Quantum theory Bohrification: topos theory and quantum theory
Spitters, Bas
Quantum theory Bohrification: topos theory and quantum theory Bas Spitters Domains XI, 9/9/2014 Bas Spitters Bohrification: topos theory and quantum theory #12;Quantum theory Point-free Topology The axiom, Krein-Millman, Alaoglu, Hahn-Banach, Gelfand, Zariski, ... Bas Spitters Bohrification: topos theory
Quantum Optimal Control Theory
G. H. Gadiyar
1994-05-10T23:59:59.000Z
The possibility of control of phenomena at microscopic level compatible with quantum mechanics and quantum field theory is outlined. The theory could be used in nanotechnology.
Vukmirovic, Nenad
2010-01-01T23:59:59.000Z
Petersilka, Density Functional Theory (Springer, New York,Quantum Dots: Theory Nenad Vukmirovi´ and Lin-Wang Wang cdensity functional theory; electronic structure; empirical
Quantum Field Theory and Representation Theory
Woit, Peter
Quantum Field Theory and Representation Theory Peter Woit woit@math.columbia.edu Department of Mathematics Columbia University Quantum Field Theory and Representation Theory p.1 #12;Outline of the talk · Quantum Mechanics and Representation Theory: Some History Quantum Field Theory and Representation Theory
Topological quantum field theories
Albert Schwarz
2000-11-29T23:59:59.000Z
Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of topological quantum field theories were constructed in my papers in late seventies) and I come to some new results, that were not published yet.
Robert Carroll
2007-11-05T23:59:59.000Z
We show some relations between Ricci flow and quantum theory via Fisher information and the quantum potential.
Mario G. Silveirinha
2014-06-09T23:59:59.000Z
Here, we develop a comprehensive quantum theory for the phenomenon of quantum friction. Based on a theory of macroscopic quantum electrodynamics for unstable systems, we calculate the quantum expectation of the friction force, and link the friction effect to the emergence of system instabilities related to the Cherenkov effect. These instabilities may occur due to the hybridization of particular guided modes supported by the individual moving bodies, and selection rules for the interacting modes are derived. It is proven that the quantum friction effect can take place even when the interacting bodies are lossless and made of nondispersive dielectrics.
Reverse Engineering Quantum Field Theory
Robert Oeckl
2012-10-02T23:59:59.000Z
An approach to the foundations of quantum theory is advertised that proceeds by "reverse engineering" quantum field theory. As a concrete instance of this approach, the general boundary formulation of quantum theory is outlined.
Lucien Hardy
2013-03-06T23:59:59.000Z
We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map between pure states and maximal effects such that we get unit probability. This maximal effect does not give probability equal to one for any other pure state. Information Locality: A maximal measurement is effected on a composite system if we perform maximal measurements on each of the components. Tomographic Locality: The state of a composite system can be determined from the statistics collected by making measurements on the components. Permutability: There exists a reversible transformation on any system effecting any given permutation of any given maximal set of distinguishable states for that system. Sturdiness: Filters are non-flattening. To single out quantum theory we need only add any requirement that is inconsistent with classical probability theory and consistent with quantum theory.
Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
Maroun, Michael Anthony
2013-01-01T23:59:59.000Z
The Unique Status of Condensed Matter Theory . . . . . . . .of a Satisfactory Theory . . . . . . . . . . . . BasicThe Generalized Quantum Theory The Postulates and Philosophy
Vladimir I. Zverev; Alexander M. Tishin
2009-01-29T23:59:59.000Z
In the given work the first attempt to generalize quantum uncertainty relation on macro objects is made. Business company as one of economical process participants was chosen by the authors for this purpose. The analogies between quantum micro objects and the structures which from the first sight do not have anything in common with physics are given. The proof of generalized uncertainty relation is produced. With the help of generalized uncertainty relation the authors wanted to elaborate a new non-traditional approach to the description of companies' business activity and their developing and try to formulate some advice for them. Thus, our work makes the base of quantum theory of econimics
Noncommutative Quantum Field Theories
H. O. Girotti
2003-03-19T23:59:59.000Z
We start by reviewing the formulation of noncommutative quantum mechanics as a constrained system. Then, we address to the problem of field theories defined on a noncommutative space-time manifold. The Moyal product is introduced and the appearance of the UV/IR mechanism is exemplified. The emphasis is on finding and analyzing noncommutative quantum field theories which are renormalizable and free of nonintegrable infrared singularities. In this last connection we give a detailed discussion of the quantization of the noncommutative Wess-Zumino model as well as of its low energy behavior.
Experimental quantum field theory
Bell, J S
1977-01-01T23:59:59.000Z
Presented here, is, in the opinion of the author, the essential minimum of quantum field theory that should be known to cultivated experimental particle physicists. The word experimental describes not only the audience aimed at but also the level of mathematical rigour aspired to. (0 refs).
Time machines and quantum theory
Mark J Hadley
2006-12-02T23:59:59.000Z
There is a deep structural link between acausal spacetimes and quantum theory. As a consequence quantum theory may resolve some "paradoxes" of time travel. Conversely, non-time-orientable spacetimes naturally give rise to electric charges and spin half. If an explanation of quantum theory is possible, then general relativity with time travel could be it.
Quantum Optimal Control Theory
J. Werschnik; E. K. U. Gross
2007-07-12T23:59:59.000Z
The control of quantum dynamics via specially tailored laser pulses is a long-standing goal in physics and chemistry. Partly, this dream has come true, as sophisticated pulse shaping experiments allow to coherently control product ratios of chemical reactions. The theoretical design of the laser pulse to transfer an initial state to a given final state can be achieved with the help of quantum optimal control theory (QOCT). This tutorial provides an introduction to QOCT. It shows how the control equations defining such an optimal pulse follow from the variation of a properly defined functional. We explain the most successful schemes to solve these control equations and show how to incorporate additional constraints in the pulse design. The algorithms are then applied to simple quantum systems and the obtained pulses are analyzed. Besides the traditional final-time control methods, the tutorial also presents an algorithm and an example to handle time-dependent control targets.
Algebraic Quantum Field Theory
Hans Halvorson; Michael Mueger
2006-02-14T23:59:59.000Z
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of the theory, we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by S. Doplicher, R. Haag, and J. E. Roberts (DHR); and we give an alternative proof of Doplicher and Roberts' reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix.
Quantum Field Theory of Fluids
Ben Gripaios; Dave Sutherland
2015-04-23T23:59:59.000Z
The quantum theory of fields is largely based on studying perturbations around non-interacting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is `freer', in the sense that the non-interacting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree- and loop-level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behaviour is radically different to both classical fluids and quantum fields, with interesting physical consequences for fluids in the low temperature regime.
Recoverability in quantum information theory
Wilde, Mark M
2015-01-01T23:59:59.000Z
The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Our proof method is elementary, relying on the method of complex interpolation, basic linear algebra, and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information...
Matthew James
2014-06-20T23:59:59.000Z
This paper explains some fundamental ideas of {\\em feedback} control of quantum systems through the study of a relatively simple two-level system coupled to optical field channels. The model for this system includes both continuous and impulsive dynamics. Topics covered in this paper include open and closed loop control, impulsive control, optimal control, quantum filtering, quantum feedback networks, and coherent feedback control.
Quantum Field Theory in Graphene
I. V. Fialkovsky; D. V. Vassilevich
2011-11-18T23:59:59.000Z
This is a short non-technical introduction to applications of the Quantum Field Theory methods to graphene. We derive the Dirac model from the tight binding model and describe calculations of the polarization operator (conductivity). Later on, we use this quantity to describe the Quantum Hall Effect, light absorption by graphene, the Faraday effect, and the Casimir interaction.
Quantum Field Theory & Gravity
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
of the universe and which has the same equation of state as that of the quantum vacuum. Gravitational Vacuum Condensate Stars Mottola and external collaborator Mazur have...
Gerbes and quantum field theory
Jouko Mickelsson
2006-03-11T23:59:59.000Z
The basic mechanism how gerbes arise in quantum field theory is explained; in particular the case of chiral fermions in background fields is treated. The role of of various gauge group extensions (central extensions of loop groups and their generalizations) is also explained, in relation to index theory computation of the Dixmier-Douady class of a gerbe.
Quantum Theory: a Pragmatist Approach
Richard Healey
2010-08-23T23:59:59.000Z
While its applications have made quantum theory arguably the most successful theory in physics, its interpretation continues to be the subject of lively debate within the community of physicists and philosophers concerned with conceptual foundations. This situation poses a problem for a pragmatist for whom meaning derives from use. While disputes about how to use quantum theory have arisen from time to time, they have typically been quickly resolved, and consensus reached, within the relevant scientific sub-community. Yet rival accounts of the meaning of quantum theory continue to proliferate . In this article I offer a diagnosis of this situation and outline a pragmatist solution to the problem it poses, leaving further details for subsequent articles.
Monte Carlo Methods in Quantum Field Theory
I. Montvay
2007-05-30T23:59:59.000Z
In these lecture notes some applications of Monte Carlo integration methods in Quantum Field Theory - in particular in Quantum Chromodynamics - are introduced and discussed.
A Naturally Renormalized Quantum Field Theory
S. Rouhani; M. V. Takook
2006-07-07T23:59:59.000Z
It was shown that quantum metric fluctuations smear out the singularities of Green's functions on the light cone [1], but it does not remove other ultraviolet divergences of quantum field theory. We have proved that the quantum field theory in Krein space, {\\it i.e.} indefinite metric quantization, removes all divergences of quantum field theory with exception of the light cone singularity [2,3]. In this paper, it is discussed that the combination of quantum field theory in Krein space together with consideration of quantum metric fluctuations, results in quantum field theory without any divergences.
Gauge Theory of Quantum Gravity
J. W. Moffat
1994-01-04T23:59:59.000Z
A gauge theory of quantum gravity is formulated, in which an internal, field dependent metric is introduced which non-linearly realizes the gauge fields on the non-compact group $SL(2,C)$, while linearly realizing them on $SU(2)$. Einstein's $SL(2,C)$ invariant theory of gravity emerges at low energies, since the extra degrees of freedom associated with the quadratic curvature and the internal metric only dominate at high energies. In a fixed internal metric gauge, only the the $SU(2)$ gauge symmetry is satisfied, the particle spectrum is identified and the Hamiltonian is shown to be bounded from below. Although Lorentz invariance is broken in this gauge, it is satisfied in general. The theory is quantized in this fixed, broken symmetry gauge as an $SU(2)$ gauge theory on a lattice with a lattice spacing equal to the Planck length. This produces a unitary and finite theory of quantum gravity.
Constructive Quantum Field Theory
Giovanni Gallavotti
2005-10-04T23:59:59.000Z
A review of the renormalization group approach to the proof of non perturbative ultraviolet stability in scalar field theories in dimension d=2,3.
Renormalization and quantum field theory
R. E. Borcherds
2011-03-09T23:59:59.000Z
The aim of this paper is to describe how to use regularization and renormalization to construct a perturbative quantum field theory from a Lagrangian. We first define renormalizations and Feynman measures, and show that although there need not exist a canonical Feynman measure, there is a canonical orbit of Feynman measures under renormalization. We then construct a perturbative quantum field theory from a Lagrangian and a Feynman measure, and show that it satisfies perturbative analogues of the Wightman axioms, extended to allow time-ordered composite operators over curved spacetimes.
Quantum Discord and its Role in Quantum Information Theory
Alexander Streltsov
2014-11-12T23:59:59.000Z
Quantum entanglement is the most popular kind of quantum correlations, and its fundamental role in several tasks in quantum information theory like quantum cryptography, quantum dense coding, and quantum teleportation is undeniable. However, recent results suggest that various applications in quantum information theory do not require entanglement, and that their performance can be captured by a new type of quantum correlations which goes beyond entanglement. Quantum discord, introduced by Zurek more than a decade ago, is the most popular candidate for such general quantum correlations. In this work we give an introduction to this modern research direction. After a short review of the main concepts of quantum theory and entanglement, we present quantum discord and general quantum correlations, and discuss three applications which are based on this new type of correlations: remote state preparation, entanglement distribution, and transmission of correlations. We also give an outlook to other research in this direction.
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.
Reformulating and Reconstructing Quantum Theory
Lucien Hardy
2011-08-25T23:59:59.000Z
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the following: [Axiom 1] Operations correspond to operators. [Axiom 2] Every complete set of physical operators corresponds to a complete set of operations. The following operational postulates are shown to be equivalent to these mathematical axioms: [P1] Sharpness. Associated with any given pure state is a unique maximal effect giving probability equal to one. This maximal effect does not give probability equal to one for any other pure state. [P2] Information locality. A maximal measurement on a composite system is effected if we perform maximal measurements on each of the components. [P3] Tomographic locality. The state of a composite system can be determined from the statistics collected by making measurements on the components. [P4] Compound permutability. There exists a compound reversible transformation on any system effecting any given permutation of any given maximal set of distinguishable states for that system. [P5] Sturdiness. Filters are non-flattening. Hence, from these postulates we can reconstruct all the usual features of quantum theory: States are represented by positive operators, transformations by completely positive trace non-increasing maps, and effects by positive operators. The Born rule (i.e. the trace rule) for calculating probabilitieso follows. A more detailed abstract is provided in the paper.
Quantum Control and Representation Theory
A. Ibort; J. M. Pérez-Pardo
2012-03-11T23:59:59.000Z
A new notion of controllability for quantum systems that takes advantage of the linear superposition of quantum states is introduced. We call such notion von Neumann controllabilty and it is shown that it is strictly weaker than the usual notion of pure state and operator controlability. We provide a simple and effective characterization of it by using tools from the theory of unitary representations of Lie groups. In this sense we are able to approach the problem of control of quantum states from a new perspective, that of the theory of unitary representations of Lie groups. A few examples of physical interest and the particular instances of compact and nilpotent dynamical Lie groups are discussed.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V. [Moscow State University, Faculty of Physics (Russian Federation)] [Moscow State University, Faculty of Physics (Russian Federation); Mnatsakanova, M. N., E-mail: mnatsak@theory.sinp.msu.ru [Moscow State University, Skobeltsyn Institute of Nuclear Physics (Russian Federation); Vernov, Yu. S. [Russian Academy of Sciences, Institute for Nuclear Research (Russian Federation)] [Russian Academy of Sciences, Institute for Nuclear Research (Russian Federation)
2013-08-15T23:59:59.000Z
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Haag's Theorem in Noncommutative Quantum Field Theory
K. V. Antipin; M. N. Mnatsakanova; Yu. S. Vernov
2012-02-05T23:59:59.000Z
Haag's theorem was extended to noncommutative quantum field theory in a general case when time does not commute with spatial variables. It was proven that if S-matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in another theory is equal to unity as well. In fact this result is valid in any SO(1,1) invariant quantum field theory, of which an important example is noncommutative quantum field theory.
RELATIVISTIC QUANTUM FIELD THEORY OF A HYPERNUCLEI
Boguta, J.
2013-01-01T23:59:59.000Z
0 Nuclei in Relativistic Field Theory of Nuclear Matter, LBLRelativistic Quantum Field Theory of Finite Nuclei, LBL prein a Relativistic Mean-Field Theory, Stanford preprint F.E.
Mehdi Farzanehpour; I. V. Tokatly
2015-06-29T23:59:59.000Z
We use analytic (current) density-potential maps of time-dependent (current) density functional theory (TD(C)DFT) to inverse engineer analytically solvable time-dependent quantum problems. In this approach the driving potential (the control signal) and the corresponding solution of the Schr\\"odinger equation are parametrized analytically in terms of the basic TD(C)DFT observables. We describe the general reconstruction strategy and illustrate it with a number of explicit examples. First we consider the real space one-particle dynamics driven by a time-dependent electromagnetic field and recover, from the general TDDFT reconstruction formulas, the known exact solution for a driven oscillator with a time-dependent frequency. Then we use analytic maps of the lattice TD(C)DFT to control quantum dynamics in a discrete space. As a first example we construct a time-dependent potential which generates prescribed dynamics on a tight-binding chain. Then our method is applied to the dynamics of spin-1/2 driven by a time dependent magnetic field. We design an analytic control pulse that transfers the system from the ground to excited state and vice versa. This pulse generates the spin flip thus operating as a quantum NOT gate.
Beyond the scalar Higgs, in lattice quantum field theory
Schroeder, Christopher Robert
2009-01-01T23:59:59.000Z
as an effective field theory . . . . . Higgs mass upperHiggs, in Lattice Quantum Field Theory by Christopher Robertin Lattice Quantum Field Theory A dissertation submitted in
Kevin Leung; Susan B. Rempe; Peter A. Schultz; Eduardo M. Sproviero; Victor S. Batista; Michael E. Chandross; Craig J. Medforth
2006-10-26T23:59:59.000Z
We apply Density Functional Theory (DFT) and the DFT+U technique to study the adsorption of transition metal porphine molecules on atomistically flat Au(111) surfaces. DFT calculations using the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional correctly predict the palladium porphine (PdP) low-spin ground state. PdP is found to adsorb preferentially on gold in a flat geometry, not in an edgewise geometry, in qualitative agreement with experiments on substituted porphyrins. It exhibits no covalent bonding to Au(111), and the binding energy is a small fraction of an eV. The DFT+U technique, parameterized to B3LYP predicted spin state ordering of the Mn d-electrons, is found to be crucial for reproducing the correct magnetic moment and geometry of the isolated manganese porphine (MnP) molecule. Adsorption of Mn(II)P on Au(111) substantially alters the Mn ion spin state. Its interaction with the gold substrate is stronger and more site-specific than PdP. The binding can be partially reversed by applying an electric potential, which leads to significant changes in the electronic and magnetic properties of adsorbed MnP, and ~ 0.1 Angstrom, changes in the Mn-nitrogen distances within the porphine macrocycle. We conjecture that this DFT+U approach may be a useful general method for modeling first row transition metal ion complexes in a condensed-matter setting.
Some Studies in Noncommutative Quantum Field Theories
Sunandan Gangopadhyay
2008-06-12T23:59:59.000Z
The central theme of this thesis is to study some aspects of noncommutative quantum mechanics and noncommutative quantum field theory. We explore how noncommutative structures can emerge and study the consequences of such structures in various physical models.
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.
Spinless Quantum Field Theory and Interpretation
Dong-Sheng Wang
2013-03-07T23:59:59.000Z
Quantum field theory is mostly known as the most advanced and well-developed theory in physics, which combines quantum mechanics and special relativity consistently. In this work, we study the spinless quantum field theory, namely the Klein-Gordon equation, and we find that there exists a Dirac form of this equation which predicts the existence of spinless fermion. For its understanding, we start from the interpretation of quantum field based on the concept of quantum scope, we also extract new meanings of wave-particle duality and quantum statistics. The existence of spinless fermion is consistent with spin-statistics theorem and also supersymmetry, and it leads to several new kinds of interactions among elementary particles. Our work contributes to the study of spinless quantum field theory and could have implications for the case of higher spin.
Quantum Information Processing Theory 1 Running head: QUANTUM INFORMATION PROCESSING THEORY
Busemeyer, Jerome R.
Quantum Information Processing Theory 1 Running head: QUANTUM INFORMATION PROCESSING THEORY Quantum, IN USA jstruebl@indiana.edu jbusemey@indiana.edu In D. Quinones (Ed.) Encyclopedia of the Sciences provides new conceptual tools for constructing social and behavioral science theories. Theoretical
Quantum control theory and applications: A survey
Daoyi Dong; Ian R Petersen
2011-01-10T23:59:59.000Z
This paper presents a survey on quantum control theory and applications from a control systems perspective. Some of the basic concepts and main developments (including open-loop control and closed-loop control) in quantum control theory are reviewed. In the area of open-loop quantum control, the paper surveys the notion of controllability for quantum systems and presents several control design strategies including optimal control, Lyapunov-based methodologies, variable structure control and quantum incoherent control. In the area of closed-loop quantum control, the paper reviews closed-loop learning control and several important issues related to quantum feedback control including quantum filtering, feedback stabilization, LQG control and robust quantum control.
On Quantum Computation Theory Wim van Dam
ten Cate, Balder
On Quantum Computation Theory Wim van Dam #12;#12;On Quantum Computation Theory #12;ILLC woensdag 9 oktober 2002, te 14.00 uur door Willem Klaas van Dam geboren te Breda. #12;Promotor: Prof. dr. P Dam, 2002 ISBN: 9057760916 #12;" . . . Many errors have been made in the world which today
Quantum communication, reference frames and gauge theory
S. J. van Enk
2006-04-26T23:59:59.000Z
We consider quantum communication in the case that the communicating parties not only do not share a reference frame but use imperfect quantum communication channels, in that each channel applies some fixed but unknown unitary rotation to each qubit. We discuss similarities and differences between reference frames within that quantum communication model and gauge fields in gauge theory. We generalize the concept of refbits and analyze various quantum communication protocols within the communication model.
Quantum measure and integration theory
Stan Gudder
2009-09-11T23:59:59.000Z
This article begins with a review of quantum measure spaces. Quantum forms and indefinite inner-product spaces are then discussed. The main part of the paper introduces a quantum integral and derives some of its properties. The quantum integral's form for simple functions is characterized and it is shown that the quantum integral generalizes the Lebesgue integral. A bounded, monotone convergence theorem for quantum integrals is obtained and it is shown that a Radon-Nikodym type theorem does not hold for quantum measures. As an example, a quantum-Lebesgue integral on the real line is considered.
Axiomatic quantum field theory in curved spacetime
S. Hollands; R. M. Wald
2008-03-13T23:59:59.000Z
The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features--such as Poincare invariance and the existence of a preferred vacuum state--that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status, and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum field theory is locally and covariantly constructed from the spacetime metric), a microlocal spectrum condition, an "associativity" condition, and the requirement that the coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved spacetime versions of the spin-statistics theorem and the PCT theorem. Some potentially significant further implications of our new viewpoint on quantum field theory are discussed.
Quantum field theory and the Standard Model
W. Hollik
2010-12-17T23:59:59.000Z
In this lecture we discuss the basic ingredients for gauge invariant quantum field theories. We give an introduction to the elements of quantum field theory, to the construction of the basic Lagrangian for a general gauge theory, and proceed with the formulation of QCD and the electroweak Standard Model with electroweak symmetry breaking via the Higgs mechanism. The phenomenology of W and Z bosons is discussed and implications for the Higgs boson are derived from comparison with experimental precision data.
Computer Stochastics in Scalar Quantum Field Theory
C. B. Lang
1993-12-01T23:59:59.000Z
This is a series of lectures on Monte Carlo results on the non-perturbative, lattice formulation approach to quantum field theory. Emphasis is put on 4D scalar quantum field theory. I discuss real space renormalization group, fixed point properties and logarithmic corrections, partition function zeroes, the triviality bound on the Higgs mass, finite size effects, Goldstone bosons and chiral perturbation theory, and the determination of scattering phase shifts for some scalar models.
An Accumulative Model for Quantum Theories
Christopher Thron
2015-06-06T23:59:59.000Z
For a general quantum theory that is describable by a path integral formalism, we construct a mathematical model of an accumulation-to-threshold process whose outcomes give predictions that are nearly identical to the given quantum theory. The model is neither local nor causal in spacetime, but is both local and causal is in a non-observable path space. The probabilistic nature of the squared wavefunction is a natural consequence of the model. We verify the model with simulations, and we discuss possible discrepancies from conventional quantum theory that might be detectable via experiment. Finally, we discuss the physical implications of the model.
3D Quantum Gravity and Effective Noncommutative Quantum Field Theory
Freidel, Laurent; Livine, Etera R. [Perimeter Institute, 31 Caroline Street, North Waterloo, Ontario N2L 2Y5, Canada, and Laboratoire de Physique, ENS Lyon, CNRS UMR 5672, 46 Allee d'Italie, 69364 Lyon Cedex 07 (France)
2006-06-09T23:59:59.000Z
We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a {kappa} deformation of the Poincare group.
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.
Topos theory and `neo-realist' quantum theory
Andreas Doering
2007-12-24T23:59:59.000Z
Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves as a `mathematical universe' with an internal logic, which is used to assign truth-values to all propositions about a physical system. We show in detail how this works for (algebraic) quantum theory.
##### 3 ## topological quantum field theory
Kawahigashi, Yasuyuki
######### ## bimodule ##### #compact ### ############ ########## ####### # ## ############ ######## bimodule) ######## fusion algebra ###### ##### # # ### tensor ### ###### ########### #### ## level ## Wess-symbol ### ##### ######### ################## ###### Fusion algebra # quantum 6j-symbol #### ##### ####### ##### paragroup #### formulation
Functional Integration for Quantum Field Theory
J. LaChapelle
2006-10-16T23:59:59.000Z
The functional integration scheme for path integrals advanced by Cartier and DeWitt-Morette is extended to the case of fields. The extended scheme is then applied to quantum field theory. Several aspects of the construction are discussed.
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 ...
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.
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.
The informationally-complete quantum theory
Zeng-Bing Chen
2015-05-25T23:59:59.000Z
Quantum mechanics is a cornerstone of our current understanding of nature and extremely successful in describing physics covering a huge range of scales. However, its interpretation remains controversial for a long time, from the early days of quantum mechanics to nowadays. What does a quantum state really mean? Is there any way out of the so-called quantum measurement problem? Here we present an informationally-complete quantum theory (ICQT) and the trinary property of nature to beat the above problems. We assume that a quantum system's state provides an informationally-complete description of the system in the trinary picture. We give a consistent formalism of quantum theory that makes the informational completeness explicitly and argue that the conventional quantum mechanics is an approximation of the ICQT. We then show how our ICQT provides a coherent picture and fresh angle of some existing problems in physics. The computational content of our theory is uncovered by defining an informationally-complete quantum computer.
Quantum Computation of Scattering in Scalar Quantum Field Theories
Stephen P. Jordan; Keith S. M. Lee; John Preskill
2011-12-20T23:59:59.000Z
Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally, and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to compute relativistic scattering amplitudes in massive phi-fourth theory in spacetime of four and fewer dimensions. The algorithm runs in a time that is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. Thus, it offers exponential speedup over existing classical methods at high precision or strong coupling.
General Covariance in Algebraic Quantum Field Theory
Romeo Brunetti; Martin Porrmann; Giuseppe Ruzzi
2005-12-17T23:59:59.000Z
In this review we report on how the problem of general covariance is treated within the algebraic approach to quantum field theory by use of concepts from category theory. Some new results on net cohomology and superselection structure attained in this framework are included.
Algebraic conformal quantum field theory in perspective
Karl-Henning Rehren
2015-01-14T23:59:59.000Z
Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete classifications. The structural insights, analytical methods and constructive tools are expected to be useful also for four-dimensional QFT.
Some convolution products in Quantum Field Theory
Herintsitohaina Ratsimbarison
2006-12-05T23:59:59.000Z
This paper aims to show constructions of scale dependence and interaction on some probabilistic models which may be revelant for renormalization theory in Quantum Field Theory. We begin with a review of the convolution product's use in the Kreimer-Connes formalism of perturbative renormalization. We show that the Wilson effective action can be obtained from a convolution product propriety of regularized Gaussian measures on the space of fields. Then, we propose a natural C*-algebraic framework for scale dependent field theories which may enhance the conceptual approach to renormalization theory. In the same spirit, we introduce a probabilistic construction of interacting theories for simple models and apply it for quantum field theory by defining a partition function in this setting.
Noncommutative Deformations of Wightman Quantum Field Theories
Harald Grosse; Gandalf Lechner
2008-08-26T23:59:59.000Z
Quantum field theories on noncommutative Minkowski space are studied in a model-independent setting by treating the noncommutativity as a deformation of quantum field theories on commutative space. Starting from an arbitrary Wightman theory, we consider special vacuum representations of its Weyl-Wigner deformed counterpart. In such representations, the effect of the noncommutativity on the basic structures of Wightman theory, in particular the covariance, locality and regularity properties of the fields, the structure of the Wightman functions, and the commutative limit, is analyzed. Despite the nonlocal structure introduced by the noncommutativity, the deformed quantum fields can still be localized in certain wedge-shaped regions, and may therefore be used to compute noncommutative corrections to two-particle S-matrix elements.
Krykunov, Mykhaylo; Seth, Mike; Ziegler, Tom [Department of Chemistry, University of Calgary, University Drive 2500, Calgary, Alberta T2N 1N4 (Canada)] [Department of Chemistry, University of Calgary, University Drive 2500, Calgary, Alberta T2N 1N4 (Canada)
2014-05-14T23:59:59.000Z
We have applied the relaxed and self-consistent extension of constricted variational density functional theory (RSCF-CV-DFT) for the calculation of the lowest charge transfer transitions in the molecular complex X-TCNE between X = benzene and TCNE = tetracyanoethylene. Use was made of functionals with a fixed fraction (?) of Hartree-Fock exchange ranging from ? = 0 to ? = 0.5 as well as functionals with a long range correction (LC) that introduces Hartree-Fock exchange for longer inter-electronic distances. A detailed comparison and analysis is given for each functional between the performance of RSCF-CV-DFT and adiabatic time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation. It is shown that in this particular case, all functionals afford the same reasonable agreement with experiment for RSCF-CV-DFT whereas only the LC-functionals afford a fair agreement with experiment using TDDFT. We have in addition calculated the CT transition energy for X-TCNE with X = toluene, o-xylene, and naphthalene employing the same functionals as for X = benzene. It is shown that the calculated charge transfer excitation energies are in as good agreement with experiment as those obtained from highly optimized LC-functionals using adiabatic TDDFT. We finally discuss the relation between the optimization of length separation parameters and orbital relaxation in the RSCF-CV-DFT scheme.
Quantum Field Theory on Noncommutative Spaces
Richard J. Szabo
2003-01-23T23:59:59.000Z
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative Yang-Mills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an in-depth study of the gauge group of noncommutative Yang-Mills theory. Some of the more mathematical ideas and techniques of noncommutative geometry are also briefly explained.
Formalism Locality in Quantum Theory and Quantum Gravity
Lucien Hardy
2008-04-01T23:59:59.000Z
We expect a theory of Quantum Gravity to be both probabilistic and have indefinite causal structure. Indefinite causal structure poses particular problems for theory formulation since many of the core ideas used in the usual approaches to theory construction depend on having definite causal structure. For example, the notion of a state across space evolving in time requires that we have some definite causal structure so we can define a state on a space-like hypersurface. We will see that many of these problems are mitigated if we are able to formulate the theory in a "formalism local" (or F-local) fashion. A formulation of a physical theory is said to be F-local if, in making predictions for any given arbitrary space-time region, we need only refer to mathematical objects pertaining to that region. This is a desirable property both on the grounds of efficiency and since, if we have indefinite causal structure, it is not clear how to select some other space-time region on which our calculations may depend. The usual ways of formulating physical theories (the time evolving state picture, the histories approach, and the local equations approach) are not F-local. We set up a framework for probabilistic theories with indefinite causal structure. This, the causaloid framework, is F-local. We describe how Quantum Theory can be formulated in the causaloid framework (in an F-local fashion). This provides yet another formulation of Quantum Theory. This formulation, however, may be particularly relevant to the problem of finding a theory of Quantum Gravity.
Generalized Probability Theories: What determines the structure of quantum theory?
