergent' if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present in the underlying deterministic system. Such theories allow for a natural explanation of the existence of gauge equivalence classes (gauge orbits), including the equivalence classes generated by general coordinate transformations. Thus, local gauge symmetries and general coordinate invariance could be emergent symmetries, and this might lead to new alleys towards understanding the flatness problem of the Universe.
On Time. 6b: Quantum Mechanical Time
C. K. Raju
2008-08-09T23:59:59.000Z
The existence of small amounts of advanced radiation, or a tilt in the arrow of time, makes the basic equations of physics mixed-type functional differential equations. The novel features of such equations point to a microphysical structure of time. This corresponds to a change of logic at the microphysical level. We show that the resulting logic is a quantum logic. This provides a natural and rigorous explanation of quantum interference. This structured-time interpretation of quantum mechanics is briefly compared with various other interpretations of q.m.
CLNS 96/1443 Peculiarities of Quantum Mechanics
CLNS 96/1443 REVISED Peculiarities of Quantum Mechanics: Origins and Meaning 1 Yuri F. Orlov Floyd The most peculiar, specifically quantum, features of quantum mechanics --- quan tum nonlocality mechanics 1 This paper, to be presented to the Nordic Symposium on Basic Problems in Quantum Physics, June
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
A Quantum Broadcasting Problem in Classical Low Power Signal Processing
Dominik Janzing; Bastian Steudel
2006-09-21T23:59:59.000Z
We pose a problem called ``broadcasting Holevo-information'': given an unknown state taken from an ensemble, the task is to generate a bipartite state transfering as much Holevo-information to each copy as possible. We argue that upper bounds on the average information over both copies imply lower bounds on the quantum capacity required to send the ensemble without information loss. This is because a channel with zero quantum capacity has a unitary extension transfering at least as much information to its environment as it transfers to the output. For an ensemble being the time orbit of a pure state under a Hamiltonian evolution, we derive such a bound on the required quantum capacity in terms of properties of the input and output energy distribution. Moreover, we discuss relations between the broadcasting problem and entropy power inequalities. The broadcasting problem arises when a signal should be transmitted by a time-invariant device such that the outgoing signal has the same timing information as the incoming signal had. Based on previous results we argue that this establishes a link between quantum information theory and the theory of low power computing because the loss of timing information implies loss of free energy.
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.
An axiomatic basis for quantum mechanics
Gianni Cassinelli; Pekka Lahti
2015-08-15T23:59:59.000Z
In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in this derivation are the co-ordinatization of generalized geometries and a theorem of Sol\\'er which characterizes Hilbert spaces among the orthomodular spaces. A generalized Wigner theorem is applied to reduce some of the assumptions of the theorem of Sol\\'er to the theory of symmetry in quantum mechanics. Since this reduction is only partial we also point out the remaining open questions.
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.
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 ...
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.
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.
Operator structure of a non quantum and a non classical system Diederik Aerts and Bart D'Hooghe
Aerts, Diederik
Operator structure of a non quantum and a non classical system Diederik Aerts and Bart D: Aerts, D. and D'Hooghe, B., 1996, "Operator structure of a non-quantum and a non-classical system", Int the set of operators of this general model, and investigate under which circumstances it is possible
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
Roma "La Sapienza", Università di
Spin-to-orbital conversion of the angular momentum of light and its classical and quantum apply. View the table of contents for this issue, or go to the journal homepage for more Home Search momentum of light and its classical and quantum applications Lorenzo Marrucci1,2 , Ebrahim Karimi1 , Sergei
Rütz, Helge; Suche, Hubertus; Silberhorn, Christine
2015-01-01T23:59:59.000Z
We propose and characterize a quantum interface between telecommunication wavelengths (1311 nm) and an Yb-dipole transition (369.5 nm) based on a second order sum frequency process in a PPKTP waveguide. An external (internal) conversion efficiency above 5% (10%) is shown using classical bright light.
Laser Cooling from the Semi-Classical to the Quantum Regime.
Dalibard, Jean
Laser Cooling from the Semi-Classical to the Quantum Regime. J. DALIBARDand Y. CASTIN Laboratoire with mul- tiple quasi-resonant laser beams [l]. The lirnits of laser cooling in these so-called optical; = a few -, M where hk is the momentum of a photon involved in the cooling process and M is the atomic mass
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.
Joao Batista Rosa Silva; Rubens Viana Ramos
2006-07-26T23:59:59.000Z
Aiming the construction of quantum computers and quantum communication systems based on optical devices, in this work we present possible implementations of quantum and classical CNOTs gates, as well an optical setup for generation and distribution of bipartite entangled states, using linear optical devices and photon number quantum non-demolition measurement.
Emergence and Computation at the Edge of Classical and Quantum Systems
Ignazio Licata
2007-11-19T23:59:59.000Z
The problem of emergence in physical theories makes necessary to build a general theory of the relationships between the observed system and the observing system. It can be shown that there exists a correspondence between classical systems and computational dynamics according to the Shannon-Turing model. A classical system is an informational closed system with respect to the observer; this characterizes the emergent processes in classical physics as phenomenological emergence. In quantum systems, the analysis based on the computation theory fails. It is here shown that a quantum system is an informational open system with respect to the observer and able to exhibit processes of observational, radical emergence. Finally, we take into consideration the role of computation in describing the physical world.
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.
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.
Philosophy of Mind and the Problem of Free Will in the Light of Quantum Mechanics.
Stapp, Henry P
2008-01-01T23:59:59.000Z
Foundations of Quantum Mechanics. (Princeton UniversityMind, Matter, and Quantum Mechanics, (Springer, Berlin & NewMindful Universe: Quantum Mechanics and the Participating
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 $\\bar{n}\\to\\infty$.
Quantum and Classical Description of H Atom Under Magnetic Field and Quadrupole Trap Potential
Mahecha, J. [Institute of Physics, University of Antioquia, AA 1226, Medellin (Colombia); LPMC, Institute of Physics, University Paul Verlaine, 1 Bv Arago, 57078 Metz Cedex 3 (France); Salas, J. P. [Area of Applied Physics, University of La Rioja, C/Madre de Dios 51, 26006, Logrono (Spain)
2006-12-01T23:59:59.000Z
A discussion regarding the energy levels spectrum of quantum systems whose classical analogous has states of chaotic motion is presented. The chaotic dynamics of the classical underlying system has its manifestation in the wave functions (in the form of 'scars') and in the energy levels (in the form of 'statistical repulsion' of the energy levels). The above mentioned signatures are named 'quantum chaos'. A typical study of quantum chaos requires finding accurate energy eigenvalues of highly excited states, to calculate the nearest neighbors spacing between levels, to perform the 'unfolding' of the spectrum in order to separate the fluctuations, and finally to find the probability distribution of the unfolded spectrum. This is exemplified by the hydrogen atom under uniform magnetic field and a quadrupole electric field.
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.
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.
Semi-classical approach to quantum black holes
Euro Spallucci; Anais Smailagic
2014-10-07T23:59:59.000Z
In this Chapter we would like to review a "~phenomenological~" approach taking into account the most fundamental feature of string theory or, more in general, of quantum gravity, whatever its origin, which is the existence of a minimal length in the space-time fabric. This length is generally identified with the Planck length, or the string length, but it could be also much longer down to the TeV region. A simple and effective way to keep track of the effects the minimal length in black hole geometries is to solve the Einstein equations with an energy momentum tensor describing non point-like matter. The immediate consequence is the absence of any curvature singularity. Where textbook solutions of the Einstein equations loose any physical meaning because of infinite tidal forces, we find a de Sitter vacuum core of high, but finite, energy density and pressure. An additional improvement regards the final stage of the black hole evaporation leading to a vanishing Hawking temperature even in the neutral, non-rotating, case. In spite of th simplicity of this model we are able to describe the final stage of the black hole evaporation, resulting in a cold remnant with a degenerate, extremal, horizon of radius of the order of the minimal length. In this chapter we shall describe only neutral, spherically symmetric, regular black holes although charged, rotating and higher dimensional black holes can be found in the literature.