Peter Janotta; Haye Hinrichsen
2014-08-13T23:59:59.000Z
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical structure of quantum theory. This review paper tries to present the framework and recent results to a broader readership in an accessible manner. To achieve this, we follow a constructive approach. Starting from few basic physically motivated assumptions we show how a given set of observations can be manifested in an operational theory. Furthermore, we characterize consistency conditions limiting the range of possible extensions. In this framework classical and quantum theory appear as special cases, and the aim is to understand what distinguishes quantum mechanics as the fundamental theory realized in nature. It turns out non-classical features of single systems can equivalently result from higher dimensional classical theories that have been restricted. Entanglement and non-locality, however, are shown to be genuine non-classical features.
Quantum simulation of quantum field theory using continuous variables
Kevin Marshall; Raphael Pooser; George Siopsis; Christian Weedbrook
2015-03-27T23:59:59.000Z
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has led to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is believed to be hard using a classical computer. Building on this, we give an experimental implementation based on cluster states that is feasible with today's technology.
Burns, Lori A [ORNL; Sherrill, David [Georgia Institute of Technology; Vazquez-Mayagoitia, Alvaro [ORNL; Sumpter, Bobby G [ORNL
2011-01-01T23:59:59.000Z
A systematic study of techniques for treating non-covalent interactions within the computationally efficient density functional theory (DFT) framework is presented through comparison to benchmark-quality evaluations of binding strength com- piled for molecular complexes of diverse size and nature. In particular, the effi- cacy of functionals deliberately crafted to encompass long-range forces, a posteri- ori DFT+dispersion corrections (DFT-D2 and DFT-D3), and exchange-hole dipole moment (XDM) theory is assessed against a large collection (469 energy points) of reference interaction energies at the CCSD(T) level of theory extrapolated to the estimated complete basis set limit. The established S22 and JSCH test sets of minimum-energy structures, as well as collections of dispersion-bound (NBC10) and hydrogen-bonded (HBC6) dissociation curves and a pairwise decomposition of a protein-ligand reaction site (HSG), comprise the chemical systems for this work. From evaluations of accuracy, consistency, and efficiency for PBE-D, BP86-D, B97-D, PBE0-D, B3LYP-D, B970-D, M05-2X, M06-2X, B97X-D, B2PLYP-D, XYG3, and B3LYP-XDM methodologies, it is concluded that distinct, often contrasting, groups of these elicit the best performance within the accessible double- or robust triple- basis set regimes and among hydrogen-bonded or dispersion-dominated complexes. For overall results, M05-2X, B97-D3, and B970-D2 yield superior values in conjunc- tion with aug-cc-pVDZ, for a mean absolute deviation of 0.41 0.49 kcal/mol, and B3LYP-D3, B97-D3, B97X-D, and B2PLYP-D3 dominate with aug-cc-pVTZ, af- fording, together with XYG3/6-311+G(3df,2p), a mean absolute deviation of 0.33 0.38 kcal/mol.
Undergraduate Lecture Notes in Topological Quantum Field Theory
Vladimir G. Ivancevic; Tijana T. Ivancevic
2008-12-11T23:59:59.000Z
These third-year lecture notes are designed for a 1-semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second-year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism. Keywords: quantum mechanics/field theory, path integral, Hodge decomposition, Chern-Simons and Yang-Mills gauge theories, conformal field theory
A Kinetic Theory Approach to Quantum Gravity
B. L. Hu
2002-04-22T23:59:59.000Z
We describe a kinetic theory approach to quantum gravity -- by which we mean a theory of the microscopic structure of spacetime, not a theory obtained by quantizing general relativity. A figurative conception of this program is like building a ladder with two knotted poles: quantum matter field on the right and spacetime on the left. Each rung connecting the corresponding knots represent a distinct level of structure. The lowest rung is hydrodynamics and general relativity; the next rung is semiclassical gravity, with the expectation value of quantum fields acting as source in the semiclassical Einstein equation. We recall how ideas from the statistical mechanics of interacting quantum fields helped us identify the existence of noise in the matter field and its effect on metric fluctuations, leading to the establishment of the third rung: stochastic gravity, described by the Einstein-Langevin equation. Our pathway from stochastic to quantum gravity is via the correlation hierarchy of noise and induced metric fluctuations. Three essential tasks beckon: 1) Deduce the correlations of metric fluctuations from correlation noise in the matter field; 2) Reconstituting quantum coherence -- this is the reverse of decoherence -- from these correlation functions 3) Use the Boltzmann-Langevin equations to identify distinct collective variables depicting recognizable metastable structures in the kinetic and hydrodynamic regimes of quantum matter fields and how they demand of their corresponding spacetime counterparts. This will give us a hierarchy of generalized stochastic equations -- call them the Boltzmann-Einstein hierarchy of quantum gravity -- for each level of spacetime structure, from the macroscopic (general relativity) through the mesoscopic (stochastic gravity) to the microscopic (quantum gravity).
Wavelet-Based Quantum Field Theory
Mikhail V. Altaisky
2007-11-11T23:59:59.000Z
The Euclidean quantum field theory for the fields $\\phi_{\\Delta x}(x)$, which depend on both the position $x$ and the resolution $\\Delta x$, constructed in SIGMA 2 (2006), 046, hep-th/0604170, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments.
Remarks on twisted noncommutative quantum field theory
Zahn, Jochen [II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)
2006-05-15T23:59:59.000Z
We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the twisted structure is so rigid that it is hard to derive any predictions, unless one gives up general principles of quantum theory. It is also shown that the twisted structure is not responsible for the presence or absence of UV/IR-mixing, as claimed in the literature.
Reasonable fermionic quantum information theories require relativity
Nicolai Friis
2015-02-16T23:59:59.000Z
We show that any abstract quantum information theory based on anticommuting operators must be supplemented by a superselection rule deeply rooted in relativity. While quantum information may be encoded in the Fock space generated by such operators, the unrestricted fermionic theory has a peculiar feature: Pairs of bipartition marginals of pure states need not have identical spectra. This leads to an ambiguous definition of the entropy of entanglement. We prove that this problem is removed by a superselection rule that arises from Lorentz invariance and no-signalling.
Quantum Field Theory Mark Srednicki
Akhmedov, Azer
The Spin-Statistics Theorem (3) 45 5 The LSZ Reduction Formula (3) 49 6 Path Integrals in Quantum Mechanics Quantization of Spinor Fields II (38) 246 40 Parity, Time Reversal, and Charge Conjugation (23, 39) 254 #12, 59) 369 #12;6 63 The Vertex Function in Spinor Electrodynamics (62) 378 64 The Magnetic Moment
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...
Physics 221B: Solution to HW # 8 Quantum Field Theory
Murayama, Hitoshi
Physics 221B: Solution to HW # 8 Quantum Field Theory 1) Bosonic Grand-Partition Function The solution to this problem is outlined clearly in the beginning of the lecture notes `Quantum Field Theory II
Mathematical definition of quantum field theory on a manifold
A. V. Stoyanovsky
2009-11-21T23:59:59.000Z
We give a mathematical definition of quantum field theory on a manifold, and definition of quantization of a classical field theory given by a variational principle.
Quantum field theory of relic nonequilibrium systems
Nicolas G. Underwood; Antony Valentini
2014-11-14T23:59:59.000Z
In terms of the de Broglie-Bohm pilot-wave formulation of quantum theory, we develop field-theoretical models of quantum nonequilibrium systems which could exist today as relics from the very early universe. We consider relic excited states generated by inflaton decay, as well as relic vacuum modes, for particle species that decoupled close to the Planck temperature. Simple estimates suggest that, at least in principle, quantum nonequilibrium could survive to the present day for some relic systems. The main focus of this paper is to describe the behaviour of such systems in terms of field theory, with the aim of understanding how relic quantum nonequilibrium might manifest experimentally. We show by explicit calculation that simple perturbative couplings will transfer quantum nonequilibrium from one field to another (for example from the inflaton field to its decay products). We also show that fields in a state of quantum nonequilibrium will generate anomalous spectra for standard energy measurements. Possible connections to current astrophysical observations are briefly addressed.
The Operator Tensor Formulation of Quantum Theory
Lucien Hardy
2012-01-20T23:59:59.000Z
A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter reading for example), as an operation. An operation can have zero or more quantum systems inputted into it and zero or more quantum systems outputted from it. We can wire together operations to form circuits. In the standard framework of quantum theory we must foliate the circuit then calculate the probability by evolving a state through it. This approach has three problems. First, we must introduce an arbitrary foliation of the circuit (such foliations are not unique). Second, we have to pad our expressions with identities every time two or more foliation hypersurfaces intersect a given wire. And third, we treat operations corresponding to preparations, transformations, and results in different ways. In this paper we present the operator tensor formulation of quantum theory which solves all these problems. Corresponding to every operation is an operator tensor. The probability for a circuit is given by simply replacing the operations in the circuit with the corresponding operator tensors. Wires between operator tensors correspond to multiplying the tensors in the associated subspace and then taking the partial trace over that subspace. Operator tensors must be physical (namely, they must have positive input transpose and satisfy a certain normalization condition).
Canonical quantum potential scattering theory
M. S. Hussein; W. Li; S. Wuester
2008-07-13T23:59:59.000Z
A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find non-linear first-order differential equations for the low energy scattering parameters like scattering length and effective range. They significantly simplify typical calculations, as we illustrate for atom-atom and neutron-nucleus scattering systems. A generalization to charged particle scattering is also possible.
Functorial Quantum Field Theory in the Riemannian setting
Santosh Kandel
2015-02-25T23:59:59.000Z
We construct examples of Functorial Quantum Field Theories in the Riemannian setting by quantizing free massive bosons.
Noncommutative Time in Quantum Field Theory
Tapio Salminen; Anca Tureanu
2011-07-19T23:59:59.000Z
We analyze, starting from first principles, the quantization of field theories, in order to find out to which problems a noncommutative time would possibly lead. We examine the problem in the interaction picture (Tomonaga-Schwinger equation), the Heisenberg picture (Yang-Feldman-K\\"all\\'{e}n equation) and the path integral approach. They all indicate inconsistency when time is taken as a noncommutative coordinate. The causality issue appears as the key aspect, while the unitarity problem is subsidiary. These results are consistent with string theory, which does not admit a time-space noncommutative quantum field theory as its low-energy limit, with the exception of light-like noncommutativity.
Measurement theory in local quantum physics
Kazuya Okamura; Masanao Ozawa
2015-04-24T23:59:59.000Z
In this paper, we aim at establishing measurement theory in local quantum physics. For this purpose, we discuss a representation theory of completely positive (CP) instruments. We introduce a condition called the normal extension property (NEP) and establish a one-to-one correspondence between CP instruments with NEP and statistical equivalence classes of measuring processes. We further explore a class of CP instruments having measuring processes approximately by the notion of injectivity of von Neumann algebras. The existence problem of a family of a posteriori states is discussed and it is shown that NEP is equivalent to the existence of a strongly measurable family of a posteriori states for every normal state. Moreover, two examples of CP instruments without NEP are given. To conclude the paper, local measurements in algebraic quantum field theory are developed.
Goddard III, William A.
activity of the proposed materials by density functional theory (DFT). Quantum mechanics was applied for automotive applications, sta- tionary/portable power supply, and as a component of hybrid energy systems1 reaction (HOR) at the anode.8 ORR mechanisms and electronic structures of ORR catalysts are widely
Atomic and Molecular Quantum Theory Course Number: C561 26 Group Theory Basics
Iyengar, Srinivasan S.
Atomic and Molecular Quantum Theory Course Number: C561 26 Group Theory Basics 1. Reference: "Group Theory and Quantum Mechanics" by Michael Tinkham. 2. We said earlier that we will go looking for the set, Indiana University 266 c 2003, Srinivasan S. Iyengar (instructor) #12;Atomic and Molecular Quantum Theory
Natural Philosophy and Quantum Theory
Thomas Marlow
2006-10-25T23:59:59.000Z
We attempt to show how relationalism might help in understanding Bell's theorem. We also present an analogy with Darwinian evolution in order to pedagogically hint at how one might go about using a theory in which one does not even desire to explain correlations by invoking common causes.
Some differences between Dirac's hole theory and quantum field theory
Dan Solomon
2005-06-30T23:59:59.000Z
Diracs hole theory (HT) and quantum field theory (QFT) are generally considered to be equivalent to each other. However, it has been recently shown by several researchers that this is not necessarily the case. When the change in the vacuum energy was calculated for a time independent perturbation HT and QFT yielded different results. In this paper we extend this discussion to include a time dependent perturbation for which the exact solution to the Dirac equation is known. It will be shown that for this case, also, HT and QFT yield different results. In addition, there will be some discussion of the problem of anomalies in QFT.
Real World Interpretations of Quantum Theory
Adrian Kent
2011-11-03T23:59:59.000Z
I propose a new class of interpretations, {\\it real world interpretations}, of the quantum theory of closed systems. These interpretations postulate a preferred factorization of Hilbert space and preferred projective measurements on one factor. They give a mathematical characterisation of the different possible worlds arising in an evolving closed quantum system, in which each possible world corresponds to a (generally mixed) evolving quantum state. In a realistic model, the states corresponding to different worlds should be expected to tend towards orthogonality as different possible quasiclassical structures emerge or as measurement-like interactions produce different classical outcomes. However, as the worlds have a precise mathematical definition, real world interpretations need no definition of quasiclassicality, measurement, or other concepts whose imprecision is problematic in other interpretational approaches. It is natural to postulate that precisely one world is chosen randomly, using the natural probability distribution, as the world realised in Nature, and that this world's mathematical characterisation is a complete description of reality.
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.
Contradictions of the quantum scattering theory
V. K. Ignatovich
2006-01-23T23:59:59.000Z
The standard scattering theory (SST) in non relativistic quantum mechanics (QM) is analyzed. Self-contradictions of SST are deconstructed. A direct way to calculate scattering probability without introduction of a finite volume is discussed. Substantiation of SST in textbooks with the help of wave packets is shown to be incomplete. A complete theory of wave packets scattering on a fixed center is presented, and its similarity to the plane wave scattering is demonstrated. The neutron scattering on a monatomic gas is investigated, and several problems are pointed out. A catastrophic ambiguity of the cross section is revealed, and a way to resolve this ambiguity is discussed.
Causality and chance in relativistic quantum field theories
Richard Healey
2014-05-13T23:59:59.000Z
Bell appealed to the theory of relativity in formulating his principle of local causality. But he maintained that quantum field theories do not conform to that principle, even when their field equations are relativistically covariant and their observable algebras satisfy a relativistically motivated microcausality condition. A pragmatist view of quantum theory and an interventionist approach to causation prompt the reevaluation of local causality and microcausality. Local causality cannot be understood as a reasonable requirement on relativistic quantum field theories: it is unmotivated even if applicable to them. But microcausality emerges as a sufficient condition for the consistent application of a relativistic quantum field theory.
Quantum Jet Theory I: Free fields
T. A. Larsson
2007-01-18T23:59:59.000Z
QJT (Quantum Jet Theory) is the quantum theory of jets, which can be canonically identified with truncated Taylor series. Ultralocality requires a novel quantization scheme, where dynamics is treated as a constraint in the history phase space. QJT differs from QFT since it involves a new datum: the expansion point. This difference is substantial because it leads to new gauge and diff anomalies, which are necessary to combine background independence with locality. Physically, the new ingredient is that the observer's trajectory is explicitly introduced and quantized together with the fields. In this paper the harmonic oscillator and free fields are treated within QJT, correcting previous flaws. The standard Hilbert space is recovered for the harmonic oscillator, but there are interesting modifications already for the free scalar field, due to quantization of the observer's trajectory. Only free fields are treated in detail, but the complications when interactions are introduced are briefly discussed. We also explain why QJT is necessary to resolve the conceptual problems of quantum gravity.
Scattering Theory for Open Quantum Systems
J. Behrndt; M. M. Malamud; H. Neidhardt
2006-10-31T23:59:59.000Z
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator $A_D$ in a Hilbert space $\\sH$ is used to describe an open quantum system. In this case the minimal self-adjoint dilation $\\widetilde K$ of $A_D$ can be regarded as the Hamiltonian of a closed system which contains the open system $\\{A_D,\\sH\\}$, but since $\\widetilde K$ is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family $\\{A(\\mu)\\}$ of maximal dissipative operators depending on energy $\\mu$, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single Pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm-Liouville operators arising in dissipative and quantum transmitting Schr\\"{o}dinger-Poisson systems.
Aspects of locally covariant quantum field theory
Ko Sanders
2008-09-28T23:59:59.000Z
This thesis considers various aspects of locally covariant quantum field theory (LCQFT; see Brunetti et al., Commun.Math.Phys. 237 (2003), 31-68), a mathematical framework to describe axiomatic quantum field theories in curved spacetimes. New results include: a philosophical interpretation of certain aspects of this framework in terms of modal logic; a proof that the truncated n-point functions of any Hadamard state of the free real scalar field are smooth, except for n=2; a description of he free Dirac field in a representation independent way, showing that the theory is determined entirely by the relations between the adjoint map, the charge conjugation map and the Dirac operator; a proof that the relative Cauchy evolution of the free Dirac field is related to its stress-energy-momentum tensor in the same way as for the free real scalar field (cf. loc.cit.); several results on the Reeh-Schlieder property in LCQFT, including but not limited to those of our earlier paper; a new and elegant approach to wave front sets of Banach space-valued distributions, which allows easy proofs and extensions of results in the literature.
Algebraic quantum field theory in curved spacetimes
Christopher J. Fewster; Rainer Verch
2015-04-02T23:59:59.000Z
This article sets out the framework of algebraic quantum field theory in curved spacetimes, based on the idea of local covariance. In this framework, a quantum field theory is modelled by a functor from a category of spacetimes to a category of ($C^*$)-algebras obeying supplementary conditions. Among other things: (a) the key idea of relative Cauchy evolution is described in detail, and related to the stress-energy tensor; (b) a systematic "rigidity argument" is used to generalise results from flat to curved spacetimes; (c) a detailed discussion of the issue of selection of physical states is given, linking notions of stability at microscopic, mesoscopic and macroscopic scales; (d) the notion of subtheories and global gauge transformations are formalised; (e) it is shown that the general framework excludes the possibility of there being a single preferred state in each spacetime, if the choice of states is local and covariant. Many of the ideas are illustrated by the example of the free Klein-Gordon theory, which is given a new "universal definition".
Radiation reaction in quantum field theory
Atsushi Higuchi
2004-03-30T23:59:59.000Z
We investigate radiation-reaction effects for a charged scalar particle accelerated by an external potential realized as a space-dependent mass term in quantum electrodynamics. In particular, we calculate the position shift of the final-state wave packet of the charged particle due to radiation at lowest order in the fine structure constant alpha and in the small h-bar approximation. We show that it disagrees with the result obtained using the Lorentz-Dirac formula for the radiation-reaction force, and that it agrees with the classical theory if one assumes that the particle loses its energy to radiation at each moment of time according to the Larmor formula in the static frame of the potential. However, the discrepancy is much smaller than the Compton wavelength of the particle. We also point out that the electromagnetic correction to the potential has no classical limit. (Correction. Surface terms were erroneously discarded to arrive at Eq. (59). By correcting this error we find that the position shift according to the Lorentz-Dirac theory obtained from Eq. (12) is reproduced by quantum field theory in the hbar -> 0 limit. We also find that the small V(z) approximation is unnecessary for this agreement. See Sec. VII.)
Analogy between turbulence and quantum gravity: beyond Kolmogorov's 1941 theory
S. Succi
2011-11-14T23:59:59.000Z
Simple arguments based on the general properties of quantum fluctuations have been recently shown to imply that quantum fluctuations of spacetime obey the same scaling laws of the velocity fluctuations in a homogeneous incompressible turbulent flow, as described by Kolmogorov 1941 (K41) scaling theory. Less noted, however, is the fact that this analogy rules out the possibility of a fractal quantum spacetime, in contradiction with growing evidence in quantum gravity research. In this Note, we show that the notion of a fractal quantum spacetime can be restored by extending the analogy between turbulence and quantum gravity beyond the realm of K41 theory. In particular, it is shown that compatibility of a fractal quantum-space time with the recent Horava-Lifshitz scenario for quantum gravity, implies singular quantum wavefunctions. Finally, we propose an operational procedure, based on Extended Self-Similarity techniques, to inspect the (multi)-scaling properties of quantum gravitational fluctuations.
Open quantum systems and Random Matrix Theory
Declan Mulhall
2015-01-09T23:59:59.000Z
A simple model for open quantum systems is analyzed with Random Matrix Theory. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the $\\Delta_3(L)$ statistic, width distribution and level spacing are examined as a function of the strength of this coupling. A super-radiant transition is observed, and it is seen that as it is formed, the level spacing and $\\Delta_3(L)$ statistic exhibit the signatures of missed levels.
The effective field theory treatment of quantum gravity
Donoghue, John F. [Department of Physics, University of Massachusetts, Amherst, MA 01003 (United States)
2012-09-24T23:59:59.000Z
This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime.
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.
Rigorous Definition of Quantum Field Operators in Noncommutative Quantum Field Theory
M. N. Mnatsakanova; Yu. S. Vernov
2010-02-07T23:59:59.000Z
The space, on which quantum field operators are given, is constructed in any theory, in which the usual product between test functions is substituted by the $\\star$-product (the Moyal-type product). The important example of such a theory is noncommutative quantum field theory (NC QFT). This construction is the key point in the derivation of the Wightman reconstruction theorem.
Howard Barnum
2006-11-10T23:59:59.000Z
In this paper, I propose a project of enlisting quantum information science as a source of task-oriented axioms for use in the investigation of operational theories in a general framework capable of encompassing quantum mechanics, classical theory, and more. Whatever else they may be, quantum states of systems are compendia of probabilities for the outcomes of possible operations we may perform on the systems: ``operational theories.'' I discuss appropriate general frameworks for such theories, in which convexity plays a key role. Such frameworks are appropriate for investigating what things look like from an ``inside view,'' i.e. for describing perspectival information that one subsystem of the world can have about another. Understanding how such views can combine, and whether an overall ``geometric'' picture (``outside view'') coordinating them all can be had, even if this picture is very different in nature from the structure of the perspectives within it, is the key to understanding whether we may be able to achieve a unified, ``objective'' physical view in which quantum mechanics is the appropriate description for certain perspectives, or whether quantum mechanics is truly telling us we must go beyond this ``geometric'' conception of physics. The nature of information, its flow and processing, as seen from various operational persepectives, is likely to be key to understanding whether and how such coordination and unification can be achieved.
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.
Quantum theory and the role of mind in nature
Henry P. Stapp
2001-03-09T23:59:59.000Z
Orthodox Copenhagen quantum theory renounces the quest to understand the reality in which we are imbedded, and settles for practical rules describing connections between our observations. Many physicist have regarded this renunciation of our effort to describe nature herself as premature, and John von Neumann reformulated quantum theory as a theory of an evolving objective universe interacting with human consciousness. This interaction is associated both in Copenhagen quantum theory and in von Neumann quantum theory with a sudden change that brings the objective physical state of a system in line with a subjectively felt psychical reality. The objective physical state is thereby converted from a material substrate to an informational and dispositional substrate that carries both the information incorporated into it by the psychical realities, and certain dispositions for the occurrence of future psychical realities. The present work examines and proposes solutions to two problems that have appeared to block the development of this conception of nature. The first problem is how to reconcile this theory with the principles of relativistic quantum field theory; the second problem is to understand whether, strictly within quantum theory, a person's mind can affect the activities of his brain, and if so how. Solving the first problem involves resolving a certain nonlocality question. The proposed solution to the second problem is based on a postulated connection between effort, attention, and the quantum Zeno effect. This solution explains on the basis of quantum physics a large amount of heretofore unexplained data amassed by psychologists.
Quantum theory of tensionless noncommutative p-branes
Gamboa, J. [Departamento de Fisica, Universidad de Santiago de Chile, Casilla 307, Santiago 2 (Chile); Loewe, M. [Facultad de Fisica, Pontificia Universidad Catolica de Chile, Casilla 306, Santiago 22 (Chile); Mendez, F. [INFN, Laboratorio Nazionali del Gran Sasso, SS, 17bis, 67010 Asergi, L'Aquila (Italy)
2004-11-15T23:59:59.000Z
The quantum theory involving noncommutative tensionless p-branes is studied following path integral methods. Our procedure allows a simple treatment for generally covariant noncommutative extended systems and it contains, as a particular case, the thermodynamics and the quantum tensionless string theory. The effect induced by noncommutativity in the field space is to produce a confinement among pairing of null p-branes.
Nonlocal Quantization Principle in Quantum Field Theory and Quantum Gravity
Martin Kober
2014-10-21T23:59:59.000Z
In this paper a nonlocal generalization of field quantization is suggested. This quantization principle presupposes the assumption that the commutator between a field operator an the operator of the canonical conjugated variable referring to other space-time points does not vanish as it is postulated in the usual setting of quantum field theory. Based on this presupposition the corresponding expressions for the field operators, the eigenstates and the path integral formula are determined. The nonlocal quantization principle also leads to a generalized propagator. If the dependence of the commutator between operators on different space-time points on the distance of these points is assumed to be described by a Gaussian function, one obtains that the propagator is damped by an exponential. This leads to a disappearance of UV divergences. The transfer of the nonlocal quantization principle to canonical quantum gravity is considered as well. In this case the commutator has to be assumed to depend also on the gravitational field, since the distance between two points depends on the metric field.
An additive Hamiltonian plus Landauer's Principle yields quantum theory
Chris Fields
2015-03-27T23:59:59.000Z
It is shown that no-signalling, a quantum of action, unitarity, detailed balance, Bell's theorem, the Hilbert-space representation of physical states and the Born rule all follow from the assumption of an additive Hamiltonian together with Landauer's principle. Common statements of the "classical limit" of quantum theory, as well as common assumptions made by "interpretations" of quantum theory, contradict additivity, Landauer's principle, or both.
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.
Toy Model for a Relational Formulation of Quantum Theory
David Poulin
2005-07-07T23:59:59.000Z
In the absence of an external frame of reference physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is to demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental level, from which the original "non-relational" theory emerges in a semi-classical limit. According to this thesis, the non-relational theory is therefore an approximation of the fundamental relational theory. We propose four simple rules that can be used to translate an "orthodox" quantum mechanical description into a relational description, independent of an external spacial reference frame or clock. The techniques used to construct these relational theories are motivated by a Bayesian approach to quantum mechanics, and rely on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, there is no need for a "collapse of the wave packet" in our model: the probability interpretation is only applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of "spin networks" introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semi-classical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.
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.
Quasi-probability representations of quantum theory with applications to quantum information science
Christopher Ferrie
2011-10-15T23:59:59.000Z
This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional quantum theory. We focus on both the characteristics and applications of these representations with an emphasis toward quantum information theory. We discuss the recently proposed unification of the set of possible quasi-probability representations via frame theory and then discuss the practical relevance of negativity in such representations as a criteria for quantumness.
Radiation reaction in quantum field theory
Higuchi, A
2002-01-01T23:59:59.000Z
We investigate radiation-reaction effects for a charged scalar particle accelerated by an external potential realized as a space-dependent mass term in quantum electrodynamics. In particular, we calculate the position shift of the final-state wave packet of the charged particle due to radiation at lowest order in the fine structure constant alpha and in the small h-bar approximation. This quantity turns out to be much smaller than the width of the wave packet but can be compared with the classical counterpart. We show that it disagrees with the result obtained using the Abraham-Lorentz-Dirac formula for the radiation-reaction force, and that it agrees with the classical theory if one assumes that the particle loses its energy to radiation at each moment of time according to the Larmor formula in the static frame of the potential. We also point out that the electromagnetic correction to the potential has no classical limit.
Limited Holism and Real-Vector-Space Quantum Theory
Lucien Hardy; William K. Wootters
2010-05-26T23:59:59.000Z
Quantum theory has the property of "local tomography": the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We consider in this paper a class of theories more holistic than quantum theory in that they are constrained only by "bilocal tomography": the state of any composite system is determined by the statistics of measurements on pairs of components. Under a few auxiliary assumptions, we derive certain general features of such theories. In particular, we show how the number of state parameters can depend on the number of perfectly distinguishable states. We also show that real-vector-space quantum theory, while not locally tomographic, is bilocally tomographic.
Twists of quantum groups and noncommutative field theory
P. P. Kulish
2006-06-07T23:59:59.000Z
The role of quantum universal enveloping algebras of symmetries in constructing a noncommutative geometry of space-time and corresponding field theory is discussed. It is shown that in the framework of the twist theory of quantum groups, the noncommutative (super) space-time defined by coordinates with Heisenberg commutation relations, is (super) Poincar\\'e invariant, as well as the corresponding field theory. Noncommutative parameters of global transformations are introduced.
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.
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.
Ordinary versus PT-symmetric ?ł quantum field theory
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
2012-04-01T23:59:59.000Z
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric ig?ł quantum field theory. This quantum fieldmore »theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p˛+ixł, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian g?ł quantum field theory with those of the PT-symmetric ig?ł quantum field theory. It is shown that while the conventional g?ł theory in d=6 dimensions is asymptotically free, the ig?ł theory is like a g?? theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.« less
Ordinary versus PT-symmetric ?ł quantum field theory
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
2012-04-01T23:59:59.000Z
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric ig?ł quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p˛+ixł, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian g?ł quantum field theory with those of the PT-symmetric ig?ł quantum field theory. It is shown that while the conventional g?ł theory in d=6 dimensions is asymptotically free, the ig?ł theory is like a g?? theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.
Low-Energy Effective Theories of Quantum Link and Quantum Spin Models
B. Schlittgen; U. -J. Wiese
2000-12-11T23:59:59.000Z
Quantum spin and quantum link models provide an unconventional regularization of field theory in which classical fields arise via dimensional reduction of discrete variables. This D-theory regularization leads to the same continuum theories as the conventional approach. We show this by deriving the low-energy effective Lagrangians of D-theory models using coherent state path integral techniques. We illustrate our method for the $(2+1)$-d Heisenberg quantum spin model which is the D-theory regularization of the 2-d O(3) model. Similarly, we prove that in the continuum limit a $(2+1)$-d quantum spin model with $SU(N)_L\\times SU(N)_R\\times U(1)_{L=R}$ symmetry is equivalent to the 2-d principal chiral model. Finally, we show that $(4+1)$-d SU(N) quantum link models reduce to ordinary 4-d Yang-Mills theory.
Kanematsu, Yusuke; Tachikawa, Masanori [Quantum Chemistry Division, Yokohama City University, Seto 22-2, Kanazawa-ku, Yokohama 236-0027 (Japan)] [Quantum Chemistry Division, Yokohama City University, Seto 22-2, Kanazawa-ku, Yokohama 236-0027 (Japan)
2014-04-28T23:59:59.000Z
We have developed the multicomponent hybrid density functional theory [MC-(HF+DFT)] method with polarizable continuum model (PCM) for the analysis of molecular properties including both nuclear quantum effect and solvent effect. The chemical shifts and H/D isotope shifts of the picolinic acid N-oxide (PANO) molecule in chloroform and acetonitrile solvents are applied by B3LYP electron exchange-correlation functional for our MC-(HF+DFT) method with PCM (MC-B3LYP/PCM). Our MC-B3LYP/PCM results for PANO are in reasonable agreement with the corresponding experimental chemical shifts and isotope shifts. We further investigated the applicability of our method for acetylacetone in several solvents.