The quantum-classical boundary and the moments of inertia of physical objects
C. L. Herzenberg
2009-08-12T23:59:59.000Z
During the last few years, several studies have proposed the existence of a threshold separating classical from quantum behavior of objects that is dependent on the size and mass of an object as well as being dependent on certain properties usually associated with the universe as a whole. Here, we reexamine the results of these studies and recast the threshold criteria in terms of a critical threshold value for the moments of inertia of physical objects. Physical objects having moments of inertia above this critical threshold value would be expected to behave necessarily in a classical manner in terms of their center of mass motion as entire objects, while physical objects having moments of inertia lower than this threshold value could exhibit quantum behavior unless brought into classicality by other effects. A comparison with observed values of moments of inertia is presented, and the moment of inertia is suggested as a classifying parameter for examination of the quantum versus classical behavior of objects in the mesoscale domain.
The syllabus of the Course 624 Quantum Mechanics 2
The syllabus of the Course 624 Quantum Mechanics 2 Spring 2009. Instructor V.L. Pokrovsky. 1. Many-body quantum mechanics. Second quantization. Spin and statistics. Bose- Einstein condensation. 6's phase. Landau-Zener theory. Principal textbook: E. Merzbacher, Quantum Mechanics, 3-d edition, Wiley
D'Ariano, Giacomo Mauro
situations is it possible to perfectly recover quantum coherence by monitoring the environment of decoher- ence by monitoring--i.e., measuring--the environment. On the contrary, for quantum systemsInverting Quantum Decoherence by Classical Feedback from the Environment Francesco Buscemi, Giulio
Does quantum mechanics require non-locality?
Ghenadie N. Mardari
2014-10-29T23:59:59.000Z
Non-commutative properties of single quanta must violate the limit of Bell's theorem, but not the boundary of Tsirelson's theorem. This is a consequence of three basic principles: superposition (every quantum is in many states at the same time), correspondence (only the net state of interference is real), and uncertainty (conjugate variables have inversely proportional spectra). The two conditions have only been verified with entangled pairs of quanta. It is not possible to perform incompatible measurements on the same entity. Hence, the principles of quantum mechanics cannot be verified directly. At least one of them could be wrong. Though, as shown by EPR, this can only be true if non-locality is at work. In light of the latest developments in quantum theory, even that assumption is insufficient. Non-local effects are either unable to cross Bell's limit, or forced to violate Tsirelson's bound. New layers of hidden variables are required to maintain belief in action-at-a-distance, but the three principles cannot be rejected in any case. Therefore, quantum mechanics is immune to this challenge. The hypothesis of non-locality is superfluous.
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 ...
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.
The preparation of states in quantum mechanics
Juerg Froehlich; Baptiste Schubnel
2014-09-28T23:59:59.000Z
The important problem of how to prepare a quantum mechanical system, $S$, in a specific initial state of interest - e.g., for the purposes of some experiment - is addressed. Three distinct methods of state preparation are described. One of these methods has the attractive feature that it enables one to prepare $S$ in a preassigned initial state with certainty; i.e., the probability of success in preparing $S$ in a given state is unity. This method relies on coupling $S$ to an open quantum-mechanical environment, $E$, in such a way that the dynamics of $S \\vee E$ pulls the state of $S$ towards an "attractor", which is the desired initial state of $S$. This method is analyzed in detail.
University) [Johns Hopkins University] 71 CLASSICAL AND QUANTUM MECHANICS,
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AFDC Printable Version Share this resource Send a link to EERE: Alternative Fuels Data Center Home Page to someone by E-mail Share EERE: Alternative Fuels Data Center Home Page on Facebook Tweet about EERE: Alternative Fuels Data Center Home Page on Twitter Bookmark EERE:1 First Use of Energy for All Purposes (Fuel and Nonfuel), 2002; Level:5 TablesExports to3,1,50022,3,,0,,6,1,Separation 23TribalInformation Access toTen Problems in ExperimentalUnitarity check in gravitational
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.
Physical Interpretations of Nilpotent Quantum Mechanics
Peter Rowlands
2010-04-09T23:59:59.000Z
Nilpotent quantum mechanics provides a powerful method of making efficient calculations. More importantly, however, it provides insights into a number of fundamental physical problems through its use of a dual vector space and its explicit construction of vacuum. Physical interpretation of the nilpotent formalism is discussed with respect to boson and baryon structures, the mass-gap problem, zitterbewgung, Berry phase, renormalization, and related issues.
Quantum Chaos via the Quantum Action
H. Kröger
2002-12-16T23:59:59.000Z
We discuss the concept of the quantum action with the purpose to characterize and quantitatively compute quantum chaos. As an example we consider in quantum mechanics a 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling - which is classically a chaotic system. We compare Poincar\\'e sections obtained from the quantum action with those from the classical action.
Semi-classical formula beyond the Ehrenfest time in quantum chaos. (I) Trace formula
Frederic Faure
2007-03-19T23:59:59.000Z
We consider a nonlinear area preserving Anosov map M on the torus phase space, which is the simplest example of a fully chaotic dynamics. We are interested in the quantum dynamics for long time, generated by the unitary quantum propagator Mq. The usual semi-classical Trace formula expresses Tr(Mq^t) for finite time t, in the limit hbar->0, in terms of periodic orbits of M of period t. Recent work reach time t<< tE/6 where tE=log(1/hbar)/lambda is the Ehrenfest time, and lambda is the Lyapounov coefficient. Using a semi-classical normal form description of the dynamics uniformly over phase space, we show how to extend the trace formula for longer time of the form t= C.tE where C is any constant, with an arbitrary small error.
Simultaneous emergence of curved spacetime and quantum mechanics
S S De; F Rahaman
2014-12-10T23:59:59.000Z
It is shown in this paper that the geometrically structureless spacetime manifold is converted instantaneously to a curved one, the Riemannian or may be a Finslerian spacetime with an associated Riemannian spacetime, on the appearance of quantum Weyl spinors dependent only on time in that background flat manifold and having the sympleic property in the abstract space of spinors. The scenario depicts simultaneous emergence of the gravity in accord with general relativity and quantum mechanics.The emergent gravity leads to the generalized uncertainty principle, which in turn, ushers in discrete space time. The emerged space time is specified here as to be Finslerian and the field equation in that space time has been obtained from the classical one due to the arising quantized space and time. From this field equation we find the quantum field equation for highly massive (of the Planck order) spinors in the associated Riemannian space of the Finsler space, which is in fact, the background FRW space time of the universe.These highly massive spinors provide the mass distribution complying Einstein equivalence principle. All these occurred in the indivisible minimum time considered as zero time or spontaneity.
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.
Thermodynamic Evidence for Water as a Quantum Mechanical Liquid
A. Widom; S. Sivasubramanian; D. Drosdoff; Y. N. Srivastava
2010-01-22T23:59:59.000Z
We consider general theoretical models of water and in particular the nature of the motions of the hydrogen nuclei. If the motion of hydrogen nuclei is classical, then the thermodynamic pressure equation of state for heavy water wherein the hydrogen nuclei are deuterons is identical to the pressure equation of state for light water wherein the hydrogen nuclei are protons. Since the experimental thermodynamic phase diagram for light water is clearly measurably different from the experimental thermodynamic phase diagram for heavy water, one may deduce that the motions of hydrogen nuclei are quantum mechanical in nature. This conclusion is in physical agreement with a recent analysis of X-ray, neutron and deep inelastic neutron scattering data.
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.
Bhomian Mechanics vs. Standard Quantum Mechanics: a Difference in Experimental Predictions
Artur Szczepanski
2010-02-08T23:59:59.000Z
Standard Quantum Mechanics (QM) predicts an anti-intuitive fenomenon here referred to as "quantum autoscattering", which is excluded by Bhomian Mechanics. The scheme of a gedanken experiment testing the QM prediction is briefly discussed.
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.