On a Formulation of Qubits in Quantum Field Theory
Jacques Calmet; Xavier Calmet
2012-01-21T23:59:59.000Z
Qubits have been designed in the framework of quantum mechanics. Attempts to formulate the problem in the language of quantum field theory have been proposed already. In this short note we refine the meaning of qubits within the framework of quantum field theory. We show that the notion of gauge invariance naturally leads to a generalization of qubits to QFTbits which are then the fundamental carriers of information from the quantum field theoretical point of view. The goal of this note is to stress the availability of such a generalized concept of QFTbits.
Huang, Yi-Zhi
Quantum Hall systems Representation theory of vertex operator algebras Applications The end Quantum;Quantum Hall systems Representation theory of vertex operator algebras Applications The end Outline 1 An approach to a fundamental conjecture #12;Quantum Hall systems Representation theory of vertex operator
Huang, Yi-Zhi
Quantum Hall systems Representation theory of vertex operator algebras Applications The end Quantum Science, CAS #12;Quantum Hall systems Representation theory of vertex operator algebras Applications to a fundamental conjecture #12;Quantum Hall systems Representation theory of vertex operator algebras Applications
A Process Algebra Approach to Quantum Field Theory
William Sulis
2015-02-09T23:59:59.000Z
The process algebra has been used successfully to provide a novel formulation of quantum mechanics in which non-relativistic quantum mechanics (NRQM) emerges as an effective theory asymptotically. The process algebra is applied here to the formulation of quantum field theory. The resulting QFT is intuitive, free from divergences and eliminates the distinction between particle, field and wave. There is a finite, discrete emergent space-time on which arise emergent entities which transfer information like discrete waves and interact with measurement processes like particles. The need for second quantization is eliminated and the particle and field theories rest on a common foundation, clarifying and simplifying the relationship between the two.
Z Theory and its Quantum-Relativistic Operators
Pietro Giorgio Zerbo
2006-02-08T23:59:59.000Z
The view provided by Z theory, based on its quantum-relativistic operators, is an integrated picture of the micro and macro quantities relationships. The axiomatic formulation of the theory is presented in this paper. The theory starts with the existence of the wave function, the existence of three fundamental constants h, c and G as well as the physical quantity Rc (the radius of the space-time continuum) plus the definition of a general form for the quantum-relativistic functional operators. Using such starting point the relationships between relativity, quantum mechanics and cosmological quantities can be clarified.
Limiting the complexity of quantum states: a toy theory
Valerio Scarani
2015-03-30T23:59:59.000Z
This paper discusses a restriction of quantum theory, in which very complex states would be excluded. The toy theory is phrased in the language of the circuit model for quantum computing, its key ingredient being a limitation on the number of interactions that \\textit{each} qubit may undergo. As long as one stays in the circuit model, the toy theory is consistent and may even match what we shall be ever able to do in a controlled laboratory experiment. The direct extension of the restriction beyond the circuit model conflicts with observed facts: the possibility of restricting the complexity of quantum state, while saving phenomena, remains an open question.
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.
Brane Dynamics and Four-Dimensional Quantum Field Theory
N. D. Lambert; P. C. West
1998-11-19T23:59:59.000Z
We review the relation between the classical dynamics of the M-fivebrane and the quantum low energy effective action for N=2 Yang-Mills theories. We also discuss some outstanding issues in this correspondence.
Hadamard subtractions for infrared singularities in quantum field theory
Burton, George Edmund C.
2011-06-27T23:59:59.000Z
Feynman graphs in perturbative quantum field theory are replete with infrared divergences caused by the presence of massless particles, how-ever these divergences are known to cancel order-by-order when all virtual and ...
Rigorous results in space-space noncommutative quantum field theory
M. N. Mnatsakanova; Yu. S. Vernov
2006-12-19T23:59:59.000Z
The axiomatic approach based on Wightman functions is developed in noncommutative quantum field theory. We have proved that the main results of the axiomatic approach remain valid if the noncommutativity affects only the spatial variables.
Two quantum effects in the theory of gravitation
Robinson, Sean Patrick, 1977-
2005-01-01T23:59:59.000Z
We will discuss two methods by which the formalism of quantum field theory can be included in calculating the physical effects of gravitation. In the first of these, the consequences of treating general relativity as an ...
Distinguishing decoherence from alternative quantum theories by dynamical decoupling
Christian Arenz; Robin Hillier; Martin Fraas; Daniel Burgarth
2015-08-03T23:59:59.000Z
A longstanding challenge in the foundations of quantum mechanics is the veri?cation of alternative collapse theories despite their mathematical similarity to decoherence. To this end, we suggest a novel method based on dynamical decoupling. Experimental observation of nonzero saturation of the decoupling error in the limit of fast decoupling operations can provide evidence for alternative quantum theories. As part of the analysis we prove that unbounded Hamiltonians can always be decoupled, and provide novel dilations of Lindbladians.
Energy Inequalities in Quantum Field Theory
Christopher J. Fewster
2005-01-31T23:59:59.000Z
Quantum fields are known to violate all the pointwise energy conditions of classical general relativity. We review the subject of quantum energy inequalities: lower bounds satisfied by weighted averages of the stress-energy tensor, which may be regarded as the vestiges of the classical energy conditions after quantisation. Contact is also made with thermodynamics and related issues in quantum mechanics, where such inequalities find analogues in sharp Gaarding inequalities.
Statistical theory of Coulomb blockade oscillations: Quantum chaos in quantum dots
Jalabert, R.A.; Stone, A.D.; Alhassid, Y. (Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06511 (United States))
1992-06-08T23:59:59.000Z
We develop a statistical theory of the amplitude of Coulomb blockade oscillations in semiconductor quantum dots based on the hypothesis that chaotic dynamics in the dot potential leads to behavior described by random-matrix theory. Breaking time-reversal symmetry is predicted to cause an experimentally observable change in the distribution of amplitudes. The theory is tested numerically and good agreement is found.
Young's Double Slit Experiment in Quantum Field Theory
Masakatsu Kenmoku; Kenji Kume
2011-03-01T23:59:59.000Z
Young's double slit experiment is formulated in the framework of canonical quantum field theory in view of the modern quantum optics. We adopt quantum scalar fields instead of quantum electromagnetic fields ignoring the vector freedom in gauge theory. The double slit state is introduced in Fock space corresponding to experimental setup. As observables, expectation values of energy density and positive frequency part of current with respect to the double slit state are calculated which give the interference term. Classical wave states are realized by coherent double slit states in Fock space which connect quantum particle states with classical wave states systematically. In case of incoherent sources, the interference term vanishes by averaging random phase angles as expected.
The Madelung Picture as a Foundation of Geometric Quantum Theory
Maik Reddiger
2015-09-01T23:59:59.000Z
Despite its age quantum theory remains ill-understood, which is partially to blame on its deep interwovenness with the mysterious concept of quantization. In this article we argue that a quantum theory recoursing to quantization algorithms is necessarily incomplete. To provide a new axiomatic foundation, we give a rigorous proof showing how the Schr\\"odinger equation follows from the Madelung equations, which are formulated in the language of Newtonian mechanics. We show how the Schr\\"odinger picture relates to this Madelung picture and how the "classical limit" is directly obtained. This suggests a reformulation of the correspondence principle, stating that a quantum theory must reduce to a probabilistic version of Newtonian mechanics for large masses. We then enhance the stochastic interpretation developed by Tsekov, which speculates that quantum mechanical behavior is caused by random vibrations in spacetime. A new, yet incomplete model of particle creation and annihilation is also proposed.
A Goldstone Theorem in Thermal Relativistic Quantum Field Theory
Christian D. Jaekel; Walter F. Wreszinski
2010-06-01T23:59:59.000Z
We prove a Goldstone Theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of space-like decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed.
The quantum systems control and the optimal control theory
V. F. Krotov
2008-05-22T23:59:59.000Z
Mathematical theory of the quantum systems control is based on some ideas of the optimal control theory. These ideas are developed here as applied to these systems. The results obtained meet the deficiencies in the basis and algorithms of the control synthesis and expand the application of these methods.
Entropy of quantum channel in the theory of quantum information
Wojciech Roga
2011-10-03T23:59:59.000Z
Quantum channels, also called quantum operations, are linear, trace preserving and completely positive transformations in the space of quantum states. Such operations describe discrete time evolution of an open quantum system interacting with an environment. The thesis contains an analysis of properties of quantum channels and different entropies used to quantify the decoherence introduced into the system by a given operation. Part I of the thesis provides a general introduction to the subject. In Part II, the action of a quantum channel is treated as a process of preparation of a quantum ensemble. The Holevo information associated with this ensemble is shown to be bounded by the entropy exchanged during the preparation process between the initial state and the environment. A relation between the Holevo information and the entropy of an auxiliary matrix consisting of square root fidelities between the elements of the ensemble is proved in some special cases. Weaker bounds on the Holevo information are also established. The entropy of a channel, also called the map entropy, is defined as the entropy of the state corresponding to the channel by the Jamiolkowski isomorphism. In Part III of the thesis, the additivity of the entropy of a channel is proved. The minimal output entropy, which is difficult to compute, is estimated by an entropy of a channel which is much easier to obtain. A class of quantum channels is specified, for which additivity of channel capacity is conjectured. The last part of the thesis contains characterization of Davies channels, which correspond to an interaction of a state with a thermal reservoir in the week coupling limit, under the condition of quantum detailed balance and independence of rotational and dissipative evolutions. The Davies channels are characterized for one-qubit and one-qutrit systems.
The Monte Carlo method in quantum field theory
Colin Morningstar
2007-02-20T23:59:59.000Z
This series of six lectures is an introduction to using the Monte Carlo method to carry out nonperturbative studies in quantum field theories. Path integrals in quantum field theory are reviewed, and their evaluation by the Monte Carlo method with Markov-chain based importance sampling is presented. Properties of Markov chains are discussed in detail and several proofs are presented, culminating in the fundamental limit theorem for irreducible Markov chains. The example of a real scalar field theory is used to illustrate the Metropolis-Hastings method and to demonstrate the effectiveness of an action-preserving (microcanonical) local updating algorithm in reducing autocorrelations. The goal of these lectures is to provide the beginner with the basic skills needed to start carrying out Monte Carlo studies in quantum field theories, as well as to present the underlying theoretical foundations of the method.
Generalized Gravity I : Kinematical Setting and reformalizing Quantum Field Theory
Johan Noldus
2008-04-20T23:59:59.000Z
The first part of this work deals with the development of a natural differential calculus on non-commutative manifolds. The second part extends the covariance and equivalence principle as well studies its kinematical consequences such as the arising of gauge theory. Furthermore, a manifestly causal and covariant formulation of quantum field theory is presented which surpasses the usual Hamiltonian and path integral construction. A particular representation of this theory on the kinematical structure developed in section three is moreover given.
Theory of Quantum Oscillations in Cuprate Superconductors
Eun, Jonghyoun
2012-01-01T23:59:59.000Z
Cuprate Superconductors . . . . . . . . . . . . . . . . . .J. Schried?er. Theory of superconductivity. Phys. Rev. , [Tinkham. Introduction to Superconductivity. Dover, New York,
Superconducting quantum circuits theory and application
Deng, Xiuhao
2015-01-01T23:59:59.000Z
viii General theory of Superconducting cavity coupled to2.4 Decoherence in superconductingProposed circuit for superconducting qubits . . . . .
Ioannis P. Zois
2014-01-16T23:59:59.000Z
We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT) and Noncommutative Floer Homology (NCFH). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that NCTQFT is the correct mathematical framework for a quantum field theory of all known interactions in nature (including gravity). On the other hand we hope that a possible NCFH will apply to practically every 3-manifold (and not only to homology 3-spheres as ordinary Floer Homology currently does). The two motivations are closely related since, at least in the commutative case, Floer Homology Groups constitute the space of quantum observables of (3+1)-dim Topological Quantum Field Theory. Towards this goal we present some "Noncommutative" Versions of Hodge Theory for noncommutative differentail forms and tangential cohomology for foliations.
On Hypercomplex Extensions of Quantum Theory
Daniel Sepunaru
2015-01-23T23:59:59.000Z
This paper discusses quantum mechanical schemas for describing waves with non-abelian phases, Fock spaces of annihilation-creation operators for these structures, and the Feynman recipe for obtaining descriptions of particle interactions with external fields.
Irreducibility of the set of field operators in Noncommutative Quantum Field Theory
M. N. Mnatsakanova; Yu. S. Vernov
2012-09-02T23:59:59.000Z
Irreducibility of the set of quantum field operators has been proved in noncommutative quantum field theory in the general case when time does not commute with spatial variables.
Quantum theory as a critical regime of language dynamics
Alexei Grinbaum
2015-01-12T23:59:59.000Z
Quantum mechanics relies on the cut between the observer and the quantum system, but it does not define the observer physically. We propose an informational definition based on bounded complexity of strings. Language dynamics then leads to an emergent continuous model in the critical regime. Restricting it to a subfamily of `quantum' binary codes describing `bipartite systems', we find strong evidence of an upper bound on bipartite correlations equal to 2.82537. This is measurably different from the Tsirelson bound of the CHSH inequality. If such a reconstruction of quantum theory is experimentally confirmed, it would show that the Hilbert space formalism is but an effective description of a fundamental `linguistic' theory in the critical regime.
Toolbox for reconstructing quantum theory from rules on information acquisition
Hoehn, Philipp A
2015-01-01T23:59:59.000Z
We develop a novel operational approach for reconstructing (qubit) quantum theory from elementary rules on information acquisition. The focus lies on an observer O interrogating a system S with binary questions and S's state is taken as O's `catalogue of knowledge' about S. The mathematical tools of the framework are simple and we attempt to highlight all underlying assumptions to provide a handle for future generalizations. Five principles are imposed, asserting (1) a limit on the amount of information available to O; (2) the mere existence of complementary information; (3) the possibility for O's information to be `in superposition'; (4) O's information to be preserved in between interrogations; and, (5) continuity of time evolution. This approach permits a constructive derivation of quantum theory, elucidating how the ensuing independence, complementarity and compatibility structure of O's questions matches that of projective measurements in quantum theory, how entanglement and monogamy of entanglement and...
Invariant Set Theory and the Symbolism of Quantum Measurement
T. N. Palmer
2015-02-24T23:59:59.000Z
Elements of a novel theory of quantum physics are developed, synthesising the role of symbolism in describing quantum measurement and in the topological representation of fractal invariant sets in nonlinear dynamical systems theory. In this synthesis, the universe $U$ is treated as an isolated deterministic dynamical system evolving precisely on a measure-zero fractal invariant subset $I_U$ of its state space. A non-classical approach to the physics of $U$ is developed by treating the geometry of $I_U$ as more primitive than dynamical evolution equations on $I_U$. A specific symbolic representation of $I_U$ is constructed which encodes quaternionic multiplication and from which the statistical properties of complex Hilbert Space vectors are emergent. The Hilbert Space itself arises as the singular limit of Invariant Set Theory as a fractal parameter $N \\rightarrow \\infty$. Although the Hilbert Space of quantum theory is counterfactually complete, the measure-zero set $I_U$ is counterfactually incomplete, no matter how large is $N$. Such incompleteness allows reinterpretations of familiar quantum phenomena, consistent with realism and local causality. The non-computable nature of $I_U$ ensures that these reinterpretations are neither conspiratorial nor retrocausal and, through a homeomorphism with the ring of $2^N$-adic integers, are robust to noise and hence not fine tuned. The non-commutativity of Hilbert Space observables emerges from the symbolic representation of $I_U$ through the generic number-theoretic incommensurateness of $\\phi/\\pi$ and $\\cos \\phi$. Invariant Set Theory implies a much stronger synergy between cosmology and quantum physics than exists in contemporary theory, suggesting a novel approach to synthesising gravitational and quantum physics and providing new perspectives on the dark universe and information loss in black holes.
Quantum Solution to Scalar Field Theory Models
Gordon Chalmers
2005-09-08T23:59:59.000Z
Amplitudes $A_n$ in $d$-dimensional scalar field theory are generated, to all orders in the coupling constant and at $n$-point. The amplitudes are expressed as a series in the mass $m$ and coupling $\\lambda$. The inputs are the classical scattering, and these generate, after the integrals are performed, the series expansion in the couplings $\\lambda_i$. The group theory of the scalar field theory leads to an additional permutation on the $L$ loop trace structures. Any scalar field theory, including those with higher dimension operators and in any dimension, are amenable.
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.
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.
Theory of an optomechanical quantum heat engine
Keye Zhang; Francesco Bariani; Pierre Meystre
2014-08-13T23:59:59.000Z
Coherent interconversion between optical and mechanical excitations in an optomechanical cavity can be used to engineer a quantum heat engine. This heat engine is based on an Otto cycle between a cold photonic reservoir and a hot phononic reservoir [Phys. Rev. Lett. 112, 150602 (2014)]. Building on our previous work, we (i) develop a detailed theoretical analysis of the work and the efficiency of the engine, and (ii) perform an investigation of the quantum thermodynamics underlying this scheme. In particular, we analyze the thermodynamic performance in both the dressed polariton picture and the original bare photon and phonon picture. Finally, (iii) a numerical simulation is performed to derive the full evolution of the quantum optomechanical system during the Otto cycle, by taking into account all relevant sources of noise.
Quantum chaos and regularity in $?^4$ theory
Helmut Kroeger; Xiang-Qian Luo; Harald Markum; Rainer Pullirsch
2003-09-15T23:59:59.000Z
We check the eigenvalue spectrum of the $\\Phi^{4}_{1+1}$ Hamiltonian against Poisson or Wigner behavior predicted from random matrix theory. We discuss random matrix theory as a tool to discriminate the validity of a model Hamiltonian compared to an analytically solvable Hamiltonian or experimental data.
Book Review Statistical Structure of Quantum Theory
Fuchs, Christopher A.
associated with measurement processes, including measurements with a continuous number of outcomes and commutation relations, tensor products, no-go theorems for hidden variables, and symmetry operations and a detailed exposition of quantum dynamical semigroups. Chapters 4 and 5, "Repeated and Continuous Measurement
Multi-scale quantum simulation of quantum field theory using wavelets
Gavin K. Brennen; Peter Rohde; Barry C. Sanders; Sukhwinder Singh
2014-12-02T23:59:59.000Z
A successful approach to understand field theories is to resolve the physics into different length or energy scales using the renormalization group framework. We propose a quantum simulation of quantum field theory which encodes field degrees of freedom in a wavelet basis---a multi-scale description of the theory. Since wavelets are compact wavefunctions, this encoding allows for quantum simulations to create particle excitations with compact support and provides a natural way to associate observables in the theory to finite resolution detectors. We show that the wavelet basis is well suited to compute subsystem entanglement entropy by dividing the field into contributions from short-range wavelet degrees of freedom and long-range scale degrees of freedom, of which the latter act as renormalized modes which capture the essential physics at a renormalization fixed point.
Noncommutative and Non-Anticommutative Quantum Field Theory
J. W. Moffat
2001-07-19T23:59:59.000Z
A noncommutative and non-anticommutative quantum field theory is formulated in a superspace, in which the superspace coordinates satisfy noncommutative and non-anticommutative relations. A perturbative scalar field theory is investigated in which only the non-anticommutative algebraic structure is kept, and one loop diagrams are calculated and found to be finite due to the damping caused by a Gaussian factor in the propagator.
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.
Comments on Cahill's Quantum Foam Inflow Theory of Gravity
T. D. Martin
2004-07-20T23:59:59.000Z
We reveal an underlying flaw in Reginald T. Cahill's recently promoted quantum foam inflow theory of gravity. It appears to arise from a confusion of the idea of the Galilean invariance of the acceleration of an individual flow with what is obtained as an acceleration when a homogeneous flow is superposed with an inhomogeneous flow. We also point out that the General Relativistic covering theory he creates by substituting a generalized Painleve-Gullstrand metric into Einstein's field equations leads to absurd results.
Quantum chiral field theory of $0^{-+}$ glueball
Bing An Li
2011-08-23T23:59:59.000Z
A chiral field theory of $0^{-+}$ glueball is presented. The coupling between the quark operator and the $0^{-+}$ glueball field is revealed from the U(1) anomaly. The Lagrangian of this theory is constructed by adding a $0^{-+}$ glueball field to a successful Lagrangian of chiral field theory of pseudoscalar, vector, and axial-vector mesons. Quantitative study of the physical processes of the $0^{-+}$ glueball of $m=1.405\\textrm{GeV}$ is presented. The theoretical predictions can be used to identify the $0^{-+}$ glueball.
Viscosity, Black Holes, and Quantum Field Theory
D. T. Son; A. O. Starinets
2007-07-11T23:59:59.000Z
We review recent progress in applying the AdS/CFT correspondence to finite-temperature field theory. In particular, we show how the hydrodynamic behavior of field theory is reflected in the low-momentum limit of correlation functions computed through a real-time AdS/CFT prescription, which we formulate. We also show how the hydrodynamic modes in field theory correspond to the low-lying quasinormal modes of the AdS black p-brane metric. We provide a proof of the universality of the viscosity/entropy ratio within a class of theories with gravity duals and formulate a viscosity bound conjecture. Possible implications for real systems are mentioned.
Renormalization of Noncommutative Quantum Field Theories
Amilcar R. de Queiroz; Rahul Srivastava; Sachindeo Vaidya
2013-02-14T23:59:59.000Z
We report on a comprehensive analysis of the renormalization of noncommutative \\phi^4 scalar field theories on the Groenewold-Moyal (GM) plane. These scalar field theories are twisted Poincar\\'e invariant. Our main results are that these scalar field theories are renormalizable, free of UV/IR mixing, possess the same fixed points and \\beta-functions for the couplings as their commutative counterparts. We also argue that similar results hold true for any generic noncommutative field theory with polynomial interactions and involving only pure matter fields. A secondary aim of this work is to provide a comprehensive review of different approaches for the computation of the noncommutative S-matrix: noncommutative interaction picture and noncommutative LSZ formalism.
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.
Lorentz symmetry breaking as a quantum field theory regulator
Visser, Matt
2009-01-01T23:59:59.000Z
Perturbative expansions of relativistic quantum field theories typically contain ultraviolet divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. We shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory, and discuss its implications. We shall quantify just "how much" Lorentz symmetry breaking is required to fully regulate the theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Horava's recent article [arXiv:0901.3775 [hep-th
Scheme independence as an inherent redundancy in quantum field theory
Jose I. Latorre; Tim R. Morris
2001-02-07T23:59:59.000Z
The path integral formulation of Quantum Field Theory implies an infinite set of local, Schwinger-Dyson-like relations. Exact renormalization group equations can be cast as a particular instance of these relations. Furthermore, exact scheme independence is turned into a vector field transformation of the kernel of the exact renormalization group equation under field redefinitions.
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.
221B Lecture Notes Quantum Field Theory III (Radiation Field)
Murayama, Hitoshi
221B Lecture Notes Quantum Field Theory III (Radiation Field) 1 Quantization of Radiation Field was quantized: photons. Now that we have gone through quantization of a classical field (Schr¨odinger field so far), we can proceed to quantize the Maxwell field. The basic idea is pretty much the same, except
221B Lecture Notes Quantum Field Theory IV (Radiation Field)
Murayama, Hitoshi
221B Lecture Notes Quantum Field Theory IV (Radiation Field) 1 Quantization of Radiation Field was quantized: photons. Now that we have gone through quantization of a classical field (Schr¨odinger field so far), we can proceed to quantize the Maxwell field. The basic idea is pretty much the same, except
Toolbox for reconstructing quantum theory from rules on information acquisition
Philipp A Hoehn
2014-12-29T23:59:59.000Z
We develop a novel operational approach for reconstructing (qubit) quantum theory from elementary rules on information acquisition. The focus lies on an observer O interrogating a system S with binary questions and S's state is taken as O's `catalogue of knowledge' about S. The mathematical tools of the framework are simple and we attempt to highlight all underlying assumptions to provide a handle for future generalizations. Five principles are imposed, asserting (1) a limit on the amount of information available to O; (2) the mere existence of complementary information; (3) the possibility for O's information to be `in superposition'; (4) O's information to be preserved in between interrogations; and, (5) continuity of time evolution. This approach permits a constructive derivation of quantum theory, elucidating how the ensuing independence, complementarity and compatibility structure of O's questions matches that of projective measurements in quantum theory, how entanglement and monogamy of entanglement and, more generally, how the correlation structure of arbitrarily many qubits and rebits arises. The principles yield a reversible time evolution and a quadratic measure, quantifying O's information about S. Finally, it is shown that the five principles admit two solutions for the simplest case of a single elementary system: the Bloch ball and disc as state spaces for a qubit and rebit, respectively, together with their symmetries as time evolution groups. The reconstruction is completed in a companion paper where an additional postulate eliminates the rebit case. This approach is conceptually close to the relational interpretation of quantum theory.
Simplification of additivity conjecture in quantum information theory
Motohisa Fukuda
2007-04-09T23:59:59.000Z
We simplify some conjectures in quantum information theory; the additivity of minimal output entropy, the multiplicativity of maximal output p-norm and the superadditivity of convex closure of output entropy. We construct a unital channel for a given channel so that they share the above additivity properties; we can reduce the conjectures for all channels to those for unital channels.
Noncommutative Common Cause Principles in Algebraic Quantum Field Theory
Gábor Hofer-Szabó; Péter Vecsernyés
2012-01-23T23:59:59.000Z
States in algebraic quantum field theory "typically" establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V_A and V_B, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V_A and V_B and the set {C, non-C} screens off the correlation between A and B.
Localization and diffusion in polymer quantum field theory
Michele Arzano; Marco Letizia
2014-08-13T23:59:59.000Z
Polymer quantization is a non-standard approach to quantizing a classical system inspired by background independent approaches to quantum gravity such as loop quantum gravity. When applied to field theory it introduces a characteristic polymer scale at the level of the fields classical configuration space. Compared with models with space-time discreteness or non-commutativity this is an alternative way in which a characteristic scale can be introduced in a field theoretic context. Motivated by this comparison we study here localization and diffusion properties associated with polymer field observables and dispersion relation in order to shed some light on the novel physical features introduced by polymer quantization. While localization processes seems to be only mildly affected by polymer effects, we find that polymer diffusion differs significantly from the "dimensional reduction" picture emerging in other Planck-scale models beyond local quantum field theory.
Propagation of uncertainties in the nuclear DFT models
Markus Kortelainen
2014-09-04T23:59:59.000Z
Parameters of the nuclear density functional theory (DFT) models are usually adjusted to experimental data. As a result they carry certain theoretical error, which, as a consequence, carries out to the predicted quantities. In this work we address the propagation of theoretical error, within the nuclear DFT models, from the model parameters to the predicted observables. In particularly, the focus is set on the Skyrme energy density functional models.
Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation
E. Rico; T. Pichler; M. Dalmonte; P. Zoller; S. Montangero
2014-06-07T23:59:59.000Z
We show that gauge invariant quantum link models, Abelian and non-Abelian, can be exactly described in terms of tensor networks states. Quantum link models represent an ideal bridge between high-energy to cold atom physics, as they can be used in cold-atoms in optical lattices to study lattice gauge theories. In this framework, we characterize the phase diagram of a (1+1)-d quantum link version of the Schwinger model in an external classical background electric field: the quantum phase transition from a charge and parity ordered phase with non-zero electric flux to a disordered one with a net zero electric flux configuration is described by the Ising universality class.
N=2 supersymmetric gauge theories and quantum integrable systems
Yuan Luo; Meng-Chwan Tan; Junya Yagi
2014-04-01T23:59:59.000Z
We study N=2 supersymmetric gauge theories on the product of a two-sphere and a cylinder. We show that the low-energy dynamics of a BPS sector of such a theory is described by a quantum integrable system, with the Planck constant set by the inverse of the radius of the sphere. If the sphere is replaced with a hemisphere, then our system reduces to an integrable system of the type studied by Nekrasov and Shatashvili. In this case we establish a correspondence between the effective prepotential of the gauge theory and the Yang-Yang function of the integrable system.
Perturbative quantum field theory in the framework of the fermionic projector
Finster, Felix, E-mail: finster@ur.de [Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg (Germany)] [Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg (Germany)
2014-04-15T23:59:59.000Z
We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.
Foundations for proper-time relativistic quantum theory
Tepper L. Gill; Trey Morris; Stewart K. Kurtz
2015-03-06T23:59:59.000Z
This paper is a progress report on the foundations for the canonical proper-time approach to relativistic quantum theory. We first review the the standard square-root equation of relativistic quantum theory, followed by a review of the Dirac equation, providing new insights into the physical properties of both. We then introduce the canonical proper-time theory. For completeness, we give a brief outline of the canonical proper-time approach to electrodynamics and mechanics, and then introduce the canonical proper-time approach to relativistic quantum theory. This theory leads to three new relativistic wave equations. In each case, the canonical generator of proper-time translations is strictly positive definite, so that it represents a particle. We show that the canonical proper-time extension of the Dirac equation for Hydrogen gives results that are consistently closer to the experimental data, when compared to the Dirac equation. However, these results are not sufficient to account for either the Lamb shift or the anomalous magnetic moment.
Noncommutative version of Borcherds' approach to quantum field theory
Christian Brouder; Nguyen Viet Dang; Alessandra Frabetti
2015-01-31T23:59:59.000Z
Richard Borcherds proposed an elegant geometric version of renormalized perturbative quantum field theory in curved spacetimes, where Lagrangians are sections of a Hopf algebra bundle over a smooth manifold. However, this framework looses its geometric meaning when Borcherds introduces a (graded) commutative normal product. We present a fully geometric version of Borcherds' quantization where the (external) tensor product plays the role of the normal product. We construct a noncommutative many-body Hopf algebra and a module over it which contains all the terms of the perturbative expansion and we quantize it to recover the expectation values of standard quantum field theory when the Hopf algebra fiber is (graded) cocommutative. This construction enables to the second quantize any theory described by a cocommutative Hopf algebra bundle.
Alexeev, Boris V
2008-01-01T23:59:59.000Z
Quantum solitons are discovered with the help of generalized quantum hydrodynamics (GQH). The solitons have the character of the stable quantum objects in the self consistent electric field. These effects can be considered as explanation of the existence of lightning balls. The delivered theory demonstrates the great possibilities of the generalized quantum hydrodynamics in investigation of the quantum solitons. The paper can be considered also as comments and prolongation of the materials published in the known author`s monograph (Boris V. Alexeev, Generalized Boltzmann Physical Kinetics. Elsevier. 2004). The theory leads to solitons as typical formations in the generalized quantum hydrodynamics. Key words: Foundations of the theory of transport processes; The theory of solitons; Generalized hydrodynamic equations; Foundations of quantum mechanics; The theory of lightning balls. PACS: 67.55.Fa, 67.55.Hc
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Open quantum systems and random matrix theory
Mulhall, Declan [Department of Physics/Engineering, University of Scranton, Scranton, Pennsylvania 18510-4642 (United States)
2014-10-15T23:59:59.000Z
A simple model for open quantum systems is analyzed with RMT. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the level spacing, width distribution and ?{sub 3}(L) statistic are examined as a function of the strength of this coupling. The usual super-radiant state is observed, and it is seen that as it is formed, the level spacing and ?{sub 3}(L) statistic exhibit the signatures of missed levels.