Quantum-Mechanical Description of Spin-1/2 Particles and Nuclei Channeled in Bent Crystals
Silenko, A J
2015-01-01T23:59:59.000Z
General quantum-mechanical description of relativistic particles and nuclei with spin 1/2 channeled in bent crystals is performed with the use of the cylindrical coordinate system. The previously derived Dirac equation in this system is added by terms characterizing anomalous magnetic and electric dipole moments. A transformation to the Foldy-Wouthuysen representation, a derivation of the quantum-mechanical equations of motion for particles and their spins, and a determination of classical limit of these equations are fulfilled in the general case. A physical nature of main peculiarities of description of particles and nuclei in the cylindrical coordinate system is ascertained.
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.
Quantum-Mechanical Model of Spacetime
Jarmo Makela
2007-06-20T23:59:59.000Z
We consider a possibility to construct a quantum-mechanical model of spacetime, where Planck size quantum black holes act as the fundamental constituents of space and time. Spacetime is assumed to be a graph, where black holes lie on the vertices. Our model implies that area has a discrete spectrum with equal spacing. At macroscopic length scales our model reproduces Einstein's field equation with a vanishing cosmological constant as a sort of thermodynamical equation of state of spacetime and matter fields. In the low temperature limit, where most black holes are assumed to be in the ground state, our model implies the Unruh and the Hawking effects, whereas in the high temperature limit we find, among other things, that black hole entropy depends logarithmically on the event horizon area, instead of being proportional to the area.
Hannay Angle: Yet Another Symmetry Protected Topological Order Parameter in Classical Mechanics
Kariyado, Toshikaze
2015-01-01T23:59:59.000Z
Topological way of thinking now goes beyond conventional solid materials, and topological characterization of classical mechanical systems governed by Newton's equation of motion begins to attract much attention. To have a deeper insight on physical meaning of topological numbers in mechanical systems, we demonstrate the use of the Hannay angle, a classical counterpart of the Berry phase, as a symmetry protected topological order parameter. We first derive the Hannay angle using a canonical transformation that maps the Newton's equation to the Schr\\"{o}dinger type equation. The Hannay angle is then used to characterize a simple spring-mass model topologically with a particular focus on the bulk-edge correspondence and new aspects of the symmetry in a classical system.
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.
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, ...
Lecture Script: Introduction to Computational Quantum Mechanics
Roman Schmied
2015-06-05T23:59:59.000Z
This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013 and in the Spring semester of 2015. It is aimed at advanced students of physics who are familiar with the concepts and notations of quantum mechanics. Quantum mechanics lectures can often be separated into two classes. In the first class you get to know Schroedinger's equation and find the form and dynamics of simple physical systems (square well, harmonic oscillator, hydrogen atom); most calculations are analytic and inspired by calculations originally done in the 1920s and 1930s. In the second class you learn about large systems such as molecular structures, crystalline solids, or lattice models; these calculations are usually so complicated that it is difficult for the student to understand them in all detail. This lecture tries to bridge the gap between simple analytic calculations and complicated large-scale computations. We will revisit most of the problems encountered in introductory quantum mechanics, focusing on computer implementations for finding analytical as well as numerical solutions and their visualization. Most of these calculations are too complicated to be done by hand. Even relatively simple problems, such as two interacting particles in a one-dimensional trap, do not have analytic solutions and require the use of computers for their solution and visualization. More complex problems scale exponentially with the number of degrees of freedom, and make the use of large computer simulations unavoidable. The course is taught using the Mathematica programming language; however, the concepts presented are readily translated to any other programming language.
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.
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.
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.
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.
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.
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.
Comparative description of the evolving universe in classical and quantum geometrodynamics
,
2015-01-01T23:59:59.000Z
The description of the universe evolving in time according to general relativity is given in comparison with the quantum description of the same universe in terms of quasiclassical wave functions. The spacetime geometry is determined by the Robertson-Walker metric. It is shown that the main equation of the quantum geometrodynamics is reduced to the non-linear Hamilton-Jacobi equation. Its non-linearity is caused by a new source of the gravitational field, which has a purely quantum dynamical nature, and is additional to ordinary matter sources. In quasiclassical approximation, the non-linear equation of motion is linearized and reduces to the Friedmann equation with the additional quantum source of gravity (or anti-gravity) in the form of the stiff Zel'dovich matter. The semi-classical wave functions of the universe, in which different types of matter-energies dominate, are obtained. As examples, the cases of the domination of radiation, barotropic fluid, or new quantum matter-energy are discussed. The probab...
Cao, Jianshu
2012-01-01T23:59:59.000Z
, including photovoltaic devices and artificial photosynthesis.1 For a long time, energy transfer 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
Steven Kenneth Kauffmann
2013-09-29T23:59:59.000Z
The historical Klein-Gordon transformation of complex-valued first-order in time Schroedinger equations iterates these in a naively straightforward way which changes them into complex-valued second-order in time equations that have a plethora of extraneous solutions -- the transformation is an operator-calculus analogue of the squaring of both sides of an algebraic equation. The real and imaginary parts of a Schroedinger equation, however, are well known to be precisely the dynamical equation pair of the real-valued classical Hamiltonian functional which is numerically equal to the expectation value of that Schroedinger equation's Hermitian Hamiltonian operator. The purely real-valued second-order in time Euler-Lagrange equation of the corresponding classical Lagrangian functional is also isomorphic to that Schroedinger equation, and for symmetric Hamiltonians has exactly the same formal appearance as the corresponding naive complex-valued Klein-Gordon equation, but none of the latter's extraneous solutions. These quantum Schroedinger-equation isomorphisms to classical Euler-Lagrange equations are the technical manifestation of a key theoretical aspect of the principle of complementarity, one which is elegantly illustrated by the isomorphic free-photon wave-function complement to the vector potential of source-free classical electrodynamics.
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.
PHYSICS 706 Quantum Mechanics Spring 2014 Lecturer: Maarten Golterman
Golterman, Maarten
Quantum Mechanics, 2nd edition (AddisonWesley) Prerequisites: Physics 701, 785 or permission accommodations are encouraged to contact the instructor. The Disability Programs and Resource Center (DPRC
Derivation of the coefficient squared probability law in quantum mechanics
Casey Blood
2013-06-02T23:59:59.000Z
If one assumes there is probability of perception in quantum mechanics, then unitarity dictates that it must have the coefficient squared form, in agreement with experiment.
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.
From quantum to classical dynamics: Dynamic crossover in the relativistic $O(N)$ model
Mesterházy, David; Tanizaki, Yuya
2015-01-01T23:59:59.000Z
We investigate the transition from quantum to classical dynamics in the relativistic $O(N)$ vector model using the nonperturbative functional renormalization group in the real-time formalism. In thermal equilibrium, the theory is characterized by two scales, the interaction range for coherent scattering of particles and the mean free path determined by the rate of incoherent collision with excitations in the thermal medium. Their competition determines the renormalization group flow and the effective dynamics of the model. Here we quantify the dynamic properties of the model in terms of the scale-dependent dynamic critical exponent $z$ for arbitrary temperatures and in $2 \\leq d \\leq 4$ spatial dimensions.
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.
Rasio, Frederic A.
2001-01-01T23:59:59.000Z
wave sources for LISA. We provide estimates for the numbers of sources of several categories. The detection of these sources would provide information about both binary star evolution and the dynamicsINSTITUTE OF PHYSICS PUBLISHING CLASSICAL AND QUANTUM GRAVITY Class. Quantum Grav. 18 (2001) 4025
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.
The basic Leggett inequalities don't contradict the quantum theory, neither the classical physics
Sofia Wechsler
2009-12-21T23:59:59.000Z
The basic Leggett inequalities, i.e. those inequalities in which the particular assumptions of Leggett's hidden-variable model (e.g. Malus law) were not yet introduced, are usually derived using hidden-variable distributions of probabilities (although in some cases completely general, positive probabilities would lead to the same result). This fact creates sometimes the illusion that these basic inequalities are a belonging of the hidden-variable theories and are bound to contradict the quantum theory. In the present text the basic Leggett inequalities are derived in the most general way, i.e. no assumption is made that the distribution of probabilities would result from some wave function, or from some set of classical variables. The consequence is that as long as one and the same probability distribution is used in the calculus of all the averages appearing in the basic Leggett inequalities, no contradiction may occur. These inequalities may be violated only when different averages are calculated with different distributions, for example, some of them calculated with the quantum formalism and the others with some distribution of classical parameters.
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.
Irrational Dynamical Variables and the Measurement Problem in Quantum Mechanics
Christopher Engelhardt
2015-07-08T23:59:59.000Z
The quantum mechanical measurement process is considered. A hypothetical concept of irrational dynamical variables is proposed. A possible definition of measurement is discussed along with a mathematical method to calculate experimental result probabilities. The postulates of quantum mechanics are analyzed and modified. Thought experiments and implications are considered.
Depicting qudit quantum mechanics and mutually unbiased qudit theories
André Ranchin
2014-12-30T23:59:59.000Z
We generalize the ZX calculus to quantum systems of dimension higher than two. The resulting calculus is sound and universal for quantum mechanics. We define the notion of a mutually unbiased qudit theory and study two particular instances of these theories in detail: qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits. The calculus allows us to analyze the structure of qudit stabilizer quantum mechanics and provides a geometrical picture of qudit stabilizer theory using D-toruses, which generalizes the Bloch sphere picture for qubit stabilizer quantum mechanics. We also use our framework to describe generalizations of Spekkens toy theory to higher dimensional systems. This gives a novel proof that qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits are operationally equivalent in three dimensions. The qudit pictorial calculus is a useful tool to study quantum foundations, understand the relationship between qubit and qudit quantum mechanics, and provide a novel, high level description of quantum information protocols.
Rekik, Najeh; Freedman, Holly; Hanna, Gabriel [Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2 (Canada); Hsieh, Chang-Yu [Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6 (Canada)
2013-04-14T23:59:59.000Z
We apply two approximate solutions of the quantum-classical Liouville equation (QCLE) in the mapping representation to the simulation of the laser-induced response of a quantum subsystem coupled to a classical environment. These solutions, known as the Poisson Bracket Mapping Equation (PBME) and the Forward-Backward (FB) trajectory solutions, involve simple algorithms in which the dynamics of both the quantum and classical degrees of freedom are described in terms of continuous variables, as opposed to standard surface-hopping solutions in which the classical degrees of freedom hop between potential energy surfaces dictated by the discrete adiabatic state of the quantum subsystem. The validity of these QCLE-based solutions is tested on a non-trivial electron transfer model involving more than two quantum states, a time-dependent Hamiltonian, strong subsystem-bath coupling, and an initial energy shift between the donor and acceptor states that depends on the strength of the subsystem-bath coupling. In particular, we calculate the time-dependent population of the photoexcited donor state in response to an ultrafast, on-resonance pump pulse in a three-state model of an electron transfer complex that is coupled asymmetrically to a bath of harmonic oscillators through the optically dark acceptor state. Within this approach, the three-state electron transfer complex is treated quantum mechanically, while the bath oscillators are treated classically. When compared to the more accurate QCLE-based surface-hopping solution and to the numerically exact quantum results, we find that the PBME solution is not capable of qualitatively capturing the population dynamics, whereas the FB solution is. However, when the subsystem-bath coupling is decreased (which also decreases the initial energy shift between the donor and acceptor states) or the initial shift is removed altogether, both the PBME and FB results agree better with the QCLE-based surface-hopping results. These findings highlight the challenges posed by various conditions such as a time-dependent external field, the strength of the subsystem-bath coupling, and the degree of asymmetry on the accuracy of the PBME and FB algorithms.
Bosonic seesaw mechanism in a classically conformal extension of the Standard Model
Naoyuki Haba; Hiroyuki Ishida; Nobuchika Okada; Yuya Yamaguchi
2015-08-27T23:59:59.000Z
We suggest the so-called bosonic seesaw mechanism in the context of a classically conformal $U(1)_{B-L}$ extension of the Standard Model with two Higgs doublet fields. The $U(1)_{B-L}$ symmetry is radiatively broken via the Coleman-Weinberg mechanism, which also generates the mass terms for the two Higgs doublets through quartic Higgs couplings. Their masses are all positive but, nevertheless, the electroweak symmetry breaking is realized by the bosonic seesaw mechanism. Analyzing the renormalization group evolutions for all model couplings, we find that a large hierarchy among the quartic Higgs couplings, which is crucial for the bosonic seesaw mechanism to work, is dramatically reduced toward high energies. Therefore, the bosonic seesaw is naturally realized with only a mild hierarchy, if some fundamental theory, which provides the origin of the classically conformal invariance, completes our model at some high energy, for example, the Planck scale. We identify the regions of model parameters which satisfy the perturbativity of the running couplings and the electroweak vacuum stability as well as the naturalness of the electroweak scale.
Quantum Mechanical Inclusion of the Source in the Aharonov-Bohm Effect
Philip Pearle; Anthony Rizzi
2015-06-30T23:59:59.000Z
The standard treatment of the magnetic Aharonov-Bohm (A-B) effect assumes one can calculate the phase without accounting for the source (solenoid) quantum mechanically. Recently, Vaidman, using a semi-classical calculation, showed that the source may indeed matter. He argued for what might be called a local field hypothesis---the idea that in quantum theory, as in classical physics, only field-producing potentials have physical effects. His calculation indicates that the electron's non-relativistic electric field, acting on a semi-classically treated solenoid, produces the A-B phase shift. Here, employing a model of the solenoid consisting of charged particles, we give a quantum mechanical treatment of their contribution to the phase shift under the influence of the circulating electron's electric field. We show that the phase shift of the field-producing non-relativistic vector potential gives the A-B phase shift, and how this confirms Vaidman's semi-classical prediction of that phase shift. However, we also show that the phase shift of the field-producing relativistic (retarded) scalar potential gives the negative of the A-B phase shift. This cancellation allows one to effectively treat the source as a classical entity as is done in the standard derivation of the A-B effect. We close by remarking that the apparent necessity for relativistic considerations suggests the possibility that the A-B phase shift may yet be explained in terms of field-producing potentials alone, which may vindicate the local field hypothesis.
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.
Quantum Properties of Double Kicked Systems with Classical Translational Invariance in Momentum
Itzhack Dana
2015-01-21T23:59:59.000Z
Double kicked rotors (DKRs) appear to be the simplest nonintegrable Hamiltonian systems featuring classical translational symmetry in phase space (i.e., in angular momentum) for an \\emph{infinite} set of values (the rational ones) of a parameter $\\eta$. The experimental realization of quantum DKRs by atom-optics methods motivates the study of the double kicked particle (DKP). The latter reduces, at any fixed value of the conserved quasimomentum $\\beta\\hbar$, to a generalized DKR, the \\textquotedblleft $\\beta $-DKR\\textquotedblright . We determine general quantum properties of $\\beta $-DKRs and DKPs for arbitrary rational $\\eta $. The quasienergy problem of $\\beta $-DKRs is shown to be equivalent to the energy eigenvalue problem of a finite strip of coupled lattice chains. Exact connections are then obtained between quasienergy spectra of $\\beta $-DKRs for all $\\beta $ in a generically infinite set. The general conditions of quantum resonance for $\\beta $-DKRs are shown to be the simultaneous rationality of $\\eta $, $\\beta$, and a scaled Planck constant $\\hbar _{\\mathrm{S}}$. For rational $\\hbar _{\\mathrm{S}}$ and generic values of $\\beta $, the quasienergy spectrum is found to have a staggered-ladder structure. Other spectral structures, resembling Hofstadter butterflies, are also found. Finally, we show the existence of particular DKP wave-packets whose quantum dynamics is \\emph{free}, i.e., the evolution frequencies of expectation values in these wave-packets are independent of the nonintegrability. All the results for rational $\\hbar _{\\mathrm{S}}$ exhibit unique number-theoretical features involving $\\eta $, $\\hbar _{\\mathrm{S}}$, and $\\beta $.