The paleoclassical interpretation of quantum theory
I. Schmelzer
2015-06-30T23:59:59.000Z
This interpretation establishes a completely classical ontology -- only the classical trajectory in configuration space -- and interprets the wave function as describing incomplete information (in form of a probability flow) about this trajectory. This combines basic ideas of de Broglie-Bohm theory and Nelsonian stochastics about the trajectory with a Bayesian interpretation of the wave function. Various objections are considered and discussed. In particular a regularity principle for the zeros of the wave function allows to meet the Wallstrom objection.
Towards a Quantum Theory of Solitons
Dvali, Gia; Gruending, Lukas; Rug, Tehseen
2015-01-01T23:59:59.000Z
We formulate a quantum coherent state picture for topological and non-topological solitons. We recognize that the topological charge arises from the infinite occupation number of zero momentum quanta flowing in one direction. Thus, the Noether charge of microscopic constituents gives rise to a topological charge in the macroscopic description. This fact explains the conservation of topological charge from the basic properties of coherent states. It also shows that no such conservation exists for non-topological solitons, which have finite mean occupation number. Consequently, they can have an exponentially-small but non-zero overlap with the vacuum, leading to vacuum instability. This amplitude can be interpreted as a coherent state description of false vacuum decay. Next we show that we can represent topological solitons as a convolution of two sectors that carry information about topology and energy separately, which makes their difference very transparent. Finally, we show how interaction among the soliton...
Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes
Alexander Schenkel
2012-10-03T23:59:59.000Z
The focus of this PhD thesis is on applications, new developments and extensions of the noncommutative gravity theory proposed by Julius Wess and his group. In part one we propose an extension of the usual symmetry reduction procedure to noncommutative gravity. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models. In part two we develop a new formalism for quantum field theory on noncommutative curved spacetimes by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. We also study explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories. The convergent deformation of simple toy models is investigated and it is found that these theories have an improved behaviour at short distances, i.e. in the ultraviolet. In part three we study homomorphisms between and connections on noncommutative vector bundles. We prove that all homomorphisms and connections of the deformed theory can be obtained by applying a quantization isomorphism to undeformed homomorphisms and connections. The extension of homomorphisms and connections to tensor products of bimodules is clarified. As a nontrivial application of the new mathematical formalism we extend our studies of exact noncommutative gravity solutions to more general deformations.
Quantum optimal control theory in the linear response formalism
Castro, Alberto; Tokatly, I. V. [Institute for Biocomputation and Physics of Complex Systems (BIFI) and Zaragoza Center for Advanced Modelling (ZCAM), University of Zaragoza, ES-50009 Zaragoza (Spain); Nano-Bio Spectroscopy Group and ETSF Scientific Development Centre, Departamento de Fisica de Materiales, Universidad del Pais Vasco UPV/EHU, ES-20018 San Sebastian, Spain and (Spain); IKERBASQUE, Basque Foundation for Science, ES-48011 Bilbao (Spain)
2011-09-15T23:59:59.000Z
Quantum optimal control theory (QOCT) aims at finding an external field that drives a quantum system in such a way that optimally achieves some predefined target. In practice, this normally means optimizing the value of some observable, a so-called merit function. In consequence, a key part of the theory is a set of equations, which provides the gradient of the merit function with respect to parameters that control the shape of the driving field. We show that these equations can be straightforwardly derived using the standard linear response theory, only requiring a minor generalization: the unperturbed Hamiltonian is allowed to be time dependent. As a result, the aforementioned gradients are identified with certain response functions. This identification leads to a natural reformulation of QOCT in terms of the Keldysh contour formalism of the quantum many-body theory. In particular, the gradients of the merit function can be calculated using the diagrammatic technique for nonequilibrium Green's functions, which should be helpful in the application of QOCT to computationally difficult many-electron problems.
Optimal Control Theory for Continuous Variable Quantum Gates
Rebing Wu; Raj Chakrabarti; Herschel Rabitz
2007-08-16T23:59:59.000Z
We apply the methodology of optimal control theory to the problem of implementing quantum gates in continuous variable systems with quadratic Hamiltonians. We demonstrate that it is possible to define a fidelity measure for continuous variable (CV) gate optimization that is devoid of traps, such that the search for optimal control fields using local algorithms will not be hindered. The optimal control of several quantum computing gates, as well as that of algorithms composed of these primitives, is investigated using several typical physical models and compared for discrete and continuous quantum systems. Numerical simulations indicate that the optimization of generic CV quantum gates is inherently more expensive than that of generic discrete variable quantum gates, and that the exact-time controllability of CV systems plays an important role in determining the maximum achievable gate fidelity. The resulting optimal control fields typically display more complicated Fourier spectra that suggest a richer variety of possible control mechanisms. Moreover, the ability to control interactions between qunits is important for delimiting the total control fluence. The comparative ability of current experimental protocols to implement such time-dependent controls may help determine which physical incarnations of CV quantum information processing will be the easiest to implement with optimal fidelity.
Schwinger functions in noncommutative quantum field theory
Dorothea Bahns
2009-08-31T23:59:59.000Z
It is shown that the $n$-point functions of scalar massive free fields on the noncommutative Minkowski space are distributions which are boundary values of analytic functions. Contrary to what one might expect, this construction does not provide a connection to the popular traditional Euclidean approach to noncommutative field theory (unless the time variable is assumed to commute). Instead, one finds Schwinger functions with twistings involving only momenta that are on the mass-shell. This explains why renormalization in the traditional Euclidean noncommutative framework crudely differs from renormalization in the Minkowskian regime.
Quantum statistical correlations in thermal field theories: Boundary effective theory
Bessa, A. [Escola de Ciencias e Tecnologia, Universidade Federal do Rio Grande do Norte, Caixa Postal 1524, 59072-970, Natal, RN (Brazil); Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP (Brazil); Brandt, F. T. [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP (Brazil); Carvalho, C. A. A. de; Fraga, E. S. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972, Rio de Janeiro, RJ (Brazil)
2010-09-15T23:59:59.000Z
We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field {phi}{sub c}, and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schroedinger field representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle point for fixed boundary fields, which is the classical field {phi}{sub c}, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally reduced effective theory for the thermal system. We calculate the two-point correlation as an example.
Untwisting Noncommutative R^d and the Equivalence of Quantum Field Theories
Robert Oeckl
2000-03-13T23:59:59.000Z
We show that there is a duality exchanging noncommutativity and non-trivial statistics for quantum field theory on R^d. Employing methods of quantum groups, we observe that ordinary and noncommutative R^d are related by twisting. We extend the twist to an equivalence for quantum field theory using the framework of braided quantum field theory. The twist exchanges both commutativity with noncommutativity and ordinary with non-trivial statistics. The same holds for the noncommutative torus.
Information theory of quantum systems with some hydrogenic applications
J. S. Dehesa; D. Manzano; P. S. Sánchez-Moreno; R. J. Yáńez
2010-09-14T23:59:59.000Z
The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the quantum-mechanical non-relativistic systems can be quantified by various single (Fisher information, Shannon entropy) and composite (e.g. Cramer-Rao, LMC shape and Fisher-Shannon complexity) functionals of the Schr\\"odinger probability density. First, we examine these concepts and its application to quantum systems with central potentials. Then, we calculate these measures for hydrogenic systems, emphasizing their predictive power for various physical phenomena. Finally, some recent open problems are pointed out.
Cosmological Applications of Algebraic Quantum Field Theory in Curved Spacetimes
Hack, Thomas-Paul
2015-01-01T23:59:59.000Z
This monograph provides a largely self--contained and broadly accessible exposition of two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology and a fundamental study of the perturbations in Inflation. The two central sections of the book dealing with these applications are preceded by sections containing a pedagogical introduction to the subject as well as introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation. The target reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but does not need to have a background in QFT on curved spacetimes or the algebraic approach to QFT. In particul...
Relative Entropy and Proximity of Quantum Field Theories
Vijay Balasubramanian; Jonathan J. Heckman; Alexander Maloney
2015-05-07T23:59:59.000Z
We study the question of how reliably one can distinguish two quantum field theories (QFTs). Each QFT defines a probability distribution on the space of fields. The relative entropy provides a notion of proximity between these distributions and quantifies the number of measurements required to distinguish between them. In the case of nearby conformal field theories, this reduces to the Zamolodchikov metric on the space of couplings. Our formulation quantifies the information lost under renormalization group flow from the UV to the IR and leads us to a quantification of fine-tuning. This formalism also leads us to a criterion for distinguishability of low energy effective field theories generated by the string theory landscape.
The quantum character of physical fields. Foundations of field theories
L. I. Petrova
2006-03-15T23:59:59.000Z
The existing field theories are based on the properties of closed exterior forms, which are invariant ones and correspond to conservation laws for physical fields. Hence, to understand the foundations of field theories and their unity, one has to know how such closed exterior forms are obtained. In the present paper it is shown that closed exterior forms corresponding to field theories are obtained from the equations modelling conservation (balance)laws for material media. It has been developed the evolutionary method that enables one to describe the process of obtaining closed exterior forms. The process of obtaining closed exterior forms discloses the mechanism of evolutionary processes in material media and shows that material media generate, discretely, the physical structures, from which the physical fields are formed. This justifies the quantum character of field theories. On the other hand, this process demonstrates the connection between field theories and the equations for material media and points to the fact that the foundations of field theories must be conditioned by the properties of material media. It is shown that the external and internal symmetries of field theories are conditioned by the degrees of freedom of material media. The classification parameter of physical fields and interactions, that is, the parameter of the unified field theory, is connected with the number of noncommutative balance conservation laws for material media.
Quantum field theory for condensation of bosons and fermions
De Souza, Adriano N.; Filho, Victo S. [Laboratorio de Fisica Teorica e Computacional (LFTC), Universidade Cruzeiro do Sul, 01506-000, Sao Paulo (Brazil)
2013-03-25T23:59:59.000Z
In this brief review, we describe the formalism of the quantum field theory for the analysis of the condensation phenomenon in bosonic systems, by considering the cases widely verified in laboratory of trapped gases as condensate states, either with attractive or with repulsive two-body interactions. We review the mathematical formulation of the quantum field theory for many particles in the mean-field approximation, by adopting contact interaction potential. We also describe the phenomenon of condensation in the case of fermions or the degenerate Fermi gas, also verified in laboratory in the crossover BEC-BCS limit. We explain that such a phenomenon, equivalent to the bosonic condensation, can only occur if we consider the coupling of particles in pairs behaving like bosons, as occurs in the case of Cooper's pairs in superconductivity.
Noncommutative deformations of quantum field theories, locality, and causality
Michael A. Soloviev
2010-12-16T23:59:59.000Z
We investigate noncommutative deformations of quantum field theories for different star products, particularly emphasizing the locality properties and the regularity of the deformed fields. Using functional analysis methods, we describe the basic structural features of the vacuum expectation values of star-modified products of fields and field commutators. As an alternative to microcausality, we introduce a notion of $\\theta$-locality, where $\\theta$ is the noncommutativity parameter. We also analyze the conditions for the convergence and continuity of star products and define the function algebra that is most suitable for the Moyal and Wick-Voros products. This algebra corresponds to the concept of strict deformation quantization and is a useful tool for constructing quantum field theories on a noncommutative space-time.
Quantum field theory in spaces with closed timelike curves
Boulware, D.G. (Department of Physics FM-15, University of Washington, Seattle, Washington 98195 (United States))
1992-11-15T23:59:59.000Z
Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2{pi}. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Loop Quantum Theory Applied to Biology and Nonlinear Whole Biology
Yi-Fang Chang
2008-01-02T23:59:59.000Z
The loop quantum theory, which constitutes a very small discontinuous space, as new method is applied to biology. The model of protein folding and lungs is proposed. In the model, some known results are used, and four approximate conclusions are obtained: their structures are quantized, their space regions are finite, various singularities correspond to folding and crossed points, and different types of catastrophe exist. Further, based on the inseparability and correlativity of the biological systems, the nonlinear whole biology is proposed, and four basic hypotheses are formed. It may unify reductionism and holism, structuralism and functionalism. Finally, the medical meaning of the theory is discussed briefly.
Nonlinear Dynamics of Quantum Systems and Soliton Theory
Eldad Bettelheim; Alexander G. Abanov; Paul Wiegmann
2006-10-26T23:59:59.000Z
We show that space-time evolution of one-dimensional fermionic systems is described by nonlinear equations of soliton theory. We identify a space-time dependence of a matrix element of fermionic systems related to the {\\it Orthogonality Catastrophe} or {boundary states} with the $\\tau$-function of the modified KP-hierarchy. The established relation allows to apply the apparatus of soliton theory to the study of non-linear aspects of quantum dynamics. We also describe a {\\it bosonization in momentum space} - a representation of a fermion operator by a Bose field in the presence of a boundary state.
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.
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.
Nambu-Goldstone Effective Theory of Information at Quantum Criticality
Gia Dvali; Andre Franca; Cesar Gomez; Nico Wintergerst
2015-07-10T23:59:59.000Z
We establish a fundamental connection between quantum criticality of a many-body system, such as Bose-Einstein condensates, and its capacity of information-storage and processing. For deriving the effective theory of modes in the vicinity of the quantum critical point we develop a new method by mapping a Bose-Einstein condensate of $N$-particles onto a sigma model with a continuous global (pseudo)symmetry that mixes bosons of different momenta. The Bogolyubov modes of the condensate are mapped onto the Goldstone modes of the sigma model, which become gapless at the critical point. These gapless Goldstone modes are the quantum carriers of information and entropy. Analyzing their effective theory, we observe the information-processing properties strikingly similar to the ones predicted by the black hole portrait. The energy cost per qubit of information-storage vanishes in the large-$N$ limit and the total information-storage capacity increases with $N$ either exponentially or as a power law. The longevity of information-storage also increases with $N$, whereas the scrambling time in the over-critical regime is controlled by the Lyapunov exponent and scales logarithmically with $N$. This connection reveals that the origin of black hole information storage lies in the quantum criticality of the graviton Bose-gas, and that much simpler systems that can be manufactured in table-top experiments can exhibit very similar information-processing dynamics.
Four Dimensional Quantum Yang-Mills Theory and Mass Gap
Simone Farinelli
2015-07-17T23:59:59.000Z
A quantization procedure for the Yang-Mills equations for the Minkowski space $\\mathbf{R}^{1,3}$ is carried out in such a way that field maps satisfying Wightman's axioms of Constructive Quantum Field Theory can be obtained. Moreover, the spectrum of the corresponding Hamilton operator is proven to be positive and bounded away from zero except for the case of the vacuum state which has vanishing energy level. The particles corresponding to all solution fields are bosons.
Test Functions Space in Noncommutative Quantum Field Theory
M. Chaichian; M. Mnatsakanova; A. Tureanu; Yu. Vernov
2008-07-26T23:59:59.000Z
It is proven that the $\\star$-product of field operators implies that the space of test functions in the Wightman approach to noncommutative quantum field theory is one of the Gel'fand-Shilov spaces $S^{\\beta}$ with $\\beta test functions smears the noncommutative Wightman functions, which are in this case generalized distributions, sometimes called hyperfunctions. The existence and determination of the class of the test function spaces in NC QFT is important for any rigorous treatment in the Wightman approach.
A New Look at the Position Operator in Quantum Theory
Felix M. Lev
2015-01-07T23:59:59.000Z
The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory by analogy with classical electrodynamics. As a consequence, an inevitable effect in standard theory is the wave packet spreading (WPS) of the photon coordinate wave function in directions perpendicular to the photon momentum. This leads to the following paradoxes: if the major part of photons emitted by stars are in wave packet states (what is the most probable scenario) then we should see not separate stars but only an almost continuous background from all stars; no anisotropy of the CMB radiation should be observable; data on gamma-ray bursts, signals from directional radio antennas (in particular, in experiments on Shapiro delay) and signals from pulsars show no signs of WPS. In addition, a problem arises why there are no signs of WPS for protons in the LHC ring. We argue that the above postulate is based neither on strong theoretical arguments nor on experimental data and propose a new consistent definition of the position operator. Then WPS in directions perpendicular to the particle momentum is absent and the paradoxes are resolved. Different components of the new position operator do not commute with each other and, as a consequence, there is no wave function in coordinate representation. Implications of the results for entanglement, quantum locality and the problem of time in quantum theory are discussed.
Infinite Quantum Group Symmetry of Fields in Massive 2D Quantum Field Theory
A. LeCLair; F. Smirnov
1991-08-20T23:59:59.000Z
Starting from a given S-matrix of an integrable quantum field theory in $1+1$ dimensions, and knowledge of its on-shell quantum group symmetries, we describe how to extend the symmetry to the space of fields. This is accomplished by introducing an adjoint action of the symmetry generators on fields, and specifying the form factors of descendents. The braiding relations of quantum field multiplets is shown to be given by the universal $\\CR$-matrix. We develop in some detail the case of infinite dimensional Yangian symmetry. We show that the quantum double of the Yangian is a Hopf algebra deformation of a level zero Kac-Moody algebra that preserves its finite dimensional Lie subalgebra. The fields form infinite dimensional Verma-module representations; in particular the energy-momentum tensor and isotopic current are in the same multiplet.
Quantum Defect Theory for Cold Chemistry with Product Quantum State Resolution
Hazra, Jisha; Bohn, John L; Balakrishnan, N
2014-01-01T23:59:59.000Z
We present a formalism for cold and ultracold atom-diatom chemical reactions that combines a quantum close-coupling method at short-range with quantum defect theory at long-range. The method yields full state-to-state rovibrationally resolved cross sections as in standard close-coupling (CC) calculations but at a considerably less computational expense. This hybrid approach exploits the simplicity of MQDT while treating the short-range interaction explicitly using quantum CC calculations. The method, demonstrated for D+H$_2\\to$ HD+H collisions with rovibrational quantum state resolution of the HD product, is shown to be accurate for a wide range of collision energies and initial conditions. The hybrid CC-MQDT formalism may provide an alternative approach to full CC calculations for cold and ultracold reactions.
The Quantum Spin Hall Effect: Theory and Experiment
Konig, Markus; Buhmann, Hartmut; Molenkamp, Laurens W.; /Wurzburg U.; Hughes, Taylor L.; /Stanford U., Phys. Dept.; Liu, Chao-Xing; /Tsinghua U., Beijing /Stanford U., Phys. Dept.; Qi, Xiao-Liang; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19T23:59:59.000Z
The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the helical edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. Here we review a recent theory which predicts that the QSH state can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the band structure changes from a normal to an 'inverted' type at a critical thickness d{sub c}. We present an analytical solution of the helical edge states and explicitly demonstrate their topological stability. We also review the recent experimental observation of the QSH state in HgTe/(Hg,Cd)Te quantum wells. We review both the fabrication of the sample and the experimental setup. For thin quantum wells with well width d{sub QW} < 6.3 nm, the insulating regime shows the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d{sub QW} > 6.3 nm), the nominally insulating regime shows a plateau of residual conductance close to 2e{sup 2}/h. The residual conductance is independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance is destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d{sub c} = 6.3 nm, is also independently determined from the occurrence of a magnetic field induced insulator to metal transition.
Multi-time wave functions for quantum field theory
Petrat, Sören, E-mail: petrat@math.lmu.de [Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstr. 39, 80333 München (Germany); Tumulka, Roderich, E-mail: tumulka@math.rutgers.edu [Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019 (United States)
2014-06-15T23:59:59.000Z
Multi-time wave functions such as ?(t{sub 1},x{sub 1},…,t{sub N},x{sub N}) have one time variable t{sub j} for each particle. This type of wave function arises as a relativistic generalization of the wave function ?(t,x{sub 1},…,x{sub N}) of non-relativistic quantum mechanics. We show here how a quantum field theory can be formulated in terms of multi-time wave functions. We mainly consider a particular quantum field theory that features particle creation and annihilation. Starting from the particle–position representation of state vectors in Fock space, we introduce multi-time wave functions with a variable number of time variables, set up multi-time evolution equations, and show that they are consistent. Moreover, we discuss the relation of the multi-time wave function to two other representations, the Tomonaga–Schwinger representation and the Heisenberg picture in terms of operator-valued fields on space–time. In a certain sense and under natural assumptions, we find that all three representations are equivalent; yet, we point out that the multi-time formulation has several technical and conceptual advantages. -- Highlights: •Multi-time wave functions are manifestly Lorentz-covariant objects. •We develop consistent multi-time equations with interaction for quantum field theory. •We discuss in detail a particular model with particle creation and annihilation. •We show how multi-time wave functions are related to the Tomonaga–Schwinger approach. •We show that they have a simple representation in terms of operator valued fields.
Spin from defects in two-dimensional quantum field theory
Sebastian Novak; Ingo Runkel
2015-06-24T23:59:59.000Z
We build two-dimensional quantum field theories on spin surfaces starting from theories on oriented surfaces with networks of topological defect lines and junctions. The construction uses a combinatorial description of the spin structure in terms of a triangulation equipped with extra data. The amplitude for the spin surfaces is defined to be the amplitude for the underlying oriented surface together with a defect network dual to the triangulation. Independence of the triangulation and of the other choices follows if the line defect and junctions are obtained from a Delta-separable Frobenius algebra with involutive Nakayama automorphism in the monoidal category of topological defects. For rational conformal field theory we can give a more explicit description of the defect category, and we work out two examples related to free fermions in detail: the Ising model and the so(n) WZW model at level 1.
Spin from defects in two-dimensional quantum field theory
Novak, Sebastian
2015-01-01T23:59:59.000Z
We build two-dimensional quantum field theories on spin surfaces starting from theories on oriented surfaces with networks of topological defect lines and junctions. The construction uses a combinatorial description of the spin structure in terms of a triangulation equipped with extra data. The amplitude for the spin surfaces is defined to be the amplitude for the underlying oriented surface together with a defect network dual to the triangulation. Independence of the triangulation and of the other choices follows if the line defect and junctions are obtained from a Delta-separable Frobenius algebra with involutive Nakayama automorphism in the monoidal category of topological defects. For rational conformal field theory we can give a more explicit description of the defect category, and we work out two examples related to free fermions in detail: the Ising model and the so(n) WZW model at level 1.
Nambu-Goldstone Effective Theory of Information at Quantum Criticality
Dvali, Gia; Gomez, Cesar; Wintergerst, Nico
2015-01-01T23:59:59.000Z
We establish a fundamental connection between quantum criticality of a many-body system, such as Bose-Einstein condensates, and its capacity of information-storage and processing. For deriving the effective theory of modes in the vicinity of the quantum critical point we develop a new method by mapping a Bose-Einstein condensate of $N$-particles onto a sigma model with a continuous global (pseudo)symmetry that mixes bosons of different momenta. The Bogolyubov modes of the condensate are mapped onto the Goldstone modes of the sigma model, which become gapless at the critical point. These gapless Goldstone modes are the quantum carriers of information and entropy. Analyzing their effective theory, we observe the information-processing properties strikingly similar to the ones predicted by the black hole portrait. The energy cost per qubit of information-storage vanishes in the large-$N$ limit and the total information-storage capacity increases with $N$ either exponentially or as a power law. The longevity of i...
Noncommutative Common Cause Principles in algebraic quantum field theory
Hofer-Szabo, Gabor [Research Center for the Humanities, Budapest (Hungary)] [Research Center for the Humanities, Budapest (Hungary); Vecsernyes, Peter [Wigner Research Centre for Physics, Budapest (Hungary)] [Wigner Research Centre for Physics, Budapest (Hungary)
2013-04-15T23:59:59.000Z
States in algebraic quantum field theory 'typically' establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V{sub A} and V{sub B}, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V{sub A} and V{sub B} and the set {l_brace}C, C{sup Up-Tack }{r_brace} screens off the correlation between A and B.
Finite Temperature Dynamical Correlations in Massive Integrable Quantum Field Theories
F. H. L. Essler; R. M. Konik
2009-10-07T23:59:59.000Z
We consider the finite-temperature frequency and momentum dependent two-point functions of local operators in integrable quantum field theories. We focus on the case where the zero temperature correlation function is dominated by a delta-function line arising from the coherent propagation of single particle modes. Our specific examples are the two-point function of spin fields in the disordered phase of the quantum Ising and the O(3) nonlinear sigma models. We employ a Lehmann representation in terms of the known exact zero-temperature form factors to carry out a low-temperature expansion of two-point functions. We present two different but equivalent methods of regularizing the divergences present in the Lehmann expansion: one directly regulates the integral expressions of the squares of matrix elements in the infinite volume whereas the other operates through subtracting divergences in a large, finite volume. Our central results are that the temperature broadening of the line shape exhibits a pronounced asymmetry and a shift of the maximum upwards in energy ("temperature dependent gap"). The field theory results presented here describe the scaling limits of the dynamical structure factor in the quantum Ising and integer spin Heisenberg chains. We discuss the relevance of our results for the analysis of inelastic neutron scattering experiments on gapped spin chain systems such as CsNiCl3 and YBaNiO5.
Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion Florian Marquardt,1
Clerk, Aashish
the basic theory for future ground-state cooling experiments. Cooling rates and steady-state tem- peraturesQuantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion Florian Marquardt,1 Joe P (Received 22 January 2007; published 28 August 2007) We present a quantum-mechanical theory of the cooling
Inequivalence of quantum field theories on noncommutative spacetimes: Moyal versus Wick-Voros planes
Balachandran, A. P. [Department of Physics, Syracuse University, Syracuse, New York 13244-1130 (United States); Departamento de Matematicas, Universidad Carlos III de Madrid, 28911 Leganes, Madrid (Spain); Ibort, A. [Departamento de Matematicas, Universidad Carlos III de Madrid, 28911 Leganes, Madrid (Spain); Marmo, G. [Dipartimento di Scienze Fisiche, University of Napoli and INFN, Via Cinthia I-80126 Napoli (Italy); Martone, M. [Department of Physics, Syracuse University, Syracuse, New York 13244-1130 (United States); Dipartimento di Scienze Fisiche, University of Napoli and INFN, Via Cinthia I-80126 Napoli (Italy)
2010-04-15T23:59:59.000Z
In this paper, we further develop the analysis started in an earlier paper on the inequivalence of certain quantum field theories on noncommutative spacetimes constructed using twisted fields. The issue is of physical importance. Thus it is well known that the commutation relations among spacetime coordinates, which define a noncommutative spacetime, do not constrain the deformation induced on the algebra of functions uniquely. Such deformations are all mathematically equivalent in a very precise sense. Here we show how this freedom at the level of deformations of the algebra of functions can fail on the quantum field theory side. In particular, quantum field theory on the Wick-Voros and Moyal planes are shown to be inequivalent in a few different ways. Thus quantum field theory calculations on these planes will lead to different physics even though the classical theories are equivalent. This result is reminiscent of chiral anomaly in gauge theories and has obvious physical consequences. The construction of quantum field theories on the Wick-Voros plane has new features not encountered for quantum field theories on the Moyal plane. In fact it seems impossible to construct a quantum field theory on the Wick-Voros plane which satisfies all the properties needed of field theories on noncommutative spaces. The Moyal twist seems to have unique features which make it a preferred choice for the construction of a quantum field theory on a noncommutative spacetime.
Quantum Field Theory in de Sitter Universe: Ambient Space Formalism
Mohammad Vahid Takook
2014-09-03T23:59:59.000Z
Quantum field theory in the $4$-dimensional de Sitter space-time is constructed on a unique Bunch-Davies vacuum state in the ambient space formalism in a rigorous mathematical framework. This work is based on the group representation theory and the analyticity of the complexified pseudo-Riemannian manifolds. The unitary irreducible representations of de Sitter group and their corresponding Hilbert spaces are reformulated in the ambient space formalism. Defining the creation and annihilation operators, quantum field operators and their corresponding analytic two-point functions for various spin fields ($s=0,\\frac{1}{2},1,\\frac{3}{2}, 2$) have been constructed. The various spin massless fields can be constructed in terms of the massless conformally coupled scalar field in this formalism. Then the quantum massless minimally coupled scalar field operator, for the first time, is also constructed on Bunch-Davies vacuum state which preserve the analyticity. We show that the massless fields with $s\\leq 2$ can only propagate in de Sitter ambient space formalism. The massless gauge invariant field equations with $s=1, \\frac{3}{2}, 2$ are studied by using the gauge principle. The conformal quantum spin-$2$ field, based on the gauge gravity model, is studied. The gauge spin-$\\frac{3}{2}$ fields satisfy the Grassmannian algebra, and hence, naturally provoke one to couple them with the gauge spin-$2$ field and the super-algebra is automatically appeared. We conclude that the gravitational field may be constructed by three parts, namely, the de Sitter background, the gauge spin-$2$ field and the gauge spin-$\\frac{3}{2}$ field.
"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.
Toward an axiomatic formulation of noncommutative quantum field theory
Chaichian, M.; Tureanu, A. [Department of Physics, University of Helsinki, P.O. Box 64, FIN-00014 Helsinki (Finland); Mnatsakanova, M. N. [Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119992 Vorobyevy Gory, Moscow (Russian Federation); Nishijima, K. [Department of Physics, University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Vernov, Yu. S. [Institute for Nuclear Research, Russian Academy of Sciences, 60th October Anniversary prospect 7a, 117312 Moscow (Russian Federation)
2011-03-15T23:59:59.000Z
We propose new Wightman functions as vacuum expectation values of products of field operators in the noncommutative space-time. These Wightman functions involve the *-product among the fields, compatible with the twisted Poincare symmetry of the noncommutative quantum field theory (NC QFT). In the case of only space-space noncommutativity ({theta}{sub 0i}= 0), we prove the CPT theorem using the noncommutative form of the Wightman functions. We also show that the spin-statistics theorem, demonstrated for the simplest case of a scalar field, holds in NC QFT within this formalism.
Resonant Perturbation Theory of Decoherence and Relaxation of Quantum Bits
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Merkli, M.; Berman, G. P.; Sigal, I. M.
2010-01-01T23:59:59.000Z
We describe our recent results on the resonant perturbation theory of decoherence and relaxation for quantum systems with many qubits. The approach represents a rigorous analysis of the phenomenon of decoherence and relaxation for generalN-level systems coupled to reservoirs of bosonic fields. We derive a representation of the reduced dynamics valid for all timest?0and for small but fixed interaction strength. Our approach does not involve master equation approximations and applies to a wide variety of systems which are not explicitly solvable.
Quantum Jet Theory, Observer Dependence, and Multi-dimensional Virasoro algebra
T. A. Larsson
2009-09-15T23:59:59.000Z
We review some key features of Quantum Jet Theory: observer dependence, multi-dimensional Virasoro algebra, and the prediction that spacetime has four dimensions.
Kossow, Marcel [I. Institut fuer Theoretische Physik, Universitaet Hamburg, Jungiusstrasse 9, D - 20355 Hamburg (Germany)
2008-03-15T23:59:59.000Z
An energy correction is calculated in the time-independent perturbation setup using a regularized ultraviolet finite Hamiltonian on the noncommutative Minkowski space. The correction to the energy is invariant under rotation and translation but is not Lorentz covariant, and this leads to a distortion of the dispersion relation. In the limit where the noncommutativity vanishes, the common quantum field theory on the commutative Minkowski space is reobtained. The calculations are restricted to the regularized cubic interaction.
Quantum Field Theory as a Faithful Image of Nature
Öttinger, Hans Christian
2015-01-01T23:59:59.000Z
"All men by nature desire to know," states Aristotle in the famous first sentence of his Metaphysics. Knowledge about fundamental particles and interactions, that is, knowledge about the deepest aspects of matter, is certainly high if not top on the priority list, not only for physicists and philosophers. The goal of the present book is to contribute to this knowledge by going beyond the usual presentations of quantum field theory in physics textbooks, both in mathematical approach and by critical reflections inspired by epistemology, that is, by the branch of philosophy also referred to as the theory of knowledge. Hopefully, the present book motivates physicists to appreciate philosophical ideas. Epistemology and the philosophy of the evolution of science often seem to lag behind science and to describe the developments a posteriori. As philosophy here has a profound influence on the actual shaping of an image of fundamental particles and their interactions, our development should stimulate the curiosity and...
Matter-enhanced transition probabilities in quantum field theory
Ishikawa, Kenzo, E-mail: ishikawa@particle.sci.hokudai.ac.jp; Tobita, Yutaka
2014-05-15T23:59:59.000Z
The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the S-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a finite-time interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane waves. These matter-induced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the S-matrix, S[T], that satisfies the boundary condition at T. Using S[T], the finite-size corrections of the form of 1/T are found. The corrections to Fermi’s golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths. -- Highlights: •S-matrix S[T] for the finite-time interval in relativistic field theory. •S[T] satisfies the boundary condition and gives correction of 1/T . •The large corrections for light particles breaks Lorentz invariance. •The corrections have implications to neutrino experiments.
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.
Universal scaling in fast quantum quenches in conformal field theories
Sumit R. Das; Damian A. Galante; Robert C. Myers
2015-03-05T23:59:59.000Z
We study the time evolution of a conformal field theory deformed by a relevant operator under a smooth but fast quantum quench which brings it to the conformal point. We argue that when the quench time scale $\\delta t$ is small compared to the scale set by the relevant coupling, the expectation value of the quenched operator scales universally as $\\delta g/ \\delta t ^{2\\Delta-d}$ where $\\delta g$ is the quench amplitude. This growth is further enhanced by a logarithmic factor in even dimensions. We present explicit results for free scalar and fermionic field theories, supported by an analytic understanding of the leading contribution for fast quenches. Results from this Letter suggest that this scaling result, first found in holography, is in fact universal to quantum quenches. Our considerations also show that this limit of fast smooth quenches is quite different from an instantaneous quench from one time-independent Hamiltonian to another, where the Schrodinger picture state at the time of the quench simply serves as an initial condition for subsequent evolution with the final Hamiltonian.
On general properties of Lorentz invariant formulation of noncommutative quantum field theory
Sami Saxell
2008-08-19T23:59:59.000Z
We study general properties of certain Lorentz invariant noncommutative quantum field theories proposed in the literature. We show that causality in those theories does not hold, in contrast to the canonical noncommutative field theory with the light-wedge causality condition. This is the consequence of the infinite nonlocality of the theory getting spread in all spacetime directions. We also show that the time-ordered perturbation theory arising from the Hamiltonian formulation of noncommutative quantum field theories remains inequivalent to the covariant perturbation theory with usual Feynman rules even after restoration of Lorentz symmetry.
PHYSICAL REVIEW A 84, 063806 (2011) Quantum-mechanical theory of optomechanical Brillouin cooling
Carmon, Tal
2011-01-01T23:59:59.000Z
PHYSICAL REVIEW A 84, 063806 (2011) Quantum-mechanical theory of optomechanical Brillouin cooling 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
Quantum Field Theory on the Noncommutative Plane with $E_q(2)$ Symmetry
M. Chaichian; A. Demichev; P. Presnajder
1999-04-20T23:59:59.000Z
We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we define quantum fields depending on noncommutative coordinates and construct a field theoretical action using the $E_q(2)$-invariant measure on the noncommutative plane. With the help of the partial wave decomposition we show that this quantum field theory can be considered as a second quantization of the particle theory on the noncommutative plane and that this field theory has (contrary to the common belief) even more severe ultraviolet divergences than its counterpart on the usual commutative plane. Finally, we introduce the symmetry transformations of physical states on noncommutative spaces and discuss them in detail for the case of the $E_q(2)$ quantum group.
Valley splitting theory of SiGe/Si/SiGe quantum wells Mark Friesen,1,
Coppersmith, Susan N.
Valley splitting theory of SiGe/Si/SiGe quantum wells Mark Friesen,1, * Sucismita Chutia,1 Charles an effective mass theory for SiGe/Si/SiGe quantum wells, with an emphasis on calculating the valley splitting interface, with characteristic energy splittings of order 0.11 meV for the case of SiGe/Si/SiGe quantum
Sussman, Joel L.
Noncovalent interaction or chemical bonding between alkaline earth cations and benzene? A quantum earth metal ion±benzene complexes were performed using the density-functional theory (DFT) B3LYP and ab of the al- kaline earth metal ions to benzene may be attributed to s±p and p±p interactions, which are signi
Three Dimensional Time Theory: to Unify the Principles of Basic Quantum Physics and Relativity
Xiaodong Chen
2005-10-03T23:59:59.000Z
Interpreting quantum mechanics(QM) by classical physics seems like an old topic; And unified theory is in physics frontier; But because the principles of quantum physics and relativity are so different, any theories of trying to unify 4 nature forces should not be considered as completed without truly unifying the basic principles between QM and relativity. This paper will interpret quantum physics by using two extra dimensional time as quantum hidden variables. I'll show that three dimensional time is a bridge to connect basics quantum physics, relativity and string theory. ``Quantum potential'' in Bohm's quantum hidden variable theory is derived from Einstein Lagrangian in 6-dimensional time-space geometry. Statistical effect in the measurement of single particle, non-local properties, de Broglie wave can be naturally derived from the natural properties of three dimensional time. Berry phase, double-slit interference of single particle, uncertainty relation, wave-packet collapse are discussed. The spin and g factor are derived from geometry of extra two time dimensions. Electron can be expressed as time monopole. In the last part of this paper, I'll discuss the relation between three dimensional time and unified theory. Key words: Quantum hidden variable, Interpreting of quantum physics, Berry phase, three dimensional time, unified theory
Concept of chemical bond and aromaticity based on quantum information theory
Szilvási, T; Legeza, Ö
2015-01-01T23:59:59.000Z
Quantum information theory (QIT) emerged in physics as standard technique to extract relevant information from quantum systems. It has already contributed to the development of novel fields like quantum computing, quantum cryptography, and quantum complexity. This arises the question what information is stored according to QIT in molecules which are inherently quantum systems as well. Rigorous analysis of the central quantities of QIT on systematic series of molecules offered the introduction of the concept of chemical bond and aromaticity directly from physical principles and notions. We identify covalent bond, donor-acceptor dative bond, multiple bond, charge-shift bond, and aromaticity indicating unified picture of fundamental chemical models from ab initio.
Towards quantum noncommutative {kappa}-deformed field theory
Daszkiewicz, Marcin; Lukierski, Jerzy; Woronowicz, Mariusz [Institute of Theoretical Physics, University of Wroclaw pl. Maxa Borna 9, 50-206 Wroclaw (Poland)
2008-05-15T23:59:59.000Z
We introduce a new {kappa}-star product describing the multiplication of quantized {kappa}-deformed free fields. The {kappa} deformation of local free quantum fields originates from two sources: noncommutativity of space-time and the {kappa} deformation of field oscillators algebra; we relate these two deformations. We demonstrate that for a suitable choice of {kappa}-deformed field oscillators algebra, the {kappa}-deformed version of the microcausality condition is satisfied, and it leads to the deformation of the Pauli-Jordan commutation function defined by the {kappa}-deformed mass shell. We show by constructing the {kappa}-deformed Fock space that the use of the {kappa}-deformed oscillator algebra permits one to preserve the bosonic statistics of n-particle states. The proposed star product is extended to the product of n fields, which for n=4 defines the interaction vertex in perturbative description of the noncommutative quantum {lambda}{phi}{sup 4} field theory. It appears that the classical four-momentum conservation law is satisfied at the interaction vertices.
Quantum Space-Time and Noncommutative Gauge Field Theories
Sami Saxell
2009-09-17T23:59:59.000Z
The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative space-time is the apparent loss of Lorentz invariance that has been addressed in different ways in the literature. One recently developed approach is to eliminate the Lorentz violating effects by integrating over the parameter of noncommutativity. Fundamental properties of such theories are investigated in this thesis. Another issue addressed is model building, which is difficult in the noncommutative setting due to severe restrictions on the possible gauge symmetries imposed by the noncommutativity of the space-time. Possible ways to relieve these restrictions are investigated and applied and a noncommutative version of the Minimal Supersymmetric Standard Model is presented. While putting the results obtained in the three original publications into their proper context, the introductory part of this thesis aims to provide an overview of the present situation in the field.
Analogue of the quantum total probability rule from Paraconsistent bayesian probability theory
R. Salazar; C. Jara-Figueroa; A. Delgado
2014-08-22T23:59:59.000Z
We derive an analogue of the quantum total probability rule by constructing a probability theory based on paraconsistent logic. Bayesian probability theory is constructed upon classical logic and a desiderata, that is, a set of desired properties that the theory must obey. We construct a new probability theory following the desiderata of Bayesian probability theory but replacing the classical logic by paraconsistent logic. This class of logic has been conceived to handle eventual inconsistencies or contradictions among logical propositions without leading to the trivialisation of the theory. Within this Paraconsistent bayesian probability theory it is possible to deduce a new total probability rule which depends on the probabilities assigned to the inconsistencies. Certain assignments of values for these probabilities lead to expressions identical to those of Quantum mechanics, in particular to the quantum total probability rule obtained via symmetric informationally complete positive- operator valued measure.
B. Julia-Diaz; H. Kamano; T. -S. H. Lee; A. Matsuyama; T. Sato; N. Suzuki
2009-02-18T23:59:59.000Z
Within the relativistic quantum field theory, we analyze the differences between the $\\pi N$ reaction models constructed from using (1) three-dimensional reductions of Bethe-Salpeter Equation, (2) method of unitary transformation, and (3) time-ordered perturbation theory. Their relations with the approach based on the dispersion relations of S-matrix theory are dicusssed.
Cohen, Doron
of the survival probability is manifestly related to the parametric theory of the local density of states LDOS necessitates a generalization of the theory regarding survival probability 11 . In Sec. III we re- mindQuantum irreversibility, perturbation independent decay, and the parametric theory of the local
Quantum field theory in curved spacetime, the operator product expansion, and dark energy
S. Hollands; R. M. Wald
2008-05-22T23:59:59.000Z
To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved spacetime, the theory must be formulated in a local and covariant manner in terms of locally measureable field observables. Since a generic curved spacetime does not possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require symmetries or a preferred notion of a ``vacuum state'' and ``particles''. We propose such a formulation of quantum field theory, wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients--and, thus, the quantum field theory. By contrast, ground/vacuum states--in spacetimes, such as Minkowski spacetime, where they may be defined--cannot vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than the natural scales of the theory.
Lessons for Loop Quantum Gravity from Parametrised Field Theory
Thomas Thiemann
2010-10-12T23:59:59.000Z
In a series of seminal papers, Laddha and Varadarajan have developed in depth the quantisation of Parametrised Field Theory (PFT) in the kind of discontinuous representations that are employed in Loop Quantum Gravity (LQG). In one spatial dimension (circle) PFT is very similar to the closed bosonic string and the constraint algebra is isomorphic to two mutually commuting Witt algebras. Its quantisation is therefore straightforward in LQG like representations which by design lead to non anomalous, unitary, albeit discontinuous representations of the spatial diffeomorphism group. In particular, the complete set of (distributional) solutions to the quantum constraints, a preferred and complete algebra of Dirac observables and the associated physical inner product has been constructed. On the other hand, the two copies of Witt algebras are classically isomorphic to the Dirac or hypersurface deformation algebra of General Relativity (although without structure functions). The question we address in this paper, also raised by Laddha and Varadarajan in their paper, is whether we can quantise the Dirac algebra in such a way that its space of distributional solutions coincides with the one just described. This potentially teaches us something about LQG where a classically equivalent formulation of the Dirac algebra in terms of spatial diffeomorphism Lie algebras is not at our disposal. We find that, in order to achieve this, the Hamiltonian constraint has to be quantised by methods that extend those previously considered. The amount of quantisation ambiguities is somewhat reduced but not eliminated. We also show that the algebra of Hamiltonian constraints closes in a precise sense, with soft anomalies, that is, anomalies that do not cause inconsistencies. We elaborate on the relevance of these findings for full LQG.
Investigating puzzling aspects of the quantum theory by means of its hydrodynamic formulation
Sanz, A S
2015-01-01T23:59:59.000Z
Bohmian mechanics, a hydrodynamic formulation of the quantum theory, constitutes a useful resource to analyze the role of the phase as the mechanism responsible for the dynamical evolution of quantum systems. Here this role is discussed in the context of quantum interference. Specifically, it is shown that when dealing with two wave-packet coherent superpositions this phenomenon is analogous to an effective collision of a single wave packet with a barrier. This effect is illustrated by means of a numerical simulation of Young's two-slit experiment. Furthermore, outcomes from this analysis are also applied to a realistic simulation of Wheeler's delayed choice experiment. As it is shown, in both cases the Bohmian formulation helps to understand in a natural way (and, therefore, to demystify) what are typically regarded as paradoxical aspects of the quantum theory, simply stressing the important dynamical role played by the quantum phase. Accordingly, our conception of quantum systems should not rely on artifici...
Superanalogs of symplectic and contact geometry and their applications to quantum field theory
Albert Schwarz
1994-06-17T23:59:59.000Z
The paper contains a short review of the theory of symplectic and contact manifolds and of the generalization of this theory to the case of supermanifolds. It is shown that this generalization can be used to obtain some important results in quantum field theory. In particular, regarding $N$-superconformal geometry as particular case of contact complex geometry, one can better understand $N=2$ superconformal field theory and its connection to topological conformal field theory. The odd symplectic geometry constitutes a mathematical basis of Batalin-Vilkovisky procedure of quantization of gauge theories. The exposition is based mostly on published papers. However, the paper contains also a review of some unpublished results (in the section devoted to the axiomatics of $N=2$ superconformal theory and topological quantum field theory). The paper will be published in Berezin memorial volume.
Density Functional Theory (DFT) Simulated Annealing (SA)
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Optimal quantum control in nanostructures: Theory and application...
Office of Scientific and Technical Information (OSTI)
36 MATERIALS SCIENCE; CONVERGENCE; ENERGY LEVELS; LASER RADIATION; NANOSTRUCTURES; OPTICS; OPTIMAL CONTROL; OPTIMIZATION; PULSES; QUANTUM MECHANICS; USES; WAVE FUNCTIONS Word...
THEORY OF THE CONTROL OF OBSERVABLE QUANTUM V. P. BELAVKIN
Belavkin, Viacheslav P.
. The general problem of optimal control of a quantum-mechanical system is discussed and the corre- sponding], of the dynamical observation and feedback control optimization problems for such systems has provided a means measurement and control of classical (i.e., non-quantum) Markov processes with quantum observation channels
Wen, Xiao-Gang
The projective construction is a powerful approach to deriving the bulk and edge field theories of non-Abelian fractional quantum Hall (FQH) states and yields an understanding of non-Abelian FQH states in terms of the ...
Counting degrees of freedom in quantum field theory using entanglement entropy
Mezei, Márk (Márk Koppany)
2014-01-01T23:59:59.000Z
We devote this thesis to the exploration of how to define the number of degrees of freedom in quantum field theory. Intuitively, the number of degrees of freedom should decrease along the renormalization group (RG) flow, ...
Quantum field theory solution for a short-range interacting SO(3) quantum spin-glass
C. M. S. da Conceiçăo; E. C. Marino
2009-03-02T23:59:59.000Z
We study the quenched disordered magnetic system, which is obtained from the 2D SO(3) quantum Heisenberg model, on a square lattice, with nearest neighbors interaction, by taking a Gaussian random distribution of couplings centered in an antiferromagnetic coupling, $\\bar J>0$ and with a width $\\Delta J$. Using coherent spin states we can integrate over the random variables and map the system onto a field theory, which is a generalization of the SO(3) nonlinear sigma model with different flavors corresponding to the replicas, coupling parameter proportional to $\\bar J$ and having a quartic spin interaction proportional to the disorder ($\\Delta J$). After deriving the CP$^1$ version of the system, we perform a calculation of the free energy density in the limit of zero replicas, which fully includes the quantum fluctuations of the CP$^1$ fields $z_i$. We, thereby obtain the phase diagram of the system in terms of ($T, \\bar J, \\Delta J$). This presents an ordered antiferromagnetic (AF) phase, a paramagnetic (PM) phase and a spin-glass (SG) phase. A critical curve separating the PM and SG phases ends at a quantum critical point located between the AF and SG phases, at T=0. The Edwards-Anderson order parameter, as well as the magnetic susceptibilities are explicitly obtained in each of the three phases as a function of the three control parameters. The magnetic susceptibilities show a Curie-type behavior at high temperatures and exhibit a clear cusp, characteristic of the SG transition, at the transition line. The thermodynamic stability of the phases is investigated by a careful analysis of the Hessian matrix of the free energy. We show that all principal minors of the Hessian are positive in the limit of zero replicas, implying in particular that the SG phase is stable.
Quantum theory of exciton-photon coupling in photonic crystal slabs with embedded quantum wells
D. Gerace; L. C. Andreani
2007-06-04T23:59:59.000Z
A theoretical description of radiation-matter coupling for semiconductor-based photonic crystal slabs is presented, in which quantum wells are embedded within the waveguide core layer. A full quantum theory is developed, by quantizing both the electromagnetic field with a spatial modulation of the refractive index and the exciton center of mass field in a periodic piecewise constant potential. The second-quantized hamiltonian of the interacting system is diagonalized with a generalized Hopfield method, thus yielding the complex dispersion of mixed exciton-photon modes including losses. The occurrence of both weak and strong coupling regimes is studied, and it is concluded that the new eigenstates of the system are described by quasi-particles called photonic crystal polaritons, which can occur in two situations: (i) below the light line, when a resonance between exciton and non-radiative photon levels occurs (guided polaritons), (ii) above the light line, provided the exciton-photon coupling is larger than the intrinsic radiative damping of the resonant photonic mode (radiative polaritons). For a square lattice of air holes, it is found that the energy minimum of the lower polariton branch can occur around normal incidence. The latter result has potential implications for the realization of polariton parametric interactions in photonic crystal slabs.
Dowling, Jonathan P.
Theory" Jonathan P. Dowling* Quantum Computing Group, Mail Stop 126-347 NASA Jet Propulsion Laboratory their psychic powers to alter the laws of quantum mechanics and thereby modify the outcome of events that have nonphysical effects: noncausality, nonlocality, energy non-conservation, nonunitary evolution of the wave
Unified theory of bound and scattering molecular Rydberg states as quantum maps
Lombardi, Maurice
of the quantum analysis of such states was the Quantum Defect Theory (see e.g. the review article by Seaton [1, the levels near the ionization limit follow the hydrogenic Rydberg law En = -Ry/(n+d)2 , with only a constant of this anisotropy on the ionic potential decays faster with distance r than the point charge 1/r Coulomb po- tential
Towards the theory of control in observable quantum systems
V P Belavkin
2004-08-02T23:59:59.000Z
An operational description of the controlled Markov dynamics of quantum-mechanical system is introduced. The feedback control strategies with regard to the dynamical reduction of quantum states in the course of quantum real-time measurements are discribed in terms of quantum filtering of these states. The concept of sufficient coordinates for the description of the a posteriori quantum states from a given class is introduced, and it is proved that they form a classical Markov process with values in either state operators or state vector space. The general problem of optimal control of a quantum-mechanical system is discussed and the corresponding Bellman equation in the space of sufficient coordinates is derived. The results are illustrated in the example of control of the semigroup dynamics of a quantum system that is instantaneously observed at discrete times and evolves between measurement times according to the Schroedinger equation.
Wick rotation for quantum field theories on degenerate Moyal space(-time)
Grosse, Harald; Lechner, Gandalf [Department of Physics, University of Vienna, 1090 Vienna (Austria)] [Department of Physics, University of Vienna, 1090 Vienna (Austria); Ludwig, Thomas [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig (Germany) [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig (Germany); Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany); Verch, Rainer [Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)] [Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)
2013-02-15T23:59:59.000Z
In this paper the connection between quantum field theories on flat noncommutative space(-times) in Euclidean and Lorentzian signature is studied for the case that time is still commutative. By making use of the algebraic framework of quantum field theory and an analytic continuation of the symmetry groups which are compatible with the structure of Moyal space, a general correspondence between field theories on Euclidean space satisfying a time zero condition and quantum field theories on Moyal Minkowski space is presented ('Wick rotation'). It is then shown that field theories transferred to Moyal space(-time) by Rieffel deformation and warped convolution fit into this framework, and that the processes of Wick rotation and deformation commute.
Two studies of topological quantum field theory in two dimensions
Lin, Haijian Kevin
2012-01-01T23:59:59.000Z
56] G. Segal. The definition of conformal field theory. In:ABELIAN GAUGE THEORY IN FAMILIES Definition 2.4.1. Let 0 ? wOF ABELIAN GAUGE THEORY IN FAMILIES Definition 2.2.6. Recall
A formalism-local framework for general probabilistic theories including quantum theory
Lucien Hardy
2010-05-27T23:59:59.000Z
In this paper we consider general probabilistic theories that pertain to circuits which satisfy two very natural assumptions. We provide a formalism that is local in the following very specific sense: calculations pertaining to any region of spacetime employ only mathematical objects associated with that region. We call this "formalism locality". It incorporates the idea that space and time should be treated on an equal footing. Formulations that use a foliation of spacetime to evolve a state do not have this property nor do histories-based approaches. An operation (see figure on left) has inputs and outputs (through which systems travel). A circuit is built by wiring together operations such that we have no open inputs or outputs left over. A fragment (see figure on right) is a part of a circuit and may have open inputs and outputs. We show how each operation is associated with a certain mathematical object which we call a "duotensor" (this is like a tensor but with a bit more structure). In the figure on the left we show how a duotensor is represented graphically. We can link duotensors together such that black and white dots match up to get the duotensor corresponding to any fragment. The figure on the right is the duotensor for the above fragment. Links represent summing over the corresponding indices. We can use such duotensors to make probabilistic statements pertaining to fragments. Since fragments are the circuit equivalent of arbitrary spacetime regions we have formalism locality. The probability for a circuit is given by the corresponding duotensorial calculation (which is a scalar since there are no indices left over). We show how to put classical probability theory and quantum theory into this framework. [Note: the abstract in the paper has pictures.
Embedding quantum and random optics in a larger field theory
Peter Morgan
2008-06-09T23:59:59.000Z
Introducing creation and annihilation operators for negative frequency components extends the algebra of smeared local observables of quantum optics to include an associated classical random field optics.
An Interpretation of Noncommutative Field Theory in Terms of a Quantum Shift
M. Chaichian; K. Nishijima; A. Tureanu
2005-11-08T23:59:59.000Z
Noncommutative coordinates are decomposed into a sum of geometrical ones and a universal quantum shift operator. With the help of this operator, the mapping of a commutative field theory into a noncommutative field theory (NCFT) is introduced. A general measure for the Lorentz-invariance violation in NCFT is also derived.
Density-Functional Theory and Quantum Chemistry Studies on "dry" and "wet"
Alavi, Ali
Density-Functional Theory and Quantum Chemistry Studies on "dry" and "wet" NaCl(001) vorgelegt von essential role as a food preserva- tive. However, many fundamental physical and chemical properties of Na), and defects on NaCl(001) surfaces have been examined with density-functional theory within the plane
V. P. Neznamov
2015-02-02T23:59:59.000Z
The paper presents the representation of quantum field theory without introduction of infinity bare masses and coupling constants of fermions. Counter-terms, compensating for divergent quantities in self-energy diagrams of fermions and vacuum polarization diagrams at all orders of the perturbation theory, appear in the appropriate Hamiltonians under the special time-dependent unitary transformation.
Gross, E.K.U.
Acceleration of quantum optimal control theory algorithms with mixing strategies Alberto Castro algorithms utilized in quantum optimal control theory QOCT . We show how the nonlinear equations of QOCT can optimal control theory 1Â4 QOCT answers the following question: A system can be driven, during some time
Why Renormalizable NonCommutative Quantum Field Theories?
Vincent Rivasseau
2007-11-12T23:59:59.000Z
We complete our previous recent review on noncommutative field theory, discussing in particular the constructive aproach to the Grosse-Wulkenhaar theory. We also suggest that by gluing together many Grosse-Wulkenhaar theories at high energy one can obtain an effective commutative field theory at lower energy.
Iyengar, Srinivasan S.
"niche" area called quantum dots. 1. A quantum dot is a very small chunk of semiconductor material with quantum-like properties. These are any effects that the bulk form of the same material does not possess quantum mechanical proper- ties and discrete energy levels. 3. As a first approximation these materials
Quantum gravity computers: On the theory of computation with indefinite causal structure
Lucien Hardy
2007-01-05T23:59:59.000Z
A quantum gravity computer is one for which the particular effects of quantum gravity are relevant. In general relativity, causal structure is non-fixed. In quantum theory non-fixed quantities are subject to quantum uncertainty. It is therefore likely that, in a theory of quantum gravity, we will have indefinite causal structure. This means that there will be no matter of fact as to whether a particular interval is timelike or not. We study the implications of this for the theory of computation. Classical and quantum computations consist in ivolving the state of the computer through a sequence of time steps. This will, most likely, not be possible for a quantum gravity computer because the notion of a time step makes no sense if we have indefinite causal structure. We show that it is possible to set up a model for computation even in the absence of definite causal structure by using a certain framework (the causaloid formalism) that was developed for the purpose of correlating data taken in this type of situation. Corresponding to a physical theory is a causaloid, Lambda (this is a mathematical object containing information about the causal connections between different spacetime regions). A computer is given by the pair {Lambda, S} where S is a set of gates. Working within the causaloid formalism, we explore the question of whether universal quantum gravity computers are possible. We also examine whether a quantum gravity computer might be more powerful than a quantum (or classical) computer. In particular, we ask whether indefinite causal structure can be used as a computational resource.
Theory for the optimal control of time-averaged quantities in open quantum systems
Ilia Grigorenko; Martin E. Garcia; K. H. Bennemann
2002-03-25T23:59:59.000Z
We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal control field fulfills a high order differential equation, which we solve analytically for some limiting cases. We determine quantitatively how relaxation effects limit the control of the system. The theory is applied to open two level quantum systems. An approximate analytical solution for the level occupations in terms of the applied fields is presented. Different other applications are discussed.
Exact Amplitude-Based Resummation in Quantum Field Theory: Recent Results
Ward, B F L
2012-01-01T23:59:59.000Z
We present the current status of the application of our approach of exact amplitude-based resummation in quantum field theory to two areas of investigation: precision QCD calculations of all three of us as needed for LHC physics and the resummed quantum gravity realization by one of us (B.F.L.W.) of Feynman's formulation of Einstein's theory of general relativity. We discuss recent results as they relate to experimental observations. There is reason for optimism in the attendant comparison of theory and experiment.
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.
Probability Theories with Dynamic Causal Structure: A New Framework for Quantum Gravity
Lucien Hardy
2005-09-29T23:59:59.000Z
Quantum theory is a probabilistic theory with fixed causal structure. General relativity is a deterministic theory but where the causal structure is dynamic. It is reasonable to expect that quantum gravity will be a probabilistic theory with dynamic causal structure. The purpose of this paper is to present a framework for such a probability calculus. We define an operational notion of space-time, this being composed of elementary regions. Central to this formalism is an object we call the causaloid. This object captures information about causal structure implicit in the data by quantifying the way in which the number of measurements required to establish a state for a composite region is reduced when there is a causal connection between the component regions. This formalism puts all elementary regions on an equal footing. It does not require that we impose fixed causal structure. In particular, it is not necessary to assume the existence of a background time. Remarkably, given the causaloid, we can calculate all relevant probabilities and so the causaloid is sufficient to specify the predictive aspect of a physical theory. We show how certain causaloids can be represented by suggestive diagrams and we show how to represent both classical probability theory and quantum theory by a causaloid. We do not give a causaloid formulation for general relativity though we speculate that this is possible. The work presented here suggests a research program aimed at finding a theory of quantum gravity. The idea is to use the causaloid formalism along with principles taken from the two theories to marry the dynamic causal structure of general relativity with the probabilistic structure of quantum theory.
A new look at the problem of gauge invariance in quantum field theory
Dan Solomon
2007-06-19T23:59:59.000Z
Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in order to obtain a physically correct result. In this paper we will examine this problem and determine why a theory that is supposed to be gauge invariant produces non-gauge invariant results.
Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
Lucien Hardy
2006-08-09T23:59:59.000Z
General relativity is a deterministic theory with non-fixed causal structure. Quantum theory is a probabilistic theory with fixed causal structure. In this paper we build a framework for probabilistic theories with non-fixed causal structure. This combines the radical elements of general relativity and quantum theory. The key idea in the construction is physical compression. A physical theory relates quantities. Thus, if we specify a sufficiently large set of quantities (this is the compressed set), we can calculate all the others. We apply three levels of physical compression. First, we apply it locally to quantities (actually probabilities) that might be measured in a particular region of spacetime. Then we consider composite regions. We find that there is a second level of physical compression for the composite region over and above the first level physical compression for the component regions. Each application of first and second level physical compression is quantified by a matrix. We find that these matrices themselves are related by the physical theory and can therefore be subject to compression. This is the third level of physical compression. This third level of physical compression gives rise to a new mathematical object which we call the causaloid. From the causaloid for a particular physical theory we can calculate verything the physical theory can calculate. This approach allows us to set up a framework for calculating probabilistic correlations in data without imposing a fixed causal structure (such as a background time). We show how to put quantum theory in this framework (thus providing a new formulation of this theory). We indicate how general relativity might be put into this framework and how the framework might be used to construct a theory of quantum gravity.
Minimal Length and the Existence of Some Infinitesimal Quantities in Quantum Theory and Gravity
A. E. Shalyt-Margolin
2014-12-10T23:59:59.000Z
In this work it is demonstrated that, provided a theory involves a minimal length, this theory must be free from such infinitesimal quantities as infinitely small variations in surface of the holographic screen, its volume, and entropy. The corresponding infinitesimal quantities in this case must be replaced by the "minimal variations possible" -- finite quantities dependent on the existent energies. As a result, the initial low-energy theory (quantum theory or general relativity) inevitably must be replaced by a minimal-length theory that gives very close results but operates with absolutely other mathematical apparatus.