Scott M. Cohen
2013-11-11T23:59:59.000Z
We give a conceptually simple necessary condition such that a separable quantum operation can be implemented by local operations on subsystems and classical communication between parties (LOCC), a condition which follows from a novel approach to understanding LOCC. This necessary condition holds for any number of parties and any finite number of rounds of communication and as such, also provides a completely general sufficient condition that a given separable operation cannot be exactly implemented by LOCC. Furthermore, it demonstrates an extremely strong difference between separable operations and LOCC, in that there exist examples of the former for which the condition is extensively violated. More precisely, the violation by separable operations of our necessary condition for LOCC grows without limit as the number of parties increases.
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.
The structure of supersymmetry in ${\\cal PT}$ symmetric quantum mechanics
D. Bazeia; Ashok Das; L. Greenwood; L. Losano
2009-03-17T23:59:59.000Z
The structure of supersymmetry is analyzed systematically in ${\\cal PT}$ symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional ${\\cal PT}$ symmetric quantum mechanical theories. We show that there is a richer structure present in these theories compared to the conventional theories associated with Hermitian Hamiltonians. We bring out various properties associated with these supersymmetric systems and generalize such quantum mechanical theories to higher dimensions as well as to the case of one dimensional shape invariant potentials.
What happened to the Bohr-Sommerfeld elliptic orbits in Schrodinger's wave mechanics?
Nauenberg, Michael
2015-01-01T23:59:59.000Z
Przibram, Letters on Wave Mechanics (Philosophical Library,Quantum to Classical Mechanics in Atomic Physics, CommentsSchr¨odinger’s wave mechanics? Michael Nauenberg University
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.
Koch, Christof
. Quantum Mechanics Quantum mechanics is, in the framework of this essay, the basic theory of all low-energy and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA. To whom all correspondence `text-book theory' of atoms, electrons and photons, below the energy for pair creation of massive
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.
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
NESS in quantum statistical mechanics VOJKAN JASI C1
Jaksic, Vojkan
NESS in quantum statistical mechanics VOJKAN JASI Â´C1 , CLAUDE-ALAIN PILLET2 1 Department@univ-tln.fr In this article we describe the construction of canonical Non-Equilibrium Steady States (NESS) for a small quantum]). Definition 1 Let be a state on O. We say that + is a NESS of V associated to the reference state
On a commutative ring structure in quantum mechanics
Shigeki Matsutani
2009-10-10T23:59:59.000Z
In this article, I propose a concept of the $p$-on which is modelled on the multi-photon absorptions in quantum optics. It provides a commutative ring structure in quantum mechanics. Using it, I will give an operator representation of the Riemann $\\zeta$ function.
Minnesota, University of
1 Hybrid Quantum and Classical Methods for Computing Kinetic Isotope Effects of Chemical Reactions for computing kinetic isotope effects for chemical reactions in solution and in enzymes. In the ensemble that enzymes accelerate the rates of chemical reactions has fascinated chemists and biochemists for nearly
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.
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.
A Low Temperature Expansion for Matrix Quantum Mechanics
Ying-Hsuan Lin; Shu-Heng Shao; Yifan Wang; Xi Yin
2013-04-08T23:59:59.000Z
We analyze solutions to loop-truncated Schwinger-Dyson equations in massless N=2 and N=4 Wess-Zumino matrix quantum mechanics at finite temperature, where conventional perturbation theory breaks down due to IR divergences. We find a rather intricate low temperature expansion that involves fractional power scaling in the temperature, based on a consistent "soft collinear" approximation. We conjecture that at least in the N=4 matrix quantum mechanics, such scaling behavior holds to all perturbative orders in the 1/N expansion. We discuss some preliminary results in analyzing the gauged supersymmetric quantum mechanics using Schwinger-Dyson equations, and comment on the connection to metastable microstates of black holes in the holographic dual of BFSS matrix quantum mechanics.
Born series and unitarity in noncommutative quantum mechanics
F. S. Bemfica; H. O. Girotti
2008-02-11T23:59:59.000Z
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.
No-Go Theorems Face Fluid-Dynamical Theories for Quantum Mechanics
Louis Vervoort
2014-06-16T23:59:59.000Z
Recent experiments on fluid-dynamical systems have revealed a series of striking quantum-like features of these macroscopic systems, thus reviving the quest to describe quantum mechanics by classical, in particular fluid-dynamical, theories. However, it is generally admitted that such an endeavor is impossible, on the basis of the 'no-go' theorems of Bell and Kochen-Specker. Here we show that such theorems are inoperative for fluid-dynamical models, even if these are local. Such models appear to violate one of the premises of both theorems, and can reproduce the quantum correlation of the Bell experiment. Therefore the statement that 'local hidden-variable theories are impossible' appears to be untenable for theories just slightly more general than originally envisaged by Bell. We also discuss experimental implications.
Michelson-Morley experiment within the quantum mechanics framework
D. L. Khokhlov
2008-04-17T23:59:59.000Z
It is revisited the Michelson-Morley experiment within the quantum mechanics framework. One can define the wave function of photon in the whole space at a given moment of time. The phase difference between the source and receiver is a distance between the source and receiver at the time of reception hence it does not depend on the velocity of the frame. Then one can explain the null result of the Michelson-Morley experiment within the quantum mechanics framework.
C. L. Herzenberg
2009-12-07T23:59:59.000Z
We consider an object at rest in space with a universal Hubble expansion taking place away from it. We find that a governing differential equation developed from the Schroedinger equation leads to wave functions which turn out to exhibit pronounced central localization. The extent of concentration of probability depends on the mass; objects with small masses tend to behave in a delocalized manner as ordinary quantum objects do in a static space, while quantum objects with large masses have wave functions that are largely concentrated into much smaller regions. This in turn suggests the possibility that classical behavior is being induced in quantum objects by the presence of the Hubble expansion. If the size of the localized region of concentrated probability density is larger than the size of the corresponding extended object, quantum behavior might be expected; whereas classical behavior might be expected for cases in which the region of high probability density is smaller than the size of the object. The resulting quantum-classical boundary due to Hubble expansion may be expressed in terms of a relationship between the size and mass of an object, or may be expressed in terms of a threshold moment of inertia.
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.
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".
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.
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.
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.
Tests of quantum mechanics at a {phi}-factory
Eberhard, P.H.
1994-08-09T23:59:59.000Z
Unique tests of quantum mechanics, which can only be performed at a 0-factory, are proposed for Da0ne. Each of these tests consists of measuring the difference between the predicted and the actual amount of interference between two processes leading from a single pure initial state to a single pure final state of a kaon system. Estimates are made of the upper limits that will be set for the amount of violation if the predictions of quantum mechanics turn out to be correct. They are of the order a fraction of one percent. For the case where, on the contrary, a significant violation is found, several decoherence mechanisms are considered.
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.
Introduction to nonequilibrium quantum statistical mechanics
Jaksic, Vojkan
.1 Basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 NESS and entropy production; Âscattering and NESS . . . . . . . . . . . . . . . . . . . . . . 14 4 Open quantum systems 17 4.1 Definition will discuss the scattering theory of nonÂequilibrium steady states (NESS) (this topic has been only quickly
Nikulov, A V
2015-01-01T23:59:59.000Z
Canonical description of quantization effects observed at measurements on superconducting structures seems one of the most triumphant achievements of quantum mechanics. But impartial consideration uncovers incompleteness and inconsistency of this description. Contradictions in the description of other quantum phenomena are revealed also.
A. V. Nikulov
2015-07-15T23:59:59.000Z
Canonical description of quantization effects observed at measurements on superconducting structures seems one of the most triumphant achievements of quantum mechanics. But impartial consideration uncovers incompleteness and inconsistency of this description. Contradictions in the description of other quantum phenomena are revealed also.
The H2 Double-Slit Experiment: Where Quantum and Classical Physics...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
However, since they were still entangled, a record of the electrons' "quantum-ness" could be reconstructed in the dielectron. Present-day single photoionization...
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
Quantum mechanics emerges from information theory applied to causal horizons
Lee, Jae-Weon
2010-01-01T23:59:59.000Z
It is suggested that quantum mechanics is not fundamental but emerges from information theory applied to a causal horizon. The path integral quantization and quantum randomness can be derived by considering information loss of fields or particles crossing Rindler horizons for accelerating observers. This implies that information is one of the fundamental root of all physical phenomena. The connection between this theory and Verlinde's entropic gravity theory is also investigated.