The History and Present Status of Quantum Field Theory in Curved Spacetime
Wald, R M
2006-01-01T23:59:59.000Z
Quantum field theory in curved spacetime is a theory wherein matter is treated fully in accord with the principles of quantum field theory, but gravity is treated classically in accord with general relativity. It is not expected to be an exact theory of nature, but it should provide a good approximate description when the quantum effects of gravity itself do not play a dominant role. A major impetus to the theory was provided by Hawking's calculation of particle creation by black holes, showing that black holes radiate as perfect black bodies. During the past 30 years, considerable progress has been made in giving a mathematically rigorous formulation of quantum field theory in curved spacetime. Major issues of principle with regard to the formulation of the theory arise from the lack of Poincare symmetry and the absence of a preferred vacuum state or preferred notion of ``particles''. By the mid-1980's, it was understood how all of these difficulties could be overcome for free (i.e., non-self-interacting) qu...
Anomaly constraints and string/F-theory geometry in 6D quantum gravity
Washington Taylor
2010-09-07T23:59:59.000Z
Quantum anomalies, determined by the Atiyah-Singer index theorem, place strong constraints on the space of quantum gravity theories in six dimensions with minimal supersymmetry. The conjecture of "string universality" states that all such theories which do not have anomalies or other quantum inconsistencies are realized in string theory. This paper describes this conjecture and recent work by Kumar, Morrison, and the author towards developing a global picture of the space of consistent 6D supergravities and their realization in string theory via F-theory constructions. We focus on the discrete data for each model associated with the gauge symmetry group and the representation of this group on matter fields. The 6D anomaly structure determines an integral lattice for each gravity theory, which is related to the geometry of an elliptically fibered Calabi-Yau three-fold in an F-theory construction. Possible exceptions to the string universality conjecture suggest novel constraints on low-energy gravity theories which may be identified from the structure of F-theory geometry.
Wave theories of non-laminar charged particle beams: from quantum to thermal regime
Renato Fedele; Fatema Tanjia; Dusan Jovanovic; Sergio De Nicola; Concetta Ronsivalle
2013-04-01T23:59:59.000Z
The standard classical description of non-laminar charge particle beams in paraxial approximation is extended to the context of two wave theories. The first theory is the so-called Thermal Wave Model (TWM) that interprets the paraxial thermal spreading of the beam particles as the analog of the quantum diffraction. The other theory, hereafter called Quantum Wave Model (QWM), that takes into account the individual quantum nature of the single beam particle (uncertainty principle and spin) and provides the collective description of the beam transport in the presence of the quantum paraxial diffraction. QWM can be applied to beams that are sufficiently cold to allow the particles to manifest their individual quantum nature but sufficiently warm to make overlapping-less the single-particle wave functions. In both theories, the propagation of the beam transport in plasmas or in vacuo is provided by fully similar set of nonlinear and nonlocal governing equations, where in the case of TWM the Compton wavelength (fundamental emittance) is replaced by the beam thermal emittance. In both models, the beam transport in the presence of the self-fields (space charge and inductive effects) is governed by a suitable nonlinear nonlocal 2D Schroedinger equation that is used to obtain the envelope beam equation in quantum and quantum-like regimes, respectively. An envelope equation is derived for both TWM and QWM regimes. In TWM we recover the well known Sacherer equation whilst, in QWM we obtain the evolution equation of the single-particle spot size, i.e., single quantum ray spot in the transverse plane (Compton regime). We show that such a quantum evolution equation contains the same information carried out by an evolution equation for the beam spot size (description of the beam as a whole). This is done by defining the lowest QWM state reachable by a system of overlapping-less Fermions.
Theory of the nucleus as applied to quantum chaos
Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu [St. Petersburg State University, Petersburg Nuclear Physics Institute, National Research Center Kurchatov Institute (Russian Federation)
2014-12-15T23:59:59.000Z
A critical analysis of the present-day concept of chaos in quantum systems as nothing but a quantum signature of chaos in classical mechanics is given. It is proposed to specify a regular versus a chaotic behavior on the basis of symmetries of the system being considered and global integrals of motion that are associated with these symmetries in accordance with the Liouville-Arnold theorem rather than on the basis of the concept of Lyapunov’s instability of trajectories. Numerical criteria of quantum chaos that follow from the proposed concept are analyzed.
Quantum Theory for the Binomial Model in Finance Thoery
Zeqian Chen
2010-02-19T23:59:59.000Z
In this paper, a quantum model for the binomial market in finance is proposed. We show that its risk-neutral world exhibits an intriguing structure as a disk in the unit ball of ${\\bf R}^3,$ whose radius is a function of the risk-free interest rate with two thresholds which prevent arbitrage opportunities from this quantum market. Furthermore, from the quantum mechanical point of view we re-deduce the Cox-Ross-Rubinstein binomial option pricing formula by considering Maxwell-Boltzmann statistics of the system of $N$ distinguishable particles.
UV/IR duality in noncommutative quantum field theory
Andre Fischer; Richard J. Szabo
2010-06-16T23:59:59.000Z
We review the construction of renormalizable noncommutative euclidean phi(4)-theories based on the UV/IR duality covariant modification of the standard field theory, and how the formalism can be extended to scalar field theories defined on noncommutative Minkowski space.
Green function identities in Euclidean quantum field theory
G. Sardanashvily
2006-04-01T23:59:59.000Z
Given a generic Lagrangian system of even and odd fields, we show that any infinitesimal transformation of its classical Lagrangian yields the identities which Euclidean Green functions of quantum fields satisfy.
Interpretations of Quantum Theory in the Light of Modern Cosmology
Mario Castagnino; Sebastian Fortin; Roberto Laura; Daniel Sudarsky
2014-12-24T23:59:59.000Z
The difficult issues related to the interpretation of quantum mechanics and, in particular, the "measurement problem" are revisited using as motivation the process of generation of structure from quantum fluctuations in inflationary cosmology. The unessential mathematical complexity of the particular problem is bypassed, facilitating the discussion of the conceptual issues, by considering, within the paradigm set up by the cosmological problem, another problem where symmetry serves as a focal point: a simplified version of Mott's problem.
1. P1,P2 (P1), (P2) Relativistic Quantum Field Theory
1. P1,P2 (P1), (P2) 2. 3. P1 4. P2 1 #12;P1 P2 " " Relativistic Quantum Field Theory Dirac 212p s1 212s QED 232p 212p s1 212s 232p #12;7 2009 2010 2S 2010 2011 2012 #12;8 2009 2010://tabletop.icepp.s.u- tokyo.ac.jp/Tabletop_experiments/HFS_measurement_with _quantum_oscillation.html P2(?) P1 #12
Time-reversal symmetry breaking and the field theory of quantum chaos
Simons, B.D. [Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE (United Kingdom)] [Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE (United Kingdom); Agam, O. [NEC Research Institute, 4 Independence Way, Princeton, New Jersey 08540 (United States)] [NEC Research Institute, 4 Independence Way, Princeton, New Jersey 08540 (United States); Andreev, A.V. [Institute for Theoretical Physics, University of California, Santa Barbara, California 93106 (United States)] [Institute for Theoretical Physics, University of California, Santa Barbara, California 93106 (United States)
1997-04-01T23:59:59.000Z
Recent studies have shown that the quantum statistical properties of systems which are chaotic in their classical limit can be expressed in terms of an effective field theory. Within this description, spectral properties are determined by low energy relaxation modes of the classical evolution operator. It is in the interaction of these modes that quantum interference effects are encoded. In this paper we review this general approach and discuss how the theory is modified to account for time-reversal symmetry breaking. To keep our discussion general, we will also briefly describe how the theory is modified by the presence of an additional discrete symmetry such as inversion. Throughout, parallels are drawn between quantum chaotic systems and the properties of weakly disordered conductors. {copyright} {ital 1997 American Institute of Physics.}
Topological gauge theories from supersymmetric quantum mechanics on spaces of connections
M Blau; G Thompson
1991-12-20T23:59:59.000Z
We rederive the recently introduced $N=2$ topological gauge theories, representing the Euler characteristic of moduli spaces ${\\cal M}$ of connections, from supersymmetric quantum mechanics on the infinite dimensional spaces ${\\cal A}/{\\cal G}$ of gauge orbits. To that end we discuss variants of ordinary supersymmetric quantum mechanics which have meaningful extensions to infinite-dimensional target spaces and introduce supersymmetric quantum mechanics actions modelling the Riemannian geometry of submersions and embeddings, relevant to the projections ${\\cal A}\\rightarrow {\\cal A}/{\\cal G}$ and inclusions ${\\cal M}\\subset{\\cal A}/{\\cal G}$ respectively. We explain the relation between Donaldson theory and the gauge theory of flat connections in $3d$ and illustrate the general construction by other $2d$ and $4d$ examples.
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.
Coherent versus measurement feedback: Linear systems theory for quantum information
Naoki Yamamoto
2014-10-10T23:59:59.000Z
To control a quantum system via feedback, we generally have two options in choosing control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is the measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages/disadvantages, depending on the system and the control goal, hence their comparison in several situation is important. This paper considers a general open linear quantum system with the following specific control goals; back-action evasion (BAE), generation of a quantum non-demolished (QND) variable, and generation of a decoherence-free subsystem (DFS), all of which have important roles in quantum information science. Then some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand it is shown that, for each control goal, there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of BAE, QND, and DFS in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.
Group field theory formulation of 3d quantum gravity coupled to matter fields
Daniele Oriti; James Ryan
2006-02-02T23:59:59.000Z
We present a new group field theory describing 3d Riemannian quantum gravity coupled to matter fields for any choice of spin and mass. The perturbative expansion of the partition function produces fat graphs colored with SU(2) algebraic data, from which one can reconstruct at once a 3-dimensional simplicial complex representing spacetime and its geometry, like in the Ponzano-Regge formulation of pure 3d quantum gravity, and the Feynman graphs for the matter fields. The model then assigns quantum amplitudes to these fat graphs given by spin foam models for gravity coupled to interacting massive spinning point particles, whose properties we discuss.
BF-theory in graphene: a route toward topological quantum computing?
Annalisa Marzuoli; Giandomenico Palumbo
2012-06-11T23:59:59.000Z
Besides the plenty of applications of graphene allotropes in condensed matter and nanotechnology, we argue that graphene sheets might be engineered to support room-temperature topological quantum processing of information. The argument is based on the possibility of modeling the monolayer graphene effective action by means of a 3d Topological Quantum Field Theory of BF-type able to sustain non-Abelian anyon dynamics. This feature is the basic requirement of recently proposed theoretical frameworks for fault-tolerant and decoherence protected quantum computation.
Quantum motion equation and Poincare translation invariance of noncommutative field theory
Zheng Ze Ma
2006-03-16T23:59:59.000Z
We study the Moyal commutators and their expectation values between vacuum states and non-vacuum states for noncommutative scalar field theory. For noncommutative $\\phi^{\\star4}$ scalar field theory, we derive its energy-momentum tensor from translation transformation and Lagrange field equation. We generalize the Heisenberg and quantum motion equations to the form of Moyal star-products for noncommutative $\\phi^{\\star4}$ scalar field theory for the case $\\theta^{0i}=0$ of spacetime noncommutativity. Then we demonstrate the Poincar{\\' e} translation invariance for noncommutative $\\phi^{\\star4}$ scalar field theory for the case $\\theta^{0i}=0$ of spacetime noncommutativity.
Selective Atomic Heating in Plasmas: Implications for Quantum Theory
Phillips, Jonathan
2008-01-01T23:59:59.000Z
A new model of quantum mechanics, Classical Quantum Mechanics, is based on the (nearly heretical) postulate that electrons are physical objects that obey classical physical laws. Indeed, ionization energies, excitation energies etc. are computed based on picturing electrons as bubbles of charge that symmetrically surround a nucleus. Hence, for example, simple algebraic expressions based on Newtonian force balances are used to predict ionization energies and stable excitation states with remarkable precision. One of the most startling predictions of the model is that there are stable sizes of the hydrogen atom electron (bubble diameter) that are smaller (called hydrinos) than that calculated for the standard ground state. Experimental evidence in support of this novel physical/classical version of quantum is alleged to be found in the existence of super heated hydrogen atoms reported by many teams in a variety of plasmas. It is postulated that the energy required for creating super heated H aoms comes from the...
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)].
Dynamo in Helical MHD Turbulence: Quantum Field Theory Approach
M. Hnatic; M. Jurcisin; M. Stehlik
2006-03-10T23:59:59.000Z
A quantum field model of helical MHD stochastically forced by gaussian hydrodynamic, magnetic and mixed noices is investigated. These helical noises lead to an exponential increase of magnetic fluctuations in the large scale range. Instabilities, which are produced in this process, are eliminated by spontaneous symmetry breaking mechanism accompanied by creation of the homogeneous stationary magnetic field.
Random matrix theory and critical phenomena in quantum spin chains
J. Hutchinson; J. P. Keating; F. Mezzadri
2015-03-19T23:59:59.000Z
We compute critical properties of a general class of quantum spin chains which are quadratic in the Fermi operators and can be solved exactly under certain symmetry constraints related to the classical compact groups $U(N)$, $O(N)$ and $Sp(2N)$. In particular we calculate critical exponents $s$, $\
Quantum Field Theory on Noncommutative Space-Times and the Persistence of Ultraviolet Divergences
M. Chaichian; A. Demichev; P. Presnajder
1999-04-13T23:59:59.000Z
We study properties of a scalar quantum field theory on two-dimensional noncommutative space-times. Contrary to the common belief that noncommutativity of space-time would be a key to remove the ultraviolet divergences, we show that field theories on a noncommutative plane with the most natural Heisenberg-like commutation relations among coordinates or even on a noncommutative quantum plane with $E_q(2)$-symmetry have ultraviolet divergences, while the theory on a noncommutative cylinder is ultraviolet finite. Thus, ultraviolet behaviour of a field theory on noncommutative spaces is sensitive to the topology of the space-time, namely to its compactness. We present general arguments for the case of higher space-time dimensions and as well discuss the symmetry transformations of physical states on noncommutative space-times.
Noncommutative spectral geometry and the deformed Hopf algebra structure of quantum field theory
Mairi Sakellariadou; Antonio Stabile; Giuseppe Vitiello
2013-01-11T23:59:59.000Z
We report the results obtained in the study of Alain Connes noncommutative spectral geometry construction focusing on its essential ingredient of the algebra doubling. We show that such a two-sheeted structure is related with the gauge structure of the theory, its dissipative character and carries in itself the seeds of quantization. From the algebraic point of view, the algebra doubling process has the same structure of the deformed Hops algebra structure which characterizes quantum field theory.
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.
Tunneling of the 3rd Kind: A Test of the Effective Non-locality of Quantum Field Theory
Simon A. Gardiner; Holger Gies; Joerg Jaeckel; Chris J. Wallace
2013-04-09T23:59:59.000Z
Integrating out virtual quantum fluctuations in an originally local quantum field theory results in an effective theory which is non-local. In this Letter we argue that tunneling of the 3rd kind - where particles traverse a barrier by splitting into a pair of virtual particles which recombine only after a finite distance - provides a direct test of this non-locality. We sketch a quantum-optical setup to test this effect, and investigate observable effects in a simple toy model.
An exact RG formulation of quantum gauge theory
Tim R. Morris
2001-02-19T23:59:59.000Z
A gauge invariant Wilsonian effective action is constructed for pure SU(N) Yang-Mills theory by formulating the corresponding flow equation. Manifestly gauge invariant calculations can be performed i.e. without gauge fixing or ghosts. Regularisation is implemented in a novel way which realises a spontaneously broken SU(N|N) supergauge theory. As an example we sketch the computation of the one-loop beta function, performed for the first time without any gauge fixing.
Characterizing common cause closedness of quantum probability theories
Yuichiro Kitajima; Miklos Redei
2015-03-15T23:59:59.000Z
We prove new results on common cause closedness of quantum probability spaces, where by a quantum probability space is meant the projection lattice of a non-commutative von Neumann algebra together with a countably additive probability measure on the lattice. Common cause closedness is the feature that for every correlation between a pair of commuting projections there exists in the lattice a third projection commuting with both of the correlated projections and which is a Reichenbachian common cause of the correlation. The main result we prove is that a quantum probability space is common cause closed if and only if it has at most one measure theoretic atom. This result improves earlier ones published in Z. GyenisZ and M. Redei Erkenntnis 79 (2014) 435-451. The result is discussed from the perspective of status of the Common Cause Principle. Open problems on common cause closedness of general probability spaces $(\\mathcal{L},\\phi)$ are formulated, where $\\mathcal{L}$ is an orthomodular bounded lattice and $\\phi$ is a probability measure on $\\mathcal{L}$.
Einstein-Podolsky-Rosen correlations of Dirac particles - quantum field theory approach
Pawel Caban; Jakub Rembielinski
2006-12-15T23:59:59.000Z
We calculate correlation function in the Einstein--Podolsky--Rosen type of experiment with massive relativistic Dirac particles in the framework of the quantum field theory formalism. We perform our calculations for states which are physically interesting and transforms covariantly under the full Lorentz group action, i.e. for pseudoscalar and vector state.
Tree Unitarity and Partial Wave Expansion in Noncommutative Quantum Field Theory
M. Chaichian; C. Montonen; A. Tureanu
2003-05-28T23:59:59.000Z
The validity of the tree-unitarity criterion for scattering amplitudes on the noncommutative space-time is considered, as a condition that can be used to shed light on the problem of unitarity violation in noncommutative quantum field theories when time is noncommutative. The unitarity constraints on the partial wave amplitudes in the noncommutative space-time are also derived.
Two definitions of the electric polarizability of a bound system in relativistic quantum theory
F. A. B. Coutinho; Y. Nogami; Lauro Tomio
1998-12-24T23:59:59.000Z
For the electric polarizability of a bound system in relativistic quantum theory, there are two definitions that have appeared in the literature. They differ depending on whether or not the vacuum background is included in the system. A recent confusion in this connection is clarified.
Conserved charges and quantum-group transformations in noncommutative field theories
Giovanni Amelino-Camelia; Giulia Gubitosi; Flavio Mercati; Giacomo Rosati
2010-09-16T23:59:59.000Z
The recently-developed techniques of Noether analysis of the quantum-group spacetime symmetries of some noncommutative field theories rely on the {\\it ad hoc} introduction of some peculiar auxiliary transformation parameters, which appear to have no role in the structure of the quantum group. We here show that it is possible to set up the Noether analysis directly in terms of the quantum-group symmetry transformations, and we therefore establish more robustly the attribution of the conserved charges to the symmetries of interest. We also characterize the concept of "time independence" (as needed for conserved charges) in a way that is robust enough to be applicable even to theories with space/time noncommutativity, where it might have appeared that any characterization of time independence should be vulnerable to changes of ordering convention.
Adsorption of silver dimer on graphene - A DFT study
Kaur, Gagandeep, E-mail: gaganj1981@yahoo.com [Department of Physics and Centre of Advanced Studies in Physics, Panjab University, Chandigarh-160014, India and Chandigarh Engineering College, Landran, Mohali-140307, Punjab (India); Gupta, Shuchi [Department of Physics and Centre of Advanced Studies in Physics, Panjab University, Chandigarh-160014, India and University Institute of Engineering and Technology, Panjab University, Chandigarh -160014 (India); Rani, Pooja; Dharamvir, Keya [Department of Physics and Centre of Advanced Studies in Physics, Panjab University, Chandigarh-160014 (India)
2014-04-24T23:59:59.000Z
We performed a systematic density functional theory (DFT) study of the adsorption of silver dimer (Ag{sub 2}) on graphene using SIESTA (Spanish Initiative for Electronic Simulations with Thousands of Atoms) package, in the generalized gradient approximation (GGA). The adsorption energy, geometry, and charge transfer of Ag2-graphene system are calculated. The minimum energy configuration for a silver dimer is parallel to the graphene sheet with its two atoms directly above the centre of carbon-carbon bond. The negligible charge transfer between the dimer and the surface is also indicative of a weak bond. The methodology demonstrated in this paper may be applied to larger silver clusters on graphene sheet.
Quantum Theory of Cavityless Feedback Cooling of An Optically Trapped Nanoparticle
Rodenburg, B; Vamivakas, A N; Bhattacharya, M
2015-01-01T23:59:59.000Z
We present a quantum theory of cavityless feedback cooling of an optically trapped harmonically oscillating subwavelength dielectric particle, a configuration recently realized in several experiments. Specifically, we derive a Markovian master equation that treats the mechanical as well as optical degrees of freedom quantum mechanically. Employing this equation, we solve for the nanoparticle phonon number dynamics exactly, and extract analytic expressions for the cooling timescale and the steady state phonon number. We present experimental data verifying the predictions of our model in the classical regime, and also demonstrate that quantum ground state preparation is within reach of ongoing experiments. Our work provides a quantitative framework for future theoretical modeling of the cavityless quantum optomechanics of optically trapped dielectric particles.
Quantum Theory of Cavityless Feedback Cooling of An Optically Trapped Nanoparticle
B. Rodenburg; L. P. Neukirch; A. N. Vamivakas; M. Bhattacharya
2015-03-17T23:59:59.000Z
We present a quantum theory of cavityless feedback cooling of an optically trapped harmonically oscillating subwavelength dielectric particle, a configuration recently realized in several experiments. Specifically, we derive a Markovian master equation that treats the mechanical as well as optical degrees of freedom quantum mechanically. Employing this equation, we solve for the nanoparticle phonon number dynamics exactly, and extract analytic expressions for the cooling timescale and the steady state phonon number. We present experimental data verifying the predictions of our model in the classical regime, and also demonstrate that quantum ground state preparation is within reach of ongoing experiments. Our work provides a quantitative framework for future theoretical modeling of the cavityless quantum optomechanics of optically trapped dielectric particles.
Gravity Dual for Reggeon Field Theory and Non-linear Quantum Finance
Yu Nakayama
2009-06-23T23:59:59.000Z
We study scale invariant but not necessarily conformal invariant deformations of non-relativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the non-relativistic conformal invariance. We discuss applications to scaling regime of Reggeon field theory and non-linear quantum finance. These theories possess scale invariance but may or may not break the conformal invariance, depending on the underlying symmetry assumptions.
Quantum Moduli Space of the Cascading Sp(p+M) x Sp(p) Gauge Theory
Fumikazu Koyama; Futoshi Yagi
2006-12-27T23:59:59.000Z
We extend the detailed analysis of the quantum moduli space of the cascading SU(p+M) x SU(p) gauge theory in the recent paper of Dymarsky, Klebanov, and Seiberg for the Sp(p+M) x Sp(p) cascading gauge theory, which lives on the world volume of p D3-branes and M fractional D3-branes at the tip of the orientifolded conifold. As in their paper, we also find in this case that the ratio of the deformation parameters of the quantum constraint on the different branches in the gauge theory can be reproduced by the ratio of the deformation parameters of the conifold with different numbers of mobile D3-branes.
Ultracold Atoms: How Quantum Field Theory Invaded Atomic Physics
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
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(Million Cubic Feet) Oregon (Including Vehicle Fuel) (MillionStructural Basis of5, 2014 | ReleaseUNCLASSI H E DCeeehiUltracold Atoms: How Quantum Field
Toward theory of quantum Hall effect in graphene
E. V. Gorbar; V. P. Gusynin; V. A. Miransky
2008-11-07T23:59:59.000Z
We analyze a gap equation for the propagator of Dirac quasiparticles and conclude that in graphene in a magnetic field, the order parameters connected with the quantum Hall ferromagnetism dynamics and those connected with the magnetic catalysis dynamics necessarily coexist (the latter have the form of Dirac masses and correspond to excitonic condensates). This feature of graphene could lead to important consequences, in particular, for the existence of gapless edge states. Solutions of the gap equation corresponding to recently experimentally discovered novel plateaus in graphene in strong magnetic fields are described.
Linear response theory in quantum statistical mechanics V. Jaksic1
issue of non-equilibrium steady states (NESS) in two independent steps. (A) The existence and analytic properties of NESS are assumed as an axiom. On the basis of this axiom one develops the mathematical theory to a NESS and analytical properties of this NESS are detailed dynamical problems which can be answered only
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 Field and Cosmic Field-Finite Geometrical Field Theory of Matter Motion Part Three
Jianhua Xiao
2005-12-20T23:59:59.000Z
This research establishes an operational measurement way to express the quantum field theory in a geometrical form. In four-dimensional spacetime continuum, the orthogonal rotation is defined. It forms two sets of equations: one set is geometrical equations, another set is the motion equations. The Lorentz transformation can be directly derived from the geometrical equations, and the proper time of general relativity is well expressed by time displacement field. By the motion equations, the typical time displacement field of matter motion is discussed. The research shows that the quantum field theory can be established based on the concept of orthogonal rotation. On this sense, the quantum matter motion in physics is viewed as the orthogonal rotation of spacetime continuum. In this paper, it shows that there are three typical quantum solutions. One is particle-like solution, one is generation-type solution, and one is pure wave type solution. For each typical solution, the force fields are different. Many features of quantum field can be well explained by this theoretic form. Finally, the general matter motion is discussed, the main conclusions are: (1). Geometrically, cosmic vacuum field can be described by the curvature spacetime; (2). The spatial deformation of planet is related with a planet electromagnetic field; (3). For electric charge less matter, the volume of matter will be expanding infinitely; (4).For strong electric charge matter, it shows that the volume of matter will be contracting infinitely.
Is there a "most perfect fluid" consistent with quantum field theory?
Thomas D. Cohen
2007-03-05T23:59:59.000Z
It was recently conjectured that the ratio of the shear viscosity to entropy density, $ \\eta/ s$, for any fluid always exceeds $\\hbar/(4 \\pi k_B)$. This conjecture was motivated by quantum field theoretic results obtained via the AdS/CFT correspondence and from empirical data with real fluids. A theoretical counterexample to this bound can be constructed from a nonrelativistic gas by increasing the number of species in the fluid while keeping the dynamics essentially independent of the species type. The question of whether the underlying structure of relativistic quantum field theory generically inhibits the realization of such a system and thereby preserves the possibility of a universal bound is considered here. Using rather conservative assumptions, it is shown here that a metastable gas of heavy mesons in a particular controlled regime of QCD provides a realization of the counterexample and is consistent with a well-defined underlying relativistic quantum field theory. Thus, quantum field theory appears to impose no lower bound on $\\eta/s$, at least for metastable fluids.
Emergence of equilibrium thermodynamic properties in quantum pure states. I. Theory
Barbara Fresch; Giorgio J. Moro
2010-07-21T23:59:59.000Z
Investigation on foundational aspects of quantum statistical mechanics recently entered a renaissance period due to novel intuitions from quantum information theory and to increasing attention on the dynamical aspects of single quantum systems. In the present contribution a simple but effective theoretical framework is introduced to clarify the connections between a purely mechanical description and the thermodynamic characterization of the equilibrium state of an isolated quantum system. A salient feature of our approach is the very transparent distinction between the statistical aspects and the dynamical aspects in the description of isolated quantum systems. Like in the classical statistical mechanics, the equilibrium distribution of any property is identified on the basis of the time evolution of the considered system. As a consequence equilibrium properties of quantum system appear to depend on the details of the initial state due to the abundance of constants of the motion in the Schr\\"odinger dynamics. On the other hand the study of the probability distributions of some functions, such as the entropy or the equilibrium state of a subsystem, in statistical ensembles of pure states reveals the crucial role of typicality as the bridge between macroscopic thermodynamics and microscopic quantum dynamics. We shall consider two particular ensembles: the random pure state ensemble and the fixed expectation energy ensemble. The relation between the introduced ensembles, the properties of a given isolated system, and the standard quantum statistical description are discussed throughout the presentation. Finally we point out the conditions which should be satisfied by an ensemble in order to get meaningful thermodynamical characterization of an isolated quantum system.
Low energy Lorentz violation from polymer quantum field theory
Husain, Viqar
2015-01-01T23:59:59.000Z
We analyze the response of an inertial two-level Unruh-DeWitt particle detector coupled to a polymer quantized scalar field in four-dimensional Minkowski spacetime, within first-order perturbation theory. Above a critical rapidity $\\beta_c \\approx 1.3675$, independent of the polymer mass scale $M_\\star$, two drastic changes occur: (i) the detector's excitation rate becomes nonvanishing; (ii) the excitation and de-excitation rates are of order $M_\\star$, for arbitrarily small detector energy gap. We argue that qualitatively similar results hold for any Lorentz violating theory in which field modes with spatial momentum $k$ have excitation energy of the form $|k|\\ f(|k|/M_\\star)$ where the function $f$ dips below unity.
Likos, Christos N.
Density-functional theory of freezing of quantum liquids at zero temperature using exact liquid-functional theory to study the freezing of superfluid 4 He, charged bosons, and charged fermions at zero temperature-functional theory of freezing that involve linear response, all fail to correctly describe the crystalliza- tion
Time delay for dispersive systems in quantum scattering theory
Rafael Tiedra de Aldecoa
2008-10-06T23:59:59.000Z
We consider time delay and symmetrised time delay (defined in terms of sojourn times) for quantum scattering pairs $\\{H_0=h(P),H\\}$, where $h(P)$ a dispersive operator of hypoelliptic-type. For instance $h(P)$ can be one of the usual elliptic operators such as the Schr\\"odinger operator $h(P)=P^2$ or the square-root Klein-Gordon operator $h(P)=\\sqrt{1+P^2}$. We show under general conditions that the symmetrised time delay exists for all smooth even localization functions. It is equal to the Eisenbud-Wigner time delay plus a contribution due to the non-radial component of the localization function. If the scattering operator $S$ commutes with some function of the velocity operator $\
A quantum-dynamical theory for nonlinear optical interactions in graphene
Zheshen Zhang; Paul L. Voss
2011-06-23T23:59:59.000Z
We use a quantum-dynamical model to investigate the optical response of graphene under low excitation power. Ultrafast carrier relaxation processes, which play an important role for understanding the optical response of graphene, are included phenomenologically into the model. We obtain analytical solutions for the linear and third-order nonlinear optical response of graphene, and four-wave mixing in particular. This theory shows agreement with recently reported experimental data on linear complex optical conductivity and four-wave mixing, providing evidence for ultrafast quantum-dephasing times of approximately 1 fs.
The logic of the future in the Everett-Wheeler understanding of quantum theory
Anthony Sudbery
2015-02-04T23:59:59.000Z
I discuss the problems of probability and the future in the Everett-Wheeler understanding of quantum theory. To resolve these, I propose an understanding of probability arising from a form of temporal logic: the probability of a future-tense proposition is identified with its truth value in a many-valued and context-dependent logic. I construct a lattice of tensed propositions, with truth values in the interval $[0,1]$, and derive logical properties of the truth values given by the usual quantum-mechanical formula for the probability of histories.
Probing Hawking and Unruh effects and quantum field theory in curved space by geometric invariants
Antonio Capolupo; Giuseppe Vitiello
2013-11-12T23:59:59.000Z
The presence of noncyclic geometric invariant is revealed in all the phenomena where particle generation from vacuum or vacuum condensates appear. Aharonov--Anandan invariants then can help to study such systems and can represent a new tool to be used in order to provide laboratory evidence of phenomena particulary hard to be detected, such as Hawking and Unruh effects and some features of quantum field theory in curved space simulated by some graphene morphologies. It is finally suggested that a very precise quantum thermometer can be built by exploiting geometric invariants properties.
Vladimir Mashkevich
2008-03-13T23:59:59.000Z
The aim of these notes is to elucidate some aspects of quantum field theory in curved spacetime, especially those relating to the notion of particles. A selection of issues relevant to wave-particle duality is given. The case of a generic curved spacetime is outlined. A Hamiltonian formulation of quantum field theory in curved spacetime is elaborated for a preferred reference frame with a separated space metric (a static spacetime and a reductive synchronous reference frame). Applications: (1) Black hole. (2) The universe; the cosmological redshift is obtained in the context of quantum field theory.
Hexakis(4-phormylphenoxy)cyclotriphosphazene: X-ray and DFT-calculated structures
Albayrak, Cigdem, E-mail: calbayrak@sinop.edu.tr; Kosar, Basak [Sinop University, Faculty of Education (Turkey); Odabasoglu, Mustafa [Pamukkale University, Chemical Technology Program (Turkey); Bueyuekguengoer, Orhan [Ondokuz Mayis University, Faculty of Arts and Sciences (Turkey)
2010-12-15T23:59:59.000Z
The crystal structure of hexakis(4-phormylphenoxy)cyclotriphosphazene is determined by using X-ray diffraction and then the molecular structure is investigated with density functional theory (DFT). X-Ray study shows that the title compound has C-H-{pi} interaction with phosphazene ring. The molecules in the unit cell are packed with Van der Waals and dipole-dipole interactions and the molecules are packed in zigzag shaped. Optimized molecular geometry is calculated with DFT at B3LYP/6-311G(d,p) level. The results from both experimental and theoretical calculations are compared in this study.
Failure of microcausality in quantum field theory on noncommutative spacetime
Greenberg, O.W. [High Energy Physics Division, Department of Physical Sciences, University of Helsinki, FIN-00014, Helsinki (Finland)
2006-02-15T23:59:59.000Z
The commutator of ratio {phi}(x)*{phi}(x) ratio with {partial_derivative}{sub {mu}}{sup y} ratio {phi}(y)*{phi}(y) ratio fails to vanish at equal times and thus also fails to obey microcausality at spacelike separation even for the case in which {theta}{sup 0i}=0. The failure to obey microcausality for these sample observables implies that this form of noncommutative field theory fails to obey microcausality in general. This result holds generally when there are time derivatives in the observables. We discuss possible responses to this problem.
Effective Field Theory for the Quantum Electrodynamics of a Graphene Wire
P. Faccioli; E. Lipparini
2009-06-30T23:59:59.000Z
We study the low-energy quantum electrodynamics of electrons and holes, in a thin graphene wire. We develop an effective field theory (EFT) based on an expansion in p/p_T, where p_T is the typical momentum of electrons and holes in the transverse direction, while p are the momenta in the longitudinal direction. We show that, to the lowest-order in (p/p_T), our EFT theory is formally equivalent to the exactly solvable Schwinger model. By exploiting such an analogy, we find that the ground state of the quantum wire contains a condensate of electron-hole pairs. The excitation spectrum is saturated by electron-hole collective bound-states, and we calculate the dispersion law of such modes. We also compute the DC conductivity per unit length at zero chemical potential and find g_s =e^2/h, where g_s=4 is the degeneracy factor.
Quantum field theory in spaces with closed time-like curves
Boulware, D.G.
1992-12-31T23:59:59.000Z
Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27{pi}. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Quantum field theory in spaces with closed time-like curves. [Gott space
Boulware, D.G.
1992-01-01T23:59:59.000Z
Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27[pi]. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Wu, Yue-Liang
2015-01-01T23:59:59.000Z
Treating the gravitational force on the same footing as the electroweak and strong forces, we present a quantum field theory (QFT) of gravity based on spinnic and scaling gauge symmetries. The so-called Gravifield sided on both locally flat non-coordinate space-time and globally flat Minkowski space-time is an essential ingredient for gauging global spinnic and scaling symmetries. The locally flat Gravifield space-time spanned by the Gravifield is associated with a non-commutative geometry characterized by a gauge-type field strength of Gravifield. A gauge invariant and coordinate independent action for the quantum gravity is built in the Gravifield basis, we derive equations of motion for all quantum fields with including the gravitational effect and obtain basic conservation laws for all symmetries. The equation of motion for Gravifield tensor is deduced in connection directly with the energy-momentum tensor. When the spinnic and scaling gauge symmetries are broken down to a background structure that posses...
Miransky, Vladimir A
2015-01-01T23:59:59.000Z
A range of quantum field theoretical phenomena driven by external magnetic fields and their applications in relativistic systems and quasirelativistic condensed matter ones, such as graphene and Dirac/Weyl semimetals, are reviewed. We start by introducing the underlying physics of the magnetic catalysis. The dimensional reduction of the low-energy dynamics of relativistic fermions in an external magnetic field is explained and its role in catalyzing spontaneous symmetry breaking is emphasized. The general theoretical consideration is supplemented by the analysis of the magnetic catalysis in quantum electrodynamics, chromodynamics and quasirelativistic models relevant for condensed matter physics. By generalizing the ideas of the magnetic catalysis to the case of nonzero density and temperature, we argue that other interesting phenomena take place. The chiral magnetic and chiral separation effects are perhaps the most interesting among them. In addition to the general discussion of the physics underlying chira...
Vladimir A. Miransky; Igor A. Shovkovy
2015-04-10T23:59:59.000Z
A range of quantum field theoretical phenomena driven by external magnetic fields and their applications in relativistic systems and quasirelativistic condensed matter ones, such as graphene and Dirac/Weyl semimetals, are reviewed. We start by introducing the underlying physics of the magnetic catalysis. The dimensional reduction of the low-energy dynamics of relativistic fermions in an external magnetic field is explained and its role in catalyzing spontaneous symmetry breaking is emphasized. The general theoretical consideration is supplemented by the analysis of the magnetic catalysis in quantum electrodynamics, chromodynamics and quasirelativistic models relevant for condensed matter physics. By generalizing the ideas of the magnetic catalysis to the case of nonzero density and temperature, we argue that other interesting phenomena take place. The chiral magnetic and chiral separation effects are perhaps the most interesting among them. In addition to the general discussion of the physics underlying chiral magnetic and separation effects, we also review their possible phenomenological implications in heavy-ion collisions and compact stars. We also discuss the application of the magnetic catalysis ideas for the description of the quantum Hall effect in monolayer and bilayer graphene, and conclude that the generalized magnetic catalysis, including both the magnetic catalysis condensates and the quantum Hall ferromagnetic ones, lies at the basis of this phenomenon. We also consider how an external magnetic field affects the underlying physics in a class of three-dimensional quasirelativistic condensed matter systems, Dirac semimetals. While at sufficiently low temperatures and zero density of charge carriers, such semimetals are expected to reveal the regime of the magnetic catalysis, the regime of Weyl semimetals with chiral asymmetry is realized at nonzero density...
Parallelized Solution to Semidefinite Programmings in Quantum Complexity Theory
Xiaodi Wu
2010-09-12T23:59:59.000Z
In this paper we present an equilibrium value based framework for solving SDPs via the multiplicative weight update method which is different from the one in Kale's thesis \\cite{Kale07}. One of the main advantages of the new framework is that we can guarantee the convertibility from approximate to exact feasibility in a much more general class of SDPs than previous result. Another advantage is the design of the oracle which is necessary for applying the multiplicative weight update method is much simplified in general cases. This leads to an alternative and easier solutions to the SDPs used in the previous results \\class{QIP(2)}$\\subseteq$\\class{PSPACE} \\cite{JainUW09} and \\class{QMAM}=\\class{PSPACE} \\cite{JainJUW09}. Furthermore, we provide a generic form of SDPs which can be solved in the similar way. By parallelizing every step in our solution, we are able to solve a class of SDPs in \\class{NC}. Although our motivation is from quantum computing, our result will also apply directly to any SDP which satisfies our conditions. In addition to the new framework for solving SDPs, we also provide a novel framework which improves the range of equilibrium value problems that can be solved via the multiplicative weight update method. Before this work we are only able to calculate the equilibrium value where one of the two convex sets needs to be the set of density operators. Our work demonstrates that in the case when one set is the set of density operators with further linear constraints, we are still able to approximate the equilibrium value to high precision via the multiplicative weight update method.
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.
Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
Erez Zohar; J. Ignacio Cirac; Benni Reznik
2015-03-08T23:59:59.000Z
Can high energy physics can be simulated by low-energy, nonrelativistic, many-body systems, such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in particular, they manifest neither local gauge invariance nor Lorentz invariance, which are crucial properties of the quantum field theories which are the building blocks of the standard model of elementary particles. However, it turns out, surprisingly, that there are ways to configure atomic system to manifest both local gauge invariance and Lorentz invariance. In particular, local gauge invariance can arise either as an effective, low energy, symmetry, or as an "exact" symmetry, following from the conservation laws in atomic interactions. Hence, one could hope that such quantum simulators may lead to new type of (table-top) experiments, that shall be used to study various QCD phenomena, as the con?nement of dynamical quarks, phase transitions, and other effects, which are inaccessible using the currently known computational methods. In this report, we review the Hamiltonian formulation of lattice gauge theories, and then describe our recent progress in constructing quantum simulation of Abelian and non-Abelian lattice gauge theories in 1 + 1 and 2 + 1 dimensions using ultracold atoms in optical lattices.
The density of states approach for the simulation of finite density quantum field theories
K. Langfeld; B. Lucini; A. Rago; R. Pellegrini; L. Bongiovanni
2015-03-02T23:59:59.000Z
Finite density quantum field theories have evaded first principle Monte-Carlo simulations due to the notorious sign-problem. The partition function of such theories appears as the Fourier transform of the generalised density-of-states, which is the probability distribution of the imaginary part of the action. With the advent of Wang-Landau type simulation techniques and recent advances, the density-of-states can be calculated over many hundreds of orders of magnitude. Current research addresses the question whether the achieved precision is high enough to reliably extract the finite density partition function, which is exponentially suppressed with the volume. In my talk, I review the state-of-play for the high precision calculations of the density-of-states as well as the recent progress for obtaining reliable results from highly oscillating integrals. I will review recent progress for the $Z_3$ quantum field theory for which results can be obtained from the simulation of the dual theory, which appears to free of a sign problem.
The density of states approach for the simulation of finite density quantum field theories
Langfeld, K; Rago, A; Pellegrini, R; Bongiovanni, L
2015-01-01T23:59:59.000Z
Finite density quantum field theories have evaded first principle Monte-Carlo simulations due to the notorious sign-problem. The partition function of such theories appears as the Fourier transform of the generalised density-of-states, which is the probability distribution of the imaginary part of the action. With the advent of Wang-Landau type simulation techniques and recent advances, the density-of-states can be calculated over many hundreds of orders of magnitude. Current research addresses the question whether the achieved precision is high enough to reliably extract the finite density partition function, which is exponentially suppressed with the volume. In my talk, I review the state-of-play for the high precision calculations of the density-of-states as well as the recent progress for obtaining reliable results from highly oscillating integrals. I will review recent progress for the $Z_3$ quantum field theory for which results can be obtained from the simulation of the dual theory, which appears to fr...
Serena Cenatiempo; Alessandro Giuliani
2014-07-18T23:59:59.000Z
We present a renormalization group construction of a weakly interacting Bose gas at zero temperature in the two-dimensional continuum, both in the quantum critical regime and in the presence of a condensate fraction. The construction is performed within a rigorous renormalization group scheme, borrowed from the methods of constructive field theory, which allows us to derive explicit bounds on all the orders of renormalized perturbation theory. Our scheme allows us to construct the theory of the quantum critical point completely, both in the ultraviolet and in the infrared regimes, thus extending previous heuristic approaches to this phase. For the condensate phase, we solve completely the ultraviolet problem and we investigate in detail the infrared region, up to length scales of the order $(\\lambda^3 \\rho_0)^{-1/2}$ (here $\\lambda$ is the interaction strength and $\\rho_0$ the condensate density), which is the largest length scale at which the problem is perturbative in nature. We exhibit violations to the formal Ward Identities, due to the momentum cutoff used to regularize the theory, which suggest that previous proposals about the existence of a non-perturbative non-trivial fixed point for the infrared flow should be reconsidered.
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.
Inevitability and Importance of Non-Perturbative Elements in Quantum Field Theory
Alexander P. Bakulev; Dmitry V. Shirkov
2011-02-11T23:59:59.000Z
The subject of the first section-lecture is concerned with the strength and the weakness of the perturbation theory (PT) approach, that is expansion in powers of a small parameter $\\alpha$, in Quantum Theory. We start with outlining a general troublesome feature of the main quantum theory instrument, the perturbation expansion method. The striking issue is that perturbation series in powers of $\\alpha \\ll 1$ is not a convergent series. The formal reason is an essential singularity of quantum amplitude (matrix element) $C(\\alpha)$ at the origin $\\alpha=0$. In many physically important cases one needs some alternative means of theoretical analysis. In particular, this refers to perturbative QCD (pQCD) in the low-energy domain. In the second section-lecture, we discuss the approach of Analytic Perturbation Theory (APT). We start with a short historic preamble and then discuss how combining the Dispersion Relation with the Renormalization Group (RG) techniques yields the APT with \\myMath{\\displaystyle e^{-1/\\alpha}} nonanalyticity. Next we consider the results of APT applications to low-energy QCD processes and show that in this approach the fourth-loop contributions, which appear to be on the asymptotic border in the pQCD approach, are of the order of a few per mil. Then we note that using the RG in QCD dictates the need to use the Fractional APT (FAPT) and describe its basic ingredients. As an example of the FAPT application in QCD we consider the pion form factor $F_\\pi(Q^2)$ calculation. At the end, we discuss the resummation of nonpower series in {(F)APT} with application to the estimation of the Higgs-boson-decay width $\\Gamma_{H\\to\\bar{b}b}(m_H^2)$.
3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
Winston Fairbairn; Etera R. Livine
2007-02-23T23:59:59.000Z
An effective field theory for matter coupled to three-dimensional quantum gravity was recently derived in the context of spinfoam models in hep-th/0512113. In this paper, we show how this relates to group field theories and generalized matrix models. In the first part, we realize that the effective field theory can be recasted as a matrix model where couplings between matrices of different sizes can occur. In a second part, we provide a family of classical solutions to the three-dimensional group field theory. By studying perturbations around these solutions, we generate the dynamics of the effective field theory. We identify a particular case which leads to the action of hep-th/0512113 for a massive field living in a flat non-commutative space-time. The most general solutions lead to field theories with non-linear redefinitions of the momentum which we propose to interpret as living on curved space-times. We conclude by discussing the possible extension to four-dimensional spinfoam models.
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...
CP(N-1) Quantum Field Theories with Alkaline-Earth Atoms in Optical Lattices
Laflamme, C; Dalmonte, M; Gerber, U; Mejía-Díaz, H; Bietenholz, W; Wiese, U -J; Zoller, P
2015-01-01T23:59:59.000Z
We propose a cold atom implementation to attain the continuum limit of (1+1)-d CP(N-1) quantum field theories. These theories share important features with (3+1)-d QCD, such as asymptotic freedom and $\\theta$ vacua. Moreover, their continuum limit can be accessed via the mechanism of dimensional reduction. In our scheme, the CP(N-1) degrees of freedom emerge at low energies from a ladder system of SU(N) quantum spins, where the N spin states are embodied by the nuclear Zeeman states of alkaline-earth atoms, trapped in an optical lattice. Based on Monte Carlo results, we establish that the continuum limit can be demonstrated by an atomic quantum simulation by employing the feature of asymptotic freedom. We discuss a protocol for the adiabatic state preparation of the ground state of the system, the real-time evolution of a false $\\theta$-vacuum state after a quench, and we propose experiments to unravel the phase diagram at non-zero density.
CP(N-1) Quantum Field Theories with Alkaline-Earth Atoms in Optical Lattices
C. Laflamme; W. Evans; M. Dalmonte; U. Gerber; H. Mejía-Díaz; W. Bietenholz; U. -J. Wiese; P. Zoller
2015-07-24T23:59:59.000Z
We propose a cold atom implementation to attain the continuum limit of (1+1)-d CP(N-1) quantum field theories. These theories share important features with (3+1)-d QCD, such as asymptotic freedom and $\\theta$ vacua. Moreover, their continuum limit can be accessed via the mechanism of dimensional reduction. In our scheme, the CP(N-1) degrees of freedom emerge at low energies from a ladder system of SU(N) quantum spins, where the N spin states are embodied by the nuclear Zeeman states of alkaline-earth atoms, trapped in an optical lattice. Based on Monte Carlo results, we establish that the continuum limit can be demonstrated by an atomic quantum simulation by employing the feature of asymptotic freedom. We discuss a protocol for the adiabatic state preparation of the ground state of the system, the real-time evolution of a false $\\theta$-vacuum state after a quench, and we propose experiments to unravel the phase diagram at non-zero density.
Jain, Anubhav, Ph.D. Massachusetts Institute of Technology
2011-01-01T23:59:59.000Z
This thesis relates to the emerging field of high-throughput density functional theory (DFT) computation for materials design and optimization. Although highthroughput DFT is a promising new method for materials discovery, ...
Charge transport, configuration interaction and Rydberg states under density functional theory
Cheng, Chiao-Lun
2008-01-01T23:59:59.000Z
Density functional theory (DFT) is a computationally efficient formalism for studying electronic structure and dynamics. In this work, we develop DFT-based excited-state methods to study electron transport, Rydberg excited ...
Quantum Effects in Photosynthesis | MIT-Harvard Center for Excitonics
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
quantum information and theory of quantum computation; dynamics of open quantum systems; theory of decoherence; quantum control, quantum nanoscale systems, including trapped cold...
Negative energy densities in integrable quantum field theories at one-particle level
Bostelmann, Henning
2015-01-01T23:59:59.000Z
We study the phenomenon of negative energy densities in quantum field theories with self-interaction. Specifically, we consider a class of integrable models (including the sinh-Gordon model) in which we investigate the expectation value of the energy density in one-particle states. In this situation, we classify the possible form of the stress-energy tensor from first principles. We show that one-particle states with negative energy density generically exist in non-free situations, and we establish lower bounds for the energy density (quantum energy inequalities). Demanding that these inequalities hold reduces the ambiguity in the stress-energy tensor, in some situations fixing it uniquely. Numerical results for the lowest spectral value of the energy density allow us to demonstrate how negative energy densities depend on the coupling constant and on other model parameters.
Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
Zohar, Erez; Reznik, Benni
2015-01-01T23:59:59.000Z
Can high energy physics can be simulated by low-energy, nonrelativistic, many-body systems, such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in particular, they manifest neither local gauge invariance nor Lorentz invariance, which are crucial properties of the quantum field theories which are the building blocks of the standard model of elementary particles. However, it turns out, surprisingly, that there are ways to configure atomic system to manifest both local gauge invariance and Lorentz invariance. In particular, local gauge invariance can arise either as an effective, low energy, symmetry, or as an "exact" symmetry, following from the conservation laws in atomic interactions. Hence, one could hope that such quantum simulators may lead to new type of (table-top) experiments, that shall be used to study various QCD phenomena, as the con?nement of dynamical quarks, phase transitions, and other effects, which are inacc...
Negative energy densities in integrable quantum field theories at one-particle level
Henning Bostelmann; Daniela Cadamuro
2015-02-05T23:59:59.000Z
We study the phenomenon of negative energy densities in quantum field theories with self-interaction. Specifically, we consider a class of integrable models (including the sinh-Gordon model) in which we investigate the expectation value of the energy density in one-particle states. In this situation, we classify the possible form of the stress-energy tensor from first principles. We show that one-particle states with negative energy density generically exist in non-free situations, and we establish lower bounds for the energy density (quantum energy inequalities). Demanding that these inequalities hold reduces the ambiguity in the stress-energy tensor, in some situations fixing it uniquely. Numerical results for the lowest spectral value of the energy density allow us to demonstrate how negative energy densities depend on the coupling constant and on other model parameters.
6-dimensional Kaluza-Klein Theory for Basic Quantum Particles and Electron-Photon Interaction
Xiaodong Chen
2005-01-26T23:59:59.000Z
By extending original Kaluza-Klein theory to 6-dimension, the basic quantum field equations for 0-spin particle, 1-spin particle and 1/2 spin particle with mass >0 are directly derived from 6-dimensional Einstein equations. It shows that the current quantum field equations of basic particles become pure geometry properties under 6-dimension time-space. The field equations of electron and photon can be unified in one 6-dimensional extended Maxwell equation. The equations containing interactions between electron and photon will be derived from Einstein equation under 6-dimension time-space. It shows that the interactions in QED can be considered as the effect of local geometry curvature changing instead of exchange virtual photons.
Bjřrnstad, Ottar Nordal
Stability of titanium oxide phases in Kohn-Sham density functional theory A well known problem of stability of titanium oxide phases at room temperature. That is, anatase instead of rutile is predicted as the room temperature phase for titanium oxide. In this work we try to establish the reasons
Commutativity of Substitution and Variation in Actions of Quantum Field Theory
Zhong Chao Wu
2009-11-11T23:59:59.000Z
There exists a paradox in quantum field theory: substituting a field configuration which solves a subset of the field equations into the action and varying it is not necessarily equivalent to substituting that configuration into the remaining field equations. We take the $S^4$ and Freund-Rubin-like instantons as two examples to clarify the paradox. One must match the specialized configuration field variables with the corresponding boundary conditions by adding appropriate Legendre terms to the action. Some comments are made regarding exceptional degenerate cases.
Instantaneous measurements of nonlocal variables in relativistic quantum theory (a review)
Matthew J. Lake
2015-05-17T23:59:59.000Z
This article reviews six historically important papers in the development of the theory of measurement for nonlocal variables in quantum mechanics, with special emphasis the non violation of relativistic causality. Spanning more than seventy years, we chart the major developments in the field from the declaration, by Landau and Peierls in 1931, that measurement of nonlocal variables was impossible in the relativistic regime to the demonstration, by Vaidman in 2003, that all such variables \\emph{can} be measured instantaneously without violation of causality through an appropriate act of "measurement", albeit not of a standard projective (Von Neumann) type.
Cosmological Constant as Vacuum Energy Density of Quantum Field Theories on Noncommutative Spacetime
Xiao-Jun Wang
2004-12-15T23:59:59.000Z
We propose a new approach to understand hierarchy problem for cosmological constant in terms of considering noncommutative nature of space-time. We calculate that vacuum energy density of the noncommutative quantum field theories in nontrivial background, which admits a smaller cosmological constant by introducing an higher noncommutative scale $\\mu_{NC}\\sim M_p$. The result $\\rho_\\Lambda\\sim 10^{-6}\\Lambda_{SUSY}^8M_p^4/\\mu_{NC}^8$ yields cosmological constant at the order of current observed value for supersymmetry breaking scale at 10TeV. It is the same as Banks' phenomenological formula for cosmological constant.
Quantum theory of a two-mode open-cavity laser
V. Eremeev; S. E. Skipetrov; M. Orszag
2011-08-25T23:59:59.000Z
We develop the quantum theory of an open-cavity laser assuming that only two modes compete for gain. We show that the modes interact to build up a collective mode that becomes the lasing mode when pumping exceeds a threshold. This collective mode exhibits all the features of a typical laser mode, whereas its precise behavior depends explicitly on the openness of the cavity. We approach the problem by using the density-matrix formalism and derive the master equation for the light field. Our results are of particular interest in the context random laser systems.
Dynamics of Thermal Effects in the Spin-Wave Theory of Quantum Antiferromagnets
Ángel Rivas; Miguel A. Martin-Delgado
2013-01-17T23:59:59.000Z
We derive a master equation that allows us to study non-equilibrium dynamics of a quantum antiferromagnet. By resorting to spin-wave theory, we obtain a closed analytic form for the magnon decay rates. These turn out to be closely related to form factors, which are experimentally accessible by means of neutron and Raman scattering. Furthermore, we compute the time evolution of the staggered magnetization showing that, for moderate temperatures, the magnetic order is not spoiled even if the coupling is fully isotropic.
String/Quantum Gravity motivated Uncertainty Relations and Regularisation in Field Theory
Achim Kempf
1996-12-08T23:59:59.000Z
The possibility of the existence of small correction terms to the canonical commutation relations and the uncertainty relations has recently found renewed interest. In particular, such correction terms could induce finite lower bounds $\\Delta x_0, \\Delta p_0$ to the resolution of distances and/or momenta. I review a general framework for the path integral formulation of quantum field theories on such generalised geometries, and focus then on the mechanisms by which $\\Delta p_0>0$, and/or $\\Delta x_0>0$ lead to IR and/or UV regularisation.
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.
Mishchenko, Yuriy
2004-12-01T23:59:59.000Z
MISHCHENKO, YURIY. Applications of Canonical Transformations and Nontrivial Vacuum Solutions to flavor mixing and critical phenomena in Quantum Field Theory. (Under the direction of Chueng-Ryong Ji.) In this dissertation we consider two recent applications of Bogoliubov Transformation to the phenomenology of quantum mixing and the theory of critical phenomena. In recent years quantum mixing got in the focus of the searches for New Physics due to its unparalleled sensitivity to SM parameters and indications of neutrino mixing. It was recently suggested that Bogoliubov Transformation may be important in proper definition of the flavor states that otherwise results in problems in perturbative treatment. As first part of this dissertation we investigate this conjecture and develop a complete formulation of such a mixing field theory involving introduction of general formalism, analysis of space-time conversion and phenomenological implications. As second part of this dissertati
The Computational Status of Physics: A Computable Formulation of Quantum Theory
Mike Stannett
2008-11-10T23:59:59.000Z
According to the Church-Turing Thesis (CTT), effective formal behaviours can be simulated by Turing machines; this has naturally led to speculation that physical systems can also be simulated computationally. But is this wider claim true, or do behaviours exist which are strictly hypercomputational? Several idealised computational models are known which suggest the possibility of hypercomputation, some Newtonian, some based on cosmology, some on quantum theory. While these models' physicality is debatable, they nonetheless throw into question the validity of extending CTT to include all physical systems. We consider the physicality of hypercomputational behaviour from first principles, by showing that quantum theory can be reformulated in a way that explains why physical behaviours can be regarded as 'computing something' in the standard computational state-machine sense. While this does not rule out the physicality of hypercomputation, it strongly limits the forms it can take. Our model also has physical consequences; in particular, the continuity of motion and arrow of time become theorems within the basic model.
Manfred Requardt
2004-03-17T23:59:59.000Z
We amalgamate three seemingly quite different fields of concepts and phenomena and argue that they actually represent closely related aspects of a more primordial space-time structure called by us wormhole spaces. Connes' framework of non-commutative topological spaces and ``points, speaking to each other'', a translocal web of (cor)relations, being hidden in the depth-structure of our macroscopic space-time and made visible by the application of a new geometric renormalisation process, and the apparent but difficult to understand translocal features of quantum theory. We argue that the conception of our space-time continuum as being basically an aggregate of structureless points is almost surely to poor and has to be extended and that the conceptual structure of quantum theory, in particular its translocal features like e.g. entanglement and complex superposition, are exactly a mesoscopic consequence of this microscopic wormhole structure. We emphasize the close connections with the ``small world phenomenon'' and rigorously show that the micro state of our space-time, viewed as a dynamical system, has to be critical in a scale free way as recently observed in other fields of network science. We then briefly indicate the mechanisms by which this non-local structure manages to appear in a seemingly local disguise on the surface level, thus invoking a certain Machian spirit.
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.
The Slicing Theory of Quantum Measurement: Derivation of Transient Many Worlds Behavior
Clifford Chafin
2015-03-01T23:59:59.000Z
An emergent theory of quantum measurement arises directly by considering the particular subset of many body wavefunctions that can be associated with classical condensed matter and its interaction with delocalized wavefunctions. This transfers questions of the "strangeness" of quantum mechanics from the wavefunction to the macroscopic material itself. An effectively many-worlds picture of measurement results for long times and induces a natural arrow of time. The challenging part is then justifying why our macroscopic world is dominated by such far-from-eigenstate matter. Condensing cold mesoscopic clusters provide a pathway to a partitioning of a highly correlated many body wavefunction to long lasting islands composed of classical-like bodies widely separated in Fock space. Low mass rapidly delocalizing matter that recombines with the solids "slice" the system into a set of nearby yet very weakly interacting subsystems weighted according to the Born statistics and yields a kind of many worlds picture but with the possibility of revived phase interference on iterative particle desorption, delocalization and readsorption. A proliferation of low energy photons competes with such a possibility. Causality problems associated with correlated quantum measurement are resolved and conserved quantities are preserved for the overall many body function despite their failure in each observer's bifurcating "slice-path." The necessity of such a state for a two state logic and reliable discrete state machine suggests that later stages of the universe's evolution will destroy the physical underpinnings required for consciousness and the arrow of time even without heat-death or atomic destruction. Some exotic possibilities outside the domain of usual quantum measurement are considered such as measurement with delocalized devices and revival of information from past measurements.
Exact results in N=8 Chern-Simons-matter theories and quantum geometry
Santiago Codesido; Alba Grassi; Marcos Marino
2015-06-25T23:59:59.000Z
We show that, in ABJ(M) theories with N=8 supersymmetry, the non-perturbative sector of the partition function on the three-sphere simplifies drastically. Due to this simplification, we are able to write closed form expressions for the grand potential of these theories, which determines the full large N asymptotics. Moreover, we find explicit formulae for the generating functionals of their partition functions, for all values of the rank N of the gauge group: they involve Jacobi theta functions on the spectral curve associated to the planar limit. Exact quantization conditions for the spectral problem of the Fermi gas are then obtained from the vanishing of the theta function. We also show that the partition function, as a function of N, can be extended in a natural way to an entire function on the full complex plane, and we explore some possible consequences of this fact for the quantum geometry of M-theory and for putative de Sitter extensions.
Peter Degenfeld-Schonburg; Carlos Navarrete-Benlloch; Michael J. Hartmann
2015-03-11T23:59:59.000Z
Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. In this article we apply the recently developed self-consistent projection operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.
Diffeomorphism invariant Quantum Field Theories of Connections in terms of webs
Jerzy Lewandowski; Thomas Thiemann
1999-01-07T23:59:59.000Z
In the canonical quantization of gravity in terms of the Ashtekar variables one uses paths in the 3-space to construct the quantum states. Usually, one restricts oneself to families of paths admitting only finite number of isolated intersections. This assumption implies a limitation on the diffeomorphisms invariance of the introduced structures. In this work, using the previous results of Baez and Sawin, we extend the existing results to a theory admitting all the possible piecewise smooth finite paths and loops. In particular, we $(i)$ characterize the spectrum of the Ashtekar-Isham configuration space, $(ii)$ introduce spin-web states, a generalization of the spin-network states, $(iii)$ extend the diffeomorphism averaging to the spin-web states and derive a large class of diffeomorphism invariant states and finally $(iv)$ extend the 3-geometry operators and the Hamiltonian operator.