Frank Steiner
1994-02-07T23:59:59.000Z
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace formula is discussed as a sound mathematical basis for the semiclassical quantization of chaos. Two conjectures are presented on the basis of which it is argued that there are unique fluctuation properties in quantum mechanics which are universal and, in a well defined sense, maximally random if the corresponding classical system is strongly chaotic. These properties constitute the quantum mechanical analogue of the phenomenon of chaos in classical mechanics. Thus quantum chaos has been found.
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.
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.
Physics 139B Quantum Mechanics II Fall 2009 Instructor: Howard Haber
California at Santa Cruz, University of
Physics 139B Quantum Mechanics II Fall 2009 Instructor: Howard Haber O#ce: ISB, Room 326 Phone OUTSIDE READING: Quantum Physics, by Stephen Gasiorowicz Introduction to Quantum Mechanics, by David J to Quantum Mechanics, by John S. Townsend PREREQUISITES: Physics 116C and Physics 139A. It is assumed
Physics 139B Quantum Mechanics II Fall 2009 Instructor: Howard Haber
California at Santa Cruz, University of
Physics 139B Quantum Mechanics II Fall 2009 Instructor: Howard Haber Office: ISB, Room 326 Phone OUTSIDE READING: Quantum Physics, by Stephen Gasiorowicz Introduction to Quantum Mechanics, by David J to Quantum Mechanics, by John S. Townsend PREREQUISITES: Physics 116C and Physics 139A. It is assumed
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)].
Functional Integral Approach to $C^*$-algebraic Quantum Mechanics
John LaChapelle
2015-05-27T23:59:59.000Z
The algebraic approach to quantum mechanics has been key to the development of the theory since its inception, and the approach has evolved into a mathematically rigorous $C^\\ast$-algebraic formulation of the axioms. Conversely the functional approach in the form of Feynman path integrals is far from mathematically rigorous: Nevertheless, path integrals provide an equally valid and useful formulation of the axioms of quantum mechanics. The two approaches can be merged by employing a recently developed notion of functional integration that allows to construct functional integral representations of $C^\\ast$-algebras. The merger is a hybrid formulation of the axioms of quantum mechanics in which topological groups play a leading role.
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.
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.
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.
Erik Curiel
2014-11-09T23:59:59.000Z
In the early 1970s it is was realized that there is a striking formal analogy between the Laws of black-hole mechanics and the Laws of classical thermodynamics. Before the discovery of Hawking radiation, however, it was generally thought that the analogy was only formal, and did not reflect a deep connection between gravitational and thermodynamical phenomena. It is still commonly held that the surface gravity of a stationary black hole can be construed as a true physical temperature and its area as a true entropy only when quantum effects are taken into account; in the context of classical general relativity alone, one cannot cogently construe them so. Does the use of quantum field theory in curved spacetime offer the only hope for taking the analogy seriously? I think the answer is `no'. To attempt to justify that answer, I shall begin by arguing that the standard argument to the contrary is not physically well founded, and in any event begs the question. Looking at the various ways that the ideas of "temperature" and "entropy" enter classical thermodynamics then will suggest arguments that, I claim, show the analogy between classical black-hole mechanics and classical thermodynamics should be taken more seriously, without the need to rely on or invoke quantum mechanics. In particular, I construct an analogue of a Carnot cycle in which a black hole "couples" with an ordinary thermodynamical system in such a way that its surface gravity plays the role of temperature and its area that of entropy. Thus, the connection between classical general relativity and classical thermodynamics on their own is already deep and physically significant, independent of quantum mechanics.
A Specific N = 2 Supersymmetric Quantum Mechanical Model: Supervariable Approach
Shukla, Aradhya
2015-01-01T23:59:59.000Z
By exploiting the supersymmetric invariant restrictions on the chiral and anti-chiral supervariables, we derive the off-shell nilpotent symmetry transformations for a specific (0 + 1)-dimensional N = 2 supersymmetric quantum mechanical model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables (\\theta, \\bar\\theta). We also provide the geometrical meaning to the symmetry transformations. Finally, we show that this specific N = 2 SUSY quantum mechanical model is a model for Hodge theory.
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.
Mario Castagnino; Roberto Laura
2000-06-03T23:59:59.000Z
Decoherence and the approach to the classical final limit are studied in two similar cases: the Mott and the Cosmological problems.
The quantum mechanics of perfect fluids
Solomon Endlich; Alberto Nicolis; Riccardo Rattazzi; Junpu Wang
2010-11-29T23:59:59.000Z
We consider the canonical quantization of an ordinary fluid. The resulting long-distance effective field theory is derivatively coupled, and therefore strongly coupled in the UV. The system however exhibits a number of peculiarities, associated with the vortex degrees of freedom. On the one hand, these have formally a vanishing strong-coupling energy scale, thus suggesting that the effective theory's regime of validity is vanishingly narrow. On the other hand, we prove an analog of Coleman's theorem, whereby the semiclassical vacuum has no quantum counterpart, thus suggesting that the vortex premature strong-coupling phenomenon stems from a bad identification of the ground state and of the perturbative degrees of freedom. Finally, vortices break the usual connection between short distances and high energies, thus potentially impairing the unitarity of the effective theory.
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.
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.
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
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.
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.
Simulation of Quantum Algorithms with a Symbolic Programming Language
Peter Nyman
2007-05-24T23:59:59.000Z
This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational methods. The computational language will include formulations such as quantum state, superposition and quantum operator.
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.
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.
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.
Jarzynski equality in PT-symmetric quantum mechanics
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Deffner, Sebastian; Saxena, Avadh
2015-04-13T23:59:59.000Z
We show that the quantum Jarzynski equality generalizes to PT -symmetric quantum mechanics with unbroken PT -symmetry. In the regime of broken PT -symmetry the Jarzynski equality does not hold as also the CPT -norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system – two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken PT -symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.
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
Brit. J. Phil. Sci. 58 (2007), 595604 Is Standard Quantum Mechanics
Seevinck, Michiel
2007-01-01T23:59:59.000Z
Brit. J. Phil. Sci. 58 (2007), 595604 Is Standard Quantum Mechanics Technologically Inadequate? F]) claims to have demonstrated that standard quantum mechanics is technologically inadequate is that Vermaas' claim that standard quantum mechanics is technologically inadequate evaporates. 1 Introduction 2
The role of help in Classical and Quantum Zero-Knowledge Andr Chailloux #
International Association for Cryptologic Research (IACR)
relation to the standard interactive model. In the classical case, we show that help and interaction were independently discovered by Dragos Florin Ciocan and Salil Vadhan. # Supported in part by ACI
Ryabinkin, Ilya G; Izmaylov, Artur F
2015-01-01T23:59:59.000Z
We have developed a numerical differentiation scheme which eliminates evaluation of overlap determinants in calculating the time-derivative non-adiabatic couplings (TDNACs). Evaluation of these determinants was a bottleneck in previous implementations of mixed quantum-classical methods using numerical differentiation of electronic wave functions in the Slater-determinant representation. The central idea of our approach is, first, to reduce the analytic time derivatives of Slater determinants to time derivatives of molecular orbitals, and then to apply a finite-difference formula. Benchmark calculations prove the efficiency of the proposed scheme showing impressive several-order-of-magnitude speedups of the TDNAC calculation step for midsize molecules.