One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts
Ellis, R. Keith [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Kunszt, Zoltan [Institute for Theoretical Physics (Switzerland); Melnikov, Kirill [Johns Hopkins Univ., Baltimore, MD (United States); Zanderighi, Giulia [Rudolf Peierls Centre for Theoretical Physics (United Kingdom)
2012-09-01T23:59:59.000Z
The success of the experimental program at the Tevatron re-inforced the idea that precision physics at hadron colliders is desirable and, indeed, possible. The Tevatron data strongly suggests that one-loop computations in QCD describe hard scattering well. Extrapolating this observation to the LHC, we conclude that knowledge of many short-distance processes at next-to-leading order may be required to describe the physics of hard scattering. While the field of one-loop computations is quite mature, parton multiplicities in hard LHC events are so high that traditional computational techniques become inefficient. Recently new approaches based on unitarity have been developed for calculating one-loop scattering amplitudes in quantum field theory. These methods are especially suitable for the description of multi-particle processes in QCD and are amenable to numerical implementations. We present a systematic pedagogical description of both conceptual and technical aspects of the new methods.
Silvestrelli, Pier Luigi; Ambrosetti, Alberto [Dipartimento di Fisica e Astronomia, Universitŕ di Padova, via Marzolo 8, I–35131 Padova, Italy and DEMOCRITOS National Simulation Center of the Italian Istituto Officina dei Materiali (IOM) of the Italian National Research Council (CNR), Trieste (Italy)] [Dipartimento di Fisica e Astronomia, Universitŕ di Padova, via Marzolo 8, I–35131 Padova, Italy and DEMOCRITOS National Simulation Center of the Italian Istituto Officina dei Materiali (IOM) of the Italian National Research Council (CNR), Trieste (Italy)
2014-03-28T23:59:59.000Z
The Density Functional Theory (DFT)/van der Waals-Quantum Harmonic Oscillator-Wannier function (vdW-QHO-WF) method, recently developed to include the vdW interactions in approximated DFT by combining the quantum harmonic oscillator model with the maximally localized Wannier function technique, is applied to the cases of atoms and small molecules (X=Ar, CO, H{sub 2}, H{sub 2}O) weakly interacting with benzene and with the ideal planar graphene surface. Comparison is also presented with the results obtained by other DFT vdW-corrected schemes, including PBE+D, vdW-DF, vdW-DF2, rVV10, and by the simpler Local Density Approximation (LDA) and semilocal generalized gradient approximation approaches. While for the X-benzene systems all the considered vdW-corrected schemes perform reasonably well, it turns out that an accurate description of the X-graphene interaction requires a proper treatment of many-body contributions and of short-range screening effects, as demonstrated by adopting an improved version of the DFT/vdW-QHO-WF method. We also comment on the widespread attitude of relying on LDA to get a rough description of weakly interacting systems.
Fedor Herbut
2014-12-25T23:59:59.000Z
A detailed theory of quantum premeasurement dynamics is presented in which a unitary composite-system operator that contains the relevant object-measuring-instrument interaction brings about the final premeasurement state. It does not include collapse, and it does not consider the environment. It is assumed that a discrete degenerate or non-degenerate observable is measured. Premeasurement is defined by the calibration condition, which requires that every initially statistically sharp value of the measured observable has to be detected with statistical certainty by the measuring instrument. The entire theory is derived as a logical consequence of this definition using the standard quantum formalism. The study has a comprehensive coverage, hence the article is actually a topical review. Connection is made with results of other authors, particularly with basic works on premeasurement. The article is a conceptual review, not a historical one. General exact premeasurement is defined in 7 equivalent ways. Nondemolition premeasurement, defined by requiring preservation of any sharp value of the measured observable, is characterized in 10 equivalent ways. Overmeasurement, i. e., a process in which the observable is measured on account of being a function of a finer observable that is actually measured, is discussed. Disentangled premeasurement, in which, by definition, to each result corresponds only one pointer-observable state in the final composite-system state, is investigated. Ideal premeasurement, a special case of both nondemolition premeasurement and disentangled premeasurement, is defined, and its most important properties are discussed. Finally, disentangled and entangled premeasurements, in conjunction with nondemolition or demolition premeasurements, are used for classification of all premeasurements.
Yeo, Sang Chul
Ammonia (NH[subscript 3]) nitridation on an Fe surface was studied by combining density functional theory (DFT) and kinetic Monte Carlo (kMC) calculations. A DFT calculation was performed to obtain the energy barriers ...
Engineering of Quantum Hall Effect from Type IIA String Theory on The K3 Surface
Adil Belhaj; Antonio Segui
2010-07-02T23:59:59.000Z
Using D-brane configurations on the K3 surface, we give six dimensional type IIA stringy realizations of the Quantum Hall Effect (QHE) in 1+2 dimensions. Based on the vertical and horizontal lines of the K3 Hodge diamond, we engineer two different stringy realizations. The vertical line presents a realization in terms of D2 and D6-branes wrapping the K3 surface. The horizontal one is associated with hierarchical stringy descriptions obtained from a quiver gauge theory living on a stack of D4-branes wrapping intersecting 2-spheres embedded in the K3 surface with deformed singularities. These geometries are classified by three kinds of the Kac-Moody algebras: ordinary, i.e finite dimensional, affine and indefinite. We find that no stringy QHE in 1+2 dimensions can occur in the quiver gauge theory living on intersecting 2-spheres arranged as affine Dynkin diagrams. Stringy realizations of QHE can be done only for the finite and indefinite geometries. In particular, the finite Lie algebras give models with fractional filling fractions, while the indefinite ones classify models with negative filling fractions which can be associated with the physics of holes in the graphene.
Bohr - Planck quantum theory, (Tesla) magnetic monopoles and fine structure constant
Vladan Pankovic; Darko V. Kapor; Stevica Djurovic; Miodrag Krmar
2014-10-17T23:59:59.000Z
In this work we apply Bohr-Planck (Old quantum atomic and radiation) theory, i.e. and quasi-classical methods for analysis of the magnetic monopoles and other problems. We reproduce exactly some basic elements of the Dirac magnetic monopoles theory, especially Dirac electric/magnetic charge quantization condition. Also, we suggest a new, effective, simply called Tesla model (for analogy with positions of the solenoids by Tesla inductive motor) of the magnetic monopole instead of usual effective Dirac model (half-infinite, very tinny solenoid) of the magnetic monopole. In our, i.e. Tesla model we use three equivalent tiny solenoids connected in series with a voltage source. One end of any solenoid is placed at the circumference of a circle and solenoids are directed radial toward circle center. Length of any solenoid is a bit smaller than finite circle radius so that other end of any solenoid is very close to the circle center. Angles between neighboring solenoids equal $120^{\\circ}$. All this implies that, practically, there is no magnetic field, or, magnetic pole, e.g. $S$, in the circle center, and that whole system holds only other, $N$ magnetic pole, at the ends of the solenoids at circle circumference. Finally, we reproduce relatively satisfactory value of the fine structure constant using Planck, i.e. Bose-Einstein statistics and Wien displacement law.
A Non-Riemannian Metric on Space-Time Emergent From Scalar Quantum Field Theory
Kar, Arnab
2012-01-01T23:59:59.000Z
We show that the standard deviation \\sigma(x,x') = \\sqrt{} of a scalar quantum field theory is a metric (i.e., a symmetric positive function satisfying the triangle inequality) on space-time (with imaginary time). It is very different from the Euclidean metric |x-x'|: for four dimensional free scalar field theory, \\sigma(x,x') \\to \\frac{\\sigma_{4}}{a^{2}} -\\frac{\\sigma_{4}'}{|x-x'|^{2}} + \\mathrm{O}(|x-x'|^{-3}), as |x-x'|\\to\\infty. According to \\sigma, space-time has a finite diameter \\frac{\\sigma_{4}}{a^{2}} which is not universal (i.e., depends on the UV cut-off a and the regularization method used). The Lipschitz equivalence class of the metric is independent of the cut-off. \\sigma(x,x') is not the length of the geodesic in any Riemannian metric, as it does not have the intermediate point property: for a pair (x,x') there is in general no point x" such that \\sigma(x,x')=\\sigma(x,x")+\\sigma(x",x'). Nevertheless, it is possible to embed space-time in a higher dimensional space of negative curvature so that ...
Ooi, C. H. Raymond; Beadie, G.; Kattawar, George W.; Reintjes, J. F.; Rostovtsev, Y.; Zubairy, M. Suhail; Scully, Marlan O.
2005-01-01T23:59:59.000Z
Theory of femtosecond coherent anti-Stokes Raman backscattering enhanced by quantum coherence for standoff detection of bacterial spores C. H. Raymond Ooi,1,2 Guy Beadie,3 George W. Kattawar,2 John F. Reintjes,3 Yuri Rostovtsev,1,2 M. Suhail... Zubairy,2 and Marlan O. Scully1,2 1Princeton Institute for Science of Materials and Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544-1009, USA 2Institute for Quantum Studies and Department of Physics...
Krishtal, Alisa; Genova, Alessandro; Pavanello, Michele
2015-01-01T23:59:59.000Z
Subsystem Density-Functional Theory (DFT) is an emerging technique for calculating the electronic structure of complex molecular and condensed phase systems. In this topical review, we focus on some recent advances in this field related to the computation of condensed phase systems, their excited states, and the evaluation of many-body interactions between the subsystems. As subsystem DFT is in principle an exact theory, any advance in this field can have a dual role. One is the possible applicability of a resulting method in practical calculations. The other is the possibility of shedding light on some quantum-mechanical phenomenon which is more easily treated by subdividing a supersystem into subsystems. An example of the latter is many-body interactions. In the discussion, we present some recent work from our research group as well as some new results, casting them in the current state-of-the-art in this review as comprehensively as possible.
On Conformal Field Theory and Number Theory
Huang, An
2011-01-01T23:59:59.000Z
Frontiers in Number Theory, Physics, and Ge- ometry II. (Witten, Quantum Field Theory, Crassmannians, and AlgebraicJ. Polchinski, String Theory, Vol. 1, Cambridge Univ.
Alfredo Iorio; Gaetano Lambiase
2014-12-15T23:59:59.000Z
The solutions of many issues, of the ongoing efforts to make deformed graphene a tabletop quantum field theory in curved spacetimes, are presented. A detailed explanation of the special features of curved spacetimes, originating from embedding portions of the Lobachevsky plane into $\\mathbf{R}^3$, is given, and the special role of coordinates for the physical realizations in graphene, is explicitly shown, in general, and for various examples. The Rindler spacetime is reobtained, with new important differences with respect to earlier results. The de Sitter spacetime naturally emerges, for the first time, paving the way to future applications in cosmology. The role of the BTZ black hole is also briefly addressed. The singular boundary of the pseudospheres, "Hilbert horizon", is seen to be closely related to event horizon of the Rindler, de Sitter, and BTZ kind. This gives new, and stronger, arguments for the Hawking phenomenon to take place. An important geometric parameter, $c$, overlooked in earlier work, takes here its place for physical applications, and it is shown to be related to graphene's lattice spacing, $\\ell$. It is shown that all surfaces of constant negative curvature, ${\\cal K} = -r^{-2}$, are unified, in the limit $c/r \\to 0$, where they are locally applicable to the Beltrami pseudosphere. This, and $c = \\ell$, allow us a) to have a phenomenological control on the reaching of the horizon; b) to use spacetimes different than Rindler for the Hawking phenomenon; c) to approach the generic surface of the family. An improved expression for the thermal LDOS is obtained. A non-thermal term for the total LDOS is found. It takes into account: a) the peculiarities of the graphene-based Rindler spacetime; b) the finiteness of a laboratory surface; c) the optimal use of the Minkowski quantum vacuum, through the choice of this Minkowski-static boundary.
Foukzon, Jaykov
2008-01-01T23:59:59.000Z
Advanced numerical-analytical study of the three-dimensional nonlinear stochastic partial differential equation, analogous to that proposed by V. N. Nikolaevski to describe longitudinal seismic waves, is presented. The equation has a threshold of short-wave instability and symmetry, providing long-wave dynamics. Proposed new mechanism for quantum "super chaos" generating in nonlinear dynamical systems. The hypothesis is said, that strong physical turbulence could be identified with quantum chaos of considered type.
Michele Allegra; Paolo Giorda; Seth Lloyd
2015-03-18T23:59:59.000Z
In this paper we address the problem of charaterizing coherence in dissipative (Markovian) quantum evolutions. We base our analysis on the decoherent histories formalism which is the most basic and proper approach to assess coherence properties of quantum evolutions. We introduce and test different quantifiers and we show how these are able to capture the (average) coherence of general quantum evolutions on various time scales and for different levels of environmentally induced decoherence. In order to show the effectiveness of the introduced tools, we thoroughly apply them to a paradigmatic instance of quantum process where the role of coherence is being hotly debated: exciton transport in the FMO photosynthetic complex and its most relevant trimeric subunit. Our analysis illustrates how the high efficiency of environmentally assisted transport can be traced back to the coherence properties of the evolution and the interference between pathways in the decoherent histories formalism. Indeed, we show that the bath essentially implements a quantum recoil avoiding effect on the exciton dynamics: the action of decoherence in the system is set at precisely the right level needed to preserve and sustain the benefits of the fast initial quantum delocalization of the exciton over the network, while preventing the subsequent recoil that would necessarily follow form a purely coherent dynamics. This picture becomes very clear when expressed in terms of pathways leading to the exit site: the action of the bath is seen to selectively kill the negative interference between pathways, while retaining the intial positive one.
Temperature Dependent Magnon-Phonon Coupling in bcc Fe from Theory and Experiment
Tai, Yu-Chong
- actions in bcc Fe. Parameter-free electronic structure calculations like den- sity functional theory (DFT moments (DLM) molecular dynamics [1], magnetic empirical poten- tials [2
Olivier Coquand; Bruno Machet
2014-07-08T23:59:59.000Z
1-loop quantum corrections are shown to induce large effects on the refraction index n inside a graphene strip in the presence of an external magnetic field B orthogonal to it. To this purpose, we use the tools of Quantum Field Theory to calculate the photon propagator at 1-loop inside graphene in position space, which leads to an effective vacuum polarization in a brane-like theory of photons interacting with massless electrons at locations confined inside the thin strip (its longitudinal spread is considered to be infinite). The effects factorize into quantum ones, controlled by the value of B and that of the electromagnetic coupling alpha, and a "transmittance function" U in which the geometry of the sample and the resulting confinement of electrons play the major roles. We consider photons inside the visible spectrum and magnetic fields in the range 1-20 Teslas. At B=0, quantum effects depend very weakly on alpha and n is essentially controlled by U; we recover, then, an opacity for visible light of the same order of magnitude pi * alpha_{vac} as measured experimentally.
Hazra, Jisha; Balakrishnan, N; Bohn, John L
2014-01-01T23:59:59.000Z
Multichannel quantum defect theory (MQDT) has been widely applied to resonant and non-resonant scattering in a variety of atomic collision processes. In recent years, the method has been applied to cold collisions with considerable success, and it has proven to be a computationally viable alternative to full-close coupling (CC) calculations when spin, hyperfine and external field effects are included. In this paper, we describe a hybrid approach for molecule-molecule scattering that includes the simplicity of MQDT while treating the short-range interaction explicitly using CC calculations. This hybrid approach, demonstrated for H$_2$-H$_2$ collisions in full-dimensionality, is shown to adequately reproduce cross sections for quasi-resonant rotational and vibrational transitions in the ultracold (1$\\mu$K) and $\\sim$ 1-10 K regime spanning seven orders of magnitude. It is further shown that an energy-independent short-range $K$-matrix evaluated in the ultracold regime (1$\\mu$K) can adequately characterize cross...
Ooi, C. H. Raymond; Sun, Qingqing; Zubairy, M. Suhail; Scully, Marlan O.
2007-01-01T23:59:59.000Z
Publisher?s Note: Correlation of photon pairs from the double Raman amplifier: Generalized analytical quantum Langevin theory [Phys. Rev. A 75, 013820 (2007)] C. H. Raymond Ooi, Qingqing Sun, M. Suhail Zubairy, and Marlan O. Scully #1;Received 1...
Quantum Signatures of Spacetime Graininess Quantum Signatures of Spacetime
Quantum Field Theory on Noncommutative Spacetime Implementing Poincaré Symmetry Hopf Algebras, Drinfel Quantum Mechanics on Noncommutative Spacetime 4 Quantum Field Theory on Noncommutative Spacetime Covariant Derivatives and Field Strength Noncommutative Gauge Theories 6 Signatures of Spin
Asplund, Erik; Kluener, Thorsten [Institut fuer Reine und Angewandte Chemie, Carl von Ossietzky Universitaet Oldenburg, Postfach 2503, D-26111 Oldenburg (Germany)
2012-03-28T23:59:59.000Z
In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate Hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate Hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ({Dirac_h}/2{pi})=m{sub e}=e=a{sub 0}= 1, have been used unless otherwise stated.
Oshmyansky, A
2007-01-01T23:59:59.000Z
An alternative quantum field theory for gravity is proposed for low energies based on an attractive effect between contaminants in a Bose-Einstein Condensate rather than on particle exchange. In the ``contaminant in condensate effect," contaminants cause a potential in an otherwise uniform condensate, forcing the condensate between two contaminants to a higher energy state. The energy of the system decreases as the contaminants come closer together, causing an attractive force between contaminants. It is proposed that mass-energy may have a similar effect on Einstein's space-time field, and gravity is quantized by the same method by which the contaminant in condensate effect is quantized. The resulting theory is finite and, if a physical condensate is assumed to underly the system, predictive. However, the proposed theory has several flaws at high energies and is thus limited to low energies. Falsifiable predictions are given for the case that the Higgs condensate is assumed to be the condensate underlying gr...
Alexander Oshmyansky
2007-03-08T23:59:59.000Z
An alternative quantum field theory for gravity is proposed for low energies based on an attractive effect between contaminants in a Bose-Einstein Condensate rather than on particle exchange. In the ``contaminant in condensate effect," contaminants cause a potential in an otherwise uniform condensate, forcing the condensate between two contaminants to a higher energy state. The energy of the system decreases as the contaminants come closer together, causing an attractive force between contaminants. It is proposed that mass-energy may have a similar effect on Einstein's space-time field, and gravity is quantized by the same method by which the contaminant in condensate effect is quantized. The resulting theory is finite and, if a physical condensate is assumed to underly the system, predictive. However, the proposed theory has several flaws at high energies and is thus limited to low energies. Falsifiable predictions are given for the case that the Higgs condensate is assumed to be the condensate underlying gravity.
Pair production in a strong electric field: an initial value problem in quantum field theory
Y. Kluger; J. M. Eisenberg; B. Svetitsky
2003-11-23T23:59:59.000Z
We review recent achievements in the solution of the initial-value problem for quantum back-reaction in scalar and spinor QED. The problem is formulated and solved in the semiclassical mean-field approximation for a homogeneous, time-dependent electric field. Our primary motivation in examining back-reaction has to do with applications to theoretical models of production of the quark-gluon plasma, though we here address practicable solutions for back-reaction in general. We review the application of the method of adiabatic regularization to the Klein-Gordon and Dirac fields in order to renormalize the expectation value of the current and derive a finite coupled set of ordinary differential equations for the time evolution of the system. Three time scales are involved in the problem and therefore caution is needed to achieve numerical stability for this system. Several physical features, like plasma oscillations and plateaus in the current, appear in the solution. From the plateau of the electric current one can estimate the number of pairs before the onset of plasma oscillations, while the plasma oscillations themselves yield the number of particles from the plasma frequency. We compare the field-theory solution to a simple model based on a relativistic Boltzmann-Vlasov equation, with a particle production source term inferred from the Schwinger particle creation rate and a Pauli-blocking (or Bose-enhancement) factor. This model reproduces very well the time behavior of the electric field and the creation rate of charged pairs of the semiclassical calculation. It therefore provides a simple intuitive understanding of the nature of the solution since nearly all the physical features can be expressed in terms of the classical distribution function.
Boyer, Edmond
case in which coupled cluster theory is used to obtain the density and excitation energies for benchmark and highly accurate studies, they are still too demanding for standard applications. Another
Agung Trisetyarso
2014-11-23T23:59:59.000Z
We present the recent works \\cite{trisetyarso2011} on the application of Darboux transformation on one-dimensional Dirac equation related to the field of Quantum Information and Computation (QIC). The representation of physical system in one-dimensional equation and its transformation due to the Bagrov, Baldiotti, Gitman, and Shamshutdinova (BBGS)-Darboux transformation showing the possibility admitting the concept of relativity and the trade-off of concurrent condition of quantum and classical physics play into the area of QIC. The applications in cavity quantum electrodynamics and on the proposal of quantum transistor are presented.
Error Analysis in Nuclear Density Functional Theory
Nicolas Schunck; Jordan D. McDonnell; Jason Sarich; Stefan M. Wild; Dave Higdon
2014-07-11T23:59:59.000Z
Nuclear density functional theory (DFT) is the only microscopic, global approach to the structure of atomic nuclei. It is used in numerous applications, from determining the limits of stability to gaining a deep understanding of the formation of elements in the universe or the mechanisms that power stars and reactors. The predictive power of the theory depends on the amount of physics embedded in the energy density functional as well as on efficient ways to determine a small number of free parameters and solve the DFT equations. In this article, we discuss the various sources of uncertainties and errors encountered in DFT and possible methods to quantify these uncertainties in a rigorous manner.
Photodissociation in quantum chaotic systems: Random-matrix theory of cross-section fluctuations
Fyodorov, Y.V. [Fachbereich Physik, Universitaet-GH Essen, D-45117 Essen (Germany)] [Fachbereich Physik, Universitaet-GH Essen, D-45117 Essen (Germany); Alhassid, Y. [Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520 (United States)] [Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520 (United States)
1998-11-01T23:59:59.000Z
Using the random matrix description of open quantum chaotic systems we calculate in closed form the universal autocorrelation function and the probability distribution of the total photodissociation cross section in the regime of quantum chaos. {copyright} {ital 1998} {ital The American Physical Society}
Ye, Peng
2015-01-01T23:59:59.000Z
Topological quantum field theory (TQFT) plays a very important role in understanding topological phases of quantum matter. For example, Chern-Simons theory reveals the key mechanism of charge-flux attachment for fractional quantum hall effect (FQHE). It also completely describes all the essential topological data, e.g., fractionalized statistics, fractionalized charge of quasiparticles in FQHE sytems. Very recently, a new class of topological phases -- symmetry-protected topological (SPT) phases in interacting bosonic systems has been proposed based on the (extended) group cohomology theory. In two dimensions, it has been shown that bosonic SPT phases with Abelian symmetry can be well understood in terms of Chern-Simons theory. In this paper, we attempt to achieve a complete TQFT description for all bosonic SPT phases with Abelian group symmetry in three dimensions. The TQFT description reveals the key mechanism for three dimensional bosonic SPT phases in a simple and intuitive way.
Ronnie Kosloff
2013-05-10T23:59:59.000Z
Quantum thermodynamics addresses the emergence of thermodynamical laws from quantum mechanics. The link is based on the intimate connection of quantum thermodynamics with the theory of open quantum systems. Quantum mechanics inserts dynamics into thermodynamics giving a sound foundation to finite-time-thermodynamics. The emergence of the 0-law I-law II-law and III-law of thermodynamics from quantum considerations is presented. The emphasis is on consistence between the two theories which address the same subject from different foundations. We claim that inconsistency is the result of faulty analysis pointing to flaws in approximations.
Tureanu, Anca [High Energy Physics Division, Department of Physical Sciences, University of Helsinki and Helsinki Institute of Physics, P.O. Box 64, FIN-00014 Helsinki (Finland)
2006-09-15T23:59:59.000Z
In the framework of quantum field theory on noncommutative space-time with the symmetry group O(1,1)xSO(2), we prove that the Jost-Lehmann-Dyson representation, based on the causality condition taken in connection with this symmetry, leads to the mere impossibility of drawing any conclusion on the analyticity of the 2{yields}2-scattering amplitude in cos {theta}, {theta} being the scattering angle. Discussions on the possible ways of obtaining high-energy bounds analogous to the Froissart-Martin bound on the total cross section are also presented.
Application of quantum theory of electrons to the mechanical and thermal properties of metals
Peng, Hwan-Wu
The first successful application of quantum mechanics to the problem of metallic cohesion was made by Wigner and Seitz (1938) They appoximated sodium metal by a number of isolated spheres of equal atomic volume and integrated, ...
The study of Lorenz and Rössler strange attractors by means of quantum theory
Yu. I. Bogdanov; N. A. Bogdanova
2014-12-28T23:59:59.000Z
We have developed a method for complementing an arbitrary classical dynamical system to a quantum system using the Lorenz and R\\"ossler systems as examples. The Schr\\"odinger equation for the corresponding quantum statistical ensemble is described in terms of the Hamilton-Jacobi formalism. We consider both the original dynamical system in the position space and the conjugate dynamical system corresponding to the momentum space. Such simultaneous consideration of mutually complementary position and momentum frameworks provides a deeper understanding of the nature of chaotic behavior in dynamical systems. We have shown that the new formalism provides a significant simplification of the Lyapunov exponents calculations. From the point of view of quantum optics, the Lorenz and R\\"ossler systems correspond to three modes of a quantized electromagnetic field in a medium with cubic nonlinearity. From the computational point of view, the new formalism provides a basis for the analysis of complex dynamical systems using quantum computers.
Minton, Gregory; Sahakian, Vatche [Harvey Mudd College, Physics Department, 241 Platt Boulevard, Claremont, California 91711 (United States)
2008-01-15T23:59:59.000Z
Puff field theories (PFT) arise as the decoupling limits of D3 branes in a Melvin universe and exhibit spatially nonlocal dynamics. Unlike other realizations of nonlocality in string theory, PFTs have full SO(3) rotational symmetry. In this work, we analyze the strongly coupled regime of a PFT through gravitational holography. We find a novel mechanism at the heart of the phenomenon of nonlocality: a quantum entanglement of UV and IR dynamics. In the holographic bulk, this translates to an apparent horizon splitting the space into two regions--with the UV completion of the PFT sitting at the horizon. We unravel this intricate UV-IR setting and devise a prescription for computing correlators that extends the original dictionary of holographic renormalization group. We then implement a cosmological scenario where PFT correlators set the initial conditions for primordial fluctuations. We compute the associated power spectrum of the cosmic microwave background and find that the scenario allows for a distinct stringy signature.
Unitarity bounds and RG flows in time dependent quantum field theory
Xi Dong; Bart Horn; Eva Silverstein; Gonzalo Torroba
2012-03-08T23:59:59.000Z
We generalize unitarity bounds on operator dimensions in conformal field theory to field theories with spacetime dependent couplings. Below the energy scale of spacetime variation of the couplings, their evolution can strongly affect the physics, effectively shifting the infrared operator scaling and unitarity bounds determined from correlation functions in the theory. We analyze this explicitly for large-$N$ double-trace flows, and connect these to UV complete field theories. One motivating class of examples comes from our previous work on FRW holography, where this effect explains the range of flavors allowed in the dual, time dependent, field theory.
Unitarity Bounds and RG Flows in Time Dependent Quantum Field Theory
Dong, Xi; Horn, Bart; Silverstein, Eva; Torroba, Gonzalo; /Stanford U., ITP /Stanford U., Phys. Dept. /SLAC
2012-04-05T23:59:59.000Z
We generalize unitarity bounds on operator dimensions in conformal field theory to field theories with spacetime dependent couplings. Below the energy scale of spacetime variation of the couplings, their evolution can strongly affect the physics, effectively shifting the infrared operator scaling and unitarity bounds determined from correlation functions in the theory. We analyze this explicitly for large-N double-trace flows, and connect these to UV complete field theories. One motivating class of examples comes from our previous work on FRW holography, where this effect explains the range of flavors allowed in the dual, time dependent, field theory.
(E)-2-[(2-Bromophenylimino)methyl]-5-methoxyphenol: X-ray and DFT-calculated structures
Kosar, B., E-mail: bkosar@omu.edu.tr; Albayrak, C. [Sinop University, Faculty of Education (Turkey); Odabasoglu, M. [Pamukkale University, Chemistry Program (Turkey); Bueyuekguengoer, O. [Ondokuz Mayis University, Faculty of Arts and Sciences (Turkey)
2010-12-15T23:59:59.000Z
The crystal structure of (E)-2-[(2-Bromophenylimino)methyl]-5-methoxyphenol is determined by using X-ray diffraction and then the molecular structure is investigated with density functional theory (DFT). X-Ray study shows that the title compound has a strong intramolecular O-H-N hydrogen bond and three dimensional crystal structure is primarily determined by C-H-{pi} and weak van der Waals interactions. The strong O-H-N bond is an evidence of the preference for the phenol-imine tautomeric form in the solid state. Optimized molecular geometry is calculated with DFT at the B3LYP/6-31G(d,p) level. The IR spectra of compound were recorded experimentally and calculated to compare with each other. The results from both experiment and theoretical calculations are compared in this study.
Real-Time Transport in Open Quantum Systems From $\\mathcal{PT}$-Symmetric Quantum Mechanics
Justin E. Elenewski; Hanning Chen
2014-08-07T23:59:59.000Z
Nanoscale electronic transport is of intense technological interest, with applications ranging from semiconducting devices and molecular junctions to charge migration in biological systems. Most explicit theoretical approaches treat transport using a combination of density functional theory (DFT) and non-equilibrium Green's functions. This is a static formalism, with dynamic response properties accommodated only through complicated extensions. To circumvent this limitation, the carrier density may be propagated using real-time time-dependent DFT (RT-TDDFT), with boundary conditions corresponding to an open quantum system. Complex absorbing potentials can emulate outgoing particles at the simulation boundary, although these do not account for introduction of charge density. It is demonstrated that the desired positive particle flux is afforded by a class of $\\mathcal{PT}$-symmetric generating potentials that are characterized by anisotropic transmission resonances. These potentials add density every time a particle traverses the cell boundary, and may be used to engineer a continuous pulse train for incident packets. This is a first step toward developing a complete transport formalism unique to RT-TDDFT.
Theoretical Chemistry Theory, Computation, and
Gherman, Benjamin F.
1 23 Theoretical Chemistry Accounts Theory, Computation, and Modeling ISSN 1432-881X Volume 128). In order to explore the origin of this preference, density functional theory (DFT) calculations have been-terminus of nascent eubacterial proteins during protein synthesis [14]. As PDF is essential for bacterial survival
A note on ${\\cal N}\\ge 6$ Superconformal Quantum Field Theories in three dimensions
Denis Bashkirov
2011-08-20T23:59:59.000Z
Based on the structure of the three-dimensional superconformal algebra we show that every irreducible ${\\mathcal N}=6$ three-dimensional superconformal theory containes exactly one conserved U(1)-symmetry current in the stress tensor supermultiplet and that superconformal symmetry of every ${\\mathcal N}=7$ superconformal theory is in fact enhanced to ${\\mathcal N}=8$. Moreover, an irreducible ${\\cal N}=8$ superconformal theory does not have any global symmetries. The first observation explains why all known examples of ${\\mathcal N}=6$ superconformal theories have a global abelian symmetry.
Michele Campisi; Jukka Pekola; Rosario Fazio
2014-12-02T23:59:59.000Z
We study the stochastic energetic exchanges in quantum heat engines. Due to microreversibility