Emergent Semiclassical Time in Quantum Gravity. I. Mechanical Models
Edward Anderson
2007-11-04T23:59:59.000Z
Strategies intended to resolve the problem of time in quantum gravity by means of emergent or hidden timefunctions are considered in the arena of relational particle toy models. In situations with `heavy' and `light' degrees of freedom, two notions of emergent semiclassical WKB time emerge; these are furthermore equivalent to two notions of emergent classical `Leibniz--Mach--Barbour' time. I futhermore study the semiclassical approach, in a geometric phase formalism, extended to include linear constraints, and with particular care to make explicit those approximations and assumptions used. I propose a new iterative scheme for this in the cosmologically-motivated case with one heavy degree of freedom. I find that the usual semiclassical quantum cosmology emergence of time comes hand in hand with the emergence of other qualitatively significant terms, including back-reactions on the heavy subsystem and second time derivatives. I illustrate my analysis by taking it further for relational particle models with linearly-coupled harmonic oscillator potentials. As these examples are exactly soluble by means outside the semiclassical approach, they are additionally useful for testing the justifiability of some of the approximations and assumptions habitually made in the semiclassical approach to quantum cosmology. Finally, I contrast the emergent semiclassical timefunction with its hidden dilational Euler time counterpart.
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.
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.
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.
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
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.
The Montevideo Interpretation of Quantum Mechanics: a short review
Rodolfo Gambini; Jorge Pullin
2015-02-11T23:59:59.000Z
The Montevideo interpretation of quantum mechanics, which consists in supplementing environmental decoherence with fundamental limitations in measurement stemming from gravity, has been described in several publications. However, some of them appeared before the full picture provided by the interpretation was developed. As such it can be difficult to get a good understanding via the published literature. Here we summarize it in a self contained brief presentation including all its principal elements.
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.
Electromagnetic deuteron form factors in point form relativistic quantum mechanics
N. A. Khokhlov
2015-03-10T23:59:59.000Z
A study of electromagnetic structure of the deuteron in the framework of relativistic quantum mechanics is presented. The deuteron form factors dependencies on the transferred 4-momentum Q are calculated. We compare results obtained with different realistic deuteron wave functions stemming from Nijmegen-I, Nijmegen-II, JISP16, CD-Bonn, Paris and Moscow (with forbidden states) potentials. A nucleon form factor parametrization consistent with modern experimental analysis was used as an input data.
Supporting Information for Mixed Quantum Mechanical/Molecular Mechanical (QM/MM) Study
Gherman, Benjamin F.
S1 Supporting Information for Mixed Quantum Mechanical/Molecular Mechanical (QM/MM) Study geometries for the QM/MM-optimized R61 acyl-enzyme intermediate protonation/hydrogen bond configurations-blue, O-red, H-gray, S-yellow. (1) (2a) #12;S3 (3) #12;S4 Figure S2. Active site geometries for the QM/MM
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 ...
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.
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.
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.
Piero Chiarelli
2013-05-20T23:59:59.000Z
In the present paper the gas, liquid and solid phases made of structureless particles, are visited to the light of the quantum stochastic hydrodynamic analogy (SQHA). The SQHA shows that the open quantum mechanical behavior is maintained on a distance shorter than the theory-defined quantum correlation length (lc). When, the physical length of the problem is larger than lc, the model shows that the quantum (potential) interactions may have a finite range of interaction maintaining the non-local behavior on a finite distance quantum non-locality length lq. The present work shows that when the mean molecular distance is larger than the quantum non-locality length we have a classical phases (gas and van der Waals liquids) while when the mean molecular distance becomes smaller than lq or than lc we have phases such as the solid crystal or the superfluid one, respectively, that show quantum characteristics. The model agrees with Lindemann empirical law (and explains it), for the mean square deviation of atom from the equilibrium position at melting point of crystal, and shows a connection between the maximum density at the He lambda point and that one near the water-ice solidification point.
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
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.
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.
The ZX Calculus is incomplete for Clifford+T quantum mechanics
Simon Perdrix; Quanlong Wang
2015-06-09T23:59:59.000Z
The ZX calculus is a diagrammatic language for quantum mechanics and quantum information processing. We prove that the ZX-calculus is not complete for Clifford+T quantum mechanics. The completeness for this fragment has been stated as one of the main current open problems in categorical quantum mechanics. The ZX calculus was known to be incomplete for quantum mechanics, on the other hand, it has been proved complete for Clifford quantum mechanics (a.k.a. stabilizer quantum mechanics), and for single-qubit Clifford+T quantum mechanics. The question of the completeness of the ZX calculus for Clifford+T quantum mechanics is a crucial step in the development of the ZX calculus because of its (approximate) universality for quantum mechanics (i.e. any unitary evolution can be approximated using Clifford and T gates only). We exhibit a property which is know to be true in Clifford+T quantum mechanics and prove that this equation cannot be derived in the ZX calculus by introducing a new sound interpretation of the ZX calculus in which this particular property does not hold. Finally, we propose to extend the language with a new axiom.
Angularly Deformed Special Relativity and its Results for Quantum Mechanics
Lukasz Andrzej Glinka
2015-09-15T23:59:59.000Z
In this paper, the deformed Special Relativity, which leads to an essentially new theoretical context of quantum mechanics, is presented. The formulation of the theory arises from a straightforward analogy with the Special Relativity, but its foundations are laid through the hypothesis on breakdown of the velocity-momentum parallelism which affects onto the Einstein equivalence principle between mass and energy of a relativistic particle. Furthermore, the derivation is based on the technique of an eikonal equation whose well-confirmed physical role lays the foundations of both optics and quantum mechanics. As a result, we receive the angular deformation of Special Relativity which clearly depicts the new deformation-based theoretical foundations of physics, and, moreover, offers both constructive and consistent phenomenological discussion of the theoretical issues such like imaginary mass and formal superluminal motion predicted in Special Relativity for this case. In the context of the relativistic theory, presence of deformation does not break the Poincar\\'{e} invariance, in particular the Lorentz symmetry, and provides essential modifications of both bosons described through the Klein-Gordon equation and fermions satisfying the Dirac equation. On the other hand, on the level of discussion of quantum theory, there arises the concept of emergent deformed space-time, wherein the presence of angular deformation elucidates a certain new insight into the nature of spin, as well as both the Heisenberg uncertainty principle and the Schr\\"odinger wave equation.
Nonlinear quantum-mechanical system associated with Sine-Gordon equation in (1 + 2) dimensions
Zarmi, Yair, E-mail: zarmi@bgu.ac.il [Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Midreshet Ben-Gurion, 8499000 (Israel)
2014-10-15T23:59:59.000Z
Despite the fact that it is not integrable, the (1 + 2)-dimensional Sine-Gordon equation has N-soliton solutions, whose velocities are lower than the speed of light (c = 1), for all N ? 1. Based on these solutions, a quantum-mechanical system is constructed over a Fock space of particles. The coordinate of each particle is an angle around the unit circle. U, a nonlinear functional of the particle number-operators, which obeys the Sine-Gordon equation in (1 + 2) dimensions, is constructed. Its eigenvalues on N-particle states in the Fock space are the slower-than-light, N-soliton solutions of the equation. A projection operator (a nonlinear functional of U), which vanishes on the single-particle subspace, is a mass-density generator. Its eigenvalues on multi-particle states play the role of the mass density of structures that emulate free, spatially extended, relativistic particles. The simplicity of the quantum-mechanical system allows for the incorporation of perturbations with particle interactions, which have the capacity to “annihilate” and “create” solitons – an effect that does not have an analog in perturbed classical nonlinear evolution equations.
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.
Quantum mechanical calculation of Rydberg-Rydberg Auger decay rates
Kiffner, Martin; Li, Wenhui; Jaksch, Dieter
2015-01-01T23:59:59.000Z
We present quantum mechanical calculations of the Auger decay rate $\\Gamma_A$ of two Rubidium Rydberg atoms with weakly overlapping electron clouds. The two-electron wavefunction is modelled by a single Slater determinant of $nd$ Rydberg orbitals with principal quantum number $n\\le35$. The dependence of $\\Gamma_A$ on the atom-atom separation $R$ is well described by a power law $\\Gamma_A \\propto R^{\\alpha}$ and we calculate the exponents $\\alpha$ for various initial states. For atomic separations equal to the size of the Rydberg electron wave function $R_n$ we find that $\\Gamma_A \\propto n^{-5}$. We discuss the importance of Auger decay compared to other contributions to the electron dynamics in the two Rydberg atom system.
Boltzmann-conserving classical dynamics in quantum time-correlation functions: “Matsubara dynamics”
Hele, Timothy J. H.; Willatt, Michael J.; Muolo, Andrea; Althorpe, Stuart C.
2015-04-02T23:59:59.000Z
balance condition. B. Quantum correlation functions For clarity of presentation, we will derive the results in Secs. III and IV for a one-dimensional quantum system with Hamiltonian Hˆ = Tˆ + Vˆ , kinetic energy operator Tˆ = pˆ2/2m, potential energy... the potential-energy operator in the commu- tator in powers of ? to obtain [ i ~ [Hˆ, Bˆ(t)] ] W = ? ? ?? d? eip?/~ × ?ˆ?q ??/2|Bˆ(t)|q +?/2? (24) with ?ˆ = i~m ? ?q ? ?? ? 2i ~ ?? ?=1,odd 1 ?! ??V (q) ?q? (? 2 )? (25) Noting that each power of ? can...
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.
Michele Mosca
2008-08-04T23:59:59.000Z
This article surveys the state of the art in quantum computer algorithms, including both black-box and non-black-box results. It is infeasible to detail all the known quantum algorithms, so a representative sample is given. This includes a summary of the early quantum algorithms, a description of the Abelian Hidden Subgroup algorithms (including Shor's factoring and discrete logarithm algorithms), quantum searching and amplitude amplification, quantum algorithms for simulating quantum mechanical systems, several non-trivial generalizations of the Abelian Hidden Subgroup Problem (and related techniques), the quantum walk paradigm for quantum algorithms, the paradigm of adiabatic algorithms, a family of ``topological'' algorithms, and algorithms for quantum tasks which cannot be done by a classical computer, followed by a discussion.
Toward quantum opto-mechanics in a gram-scale suspended mirror interferometer
Wipf, Christopher (Christopher Conrad)
2013-01-01T23:59:59.000Z
A new generation of interferometric gravitational wave detectors, currently under construction, will closely approach the fundamental quantum limits of measurement, serving as a prominent example of quantum mechanics at ...
Classical Models of Subatomic Particles
R. B. Mann; M. S. Morris
1993-07-21T23:59:59.000Z
We look at the program of modelling a subatomic particle---one having mass, charge, and angular momentum---as an interior solution joined to a classical general-relativistic Kerr-Newman exterior spacetime. We find that the assumption of stationarity upon which the validity of the Kerr-Newman exterior solution depends is in fact violated quantum mechanically for all known subatomic particles. We conclude that the appropriate stationary spacetime matched to any known subatomic particle is flat space.
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.
Loop formulation of supersymmetric Yang-Mills quantum mechanics
Kyle Steinhauer; Urs Wenger
2014-10-01T23:59:59.000Z
We derive the fermion loop formulation of N=4 supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice. The loop formulation naturally separates the contributions to the partition function into its bosonic and fermionic parts with fixed fermion number and provides a way to control potential fermion sign problems arising in numerical simulations of the theory. Furthermore, we present a reduced fermion matrix determinant which allows the projection into the canonical sectors of the theory and hence constitutes an alternative approach to simulate the theory on the lattice.
Classical model of confinement
Yu. P. Goncharov; N. E. Firsova
2010-04-29T23:59:59.000Z
The confinement mechanism proposed earlier and then applied successfully to meson spectroscopy by one of the authors is interpreted in classical terms. For this aim the unique solution of the Maxwell equations, an analog of the corresponding unique solution of the SU(3)-Yang-Mills equations describing linear confinement in quantum chromodynamics, is used. Motion of a charged particle is studied in the field representing magnetic part of the mentioned solution and it is shown that one deals with the full classical confinement of the charged particle in such a field: under any initial conditions the particle motion is accomplished within a finite region of space so that the particle trajectory is near magnetic field lines while the latter are compact manifolds (circles). An asymptotical expansion for the trajectory form in the strong field limit is adduced. The possible application of the obtained results in thermonuclear plasma physics is also shortly outlined.
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.
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.
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.
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.
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.
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.
Mini-Proceedings ECT*: Speakable in quantum mechanics: atomic, nuclear and subnuclear physics tests
C. Curceanu; J. Marton; E. Milotti
2011-12-06T23:59:59.000Z
Mini-Proceedings ECT*: Speakable in quantum mechanics: atomic, nuclear and subnuclear physics tests, ECT*-Trento, 29 August - 2 September, 2011
Leahy, Richard M.
and Modern Physics PHYS 190: Physics Discovery Series Upper Division Requirements* BISC 320: MolecularThis major provides a solid foundation in both the biological sciences and the fundamental concepts of classical and quantum physics through a variety of tools that include abstract thought, experimentation
Leahy, Richard M.
This major provides a solid foundation in the fundamental concepts of classical and quantum physics acquisition hardware and data analysis by software, applied specifically to experiments in modern physics applying computer technology (in either hardware or software) to produce a result useful in the physics
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.
A semiclassical study of quantum maps
Guo, Y.
1992-01-01T23:59:59.000Z
The study of the behavior of quantum systems whose classical limit exhibits chaos defines the problem of quantum chaos. One would naturally ask how quantum mechanics approaches the classical limit [h bar] = 0, and how the chaotic motion in classical systems manifests itself in the corresponding quantum counterparts. Semiclassical mechanics is the bridge between quantum mechanics and classical mechanics. For studying the quantum mechanics corresponding to generic classical motion it is desirable to use the simplest possible model. The model system the authors use is the kicked rotator. Detailed computations of both classical and quantum mechanics are feasible for this system. The relationship between invariant classical phase space structures and quantum eigenfunctions has been the focus of recent semiclassical studies. The authors study the eigenstates of the quantum standard map associated with both integrable and non-integrable regions in classical phase space. The coherent-state representation is used to make the correspondence between the quantum eigenstates and the classical phase space structure. The importance of periodic orbits in the quantum eigenstates of classically chaotic Hamiltonians has become a popular topic in study of semiclassical limits of the systems. Periodic orbits arise without any assumption in the trace formula developed by Gutzwiller. The authors calculate the semiclassical coherent-state propagator. Since computing all the complex stationary orbits is not practical, the authors make a further assumption which the authors call the periodic point dominance (PPD). The authors present arguments and evidence to show that the PPD approximation works well in hard chaos regions where the full semiclassical approximation is not practical to use. The method fails in some boundary regions where both stable and unstable points are present, but the full semiclassical approximation is not a much better method than the PPD in many situations.
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
Nonclassicality of quantum excitation of classical coherent fields in thermal environments
Shang-Bin Li; Justin Liu; Xu-Bo Zou; Guang-Can Guo
2007-10-19T23:59:59.000Z
The nonclassicality of photon-added coherent fields in the thermal channel is investigated by exploring the volume of the negative part of the Wigner function which reduces with the dissipative time. The Wigner functions become positive when the decay time exceeds a threshold value. For the case of the single photon-added coherent state, we derive the exact threshold values of decay time in the thermal channel. For arbitrary partial negative Wigner distribution function, a generic analytical relation between the mean photon number of heat bath and the threshold value of decay time is presented. Finally, the possible application of SPACSs in quantum computation has been briefly discussed. OCIS codes: 270.0270, 270.2500, 000.5490
Mechanical resonators for storage and transfer of electrical and optical quantum states
S. A. McGee; D. Meiser; C. A. Regal; K. W. Lehnert; M. J. Holland
2013-05-29T23:59:59.000Z
We study an optomechanical system in which a microwave field and an optical field are coupled to a common mechanical resonator. We explore methods that use these mechanical resonators to store quantum mechanical states and to transduce states between the electromagnetic resonators from the perspective of the effect of mechanical decoherence. Besides being of fundamental interest, this coherent quantum state transfer could have important practical implications in the field of quantum information science, as it potentially allows one to overcome intrinsic limitations of both microwave and optical platforms. We discuss several state transfer protocols and study their transfer fidelity using a fully quantum mechanical model that utilizes quantum state-diffusion techniques. This work demonstrates that mechanical decoherence should not be an insurmountable obstacle in realizing high fidelity storage and transduction.
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...
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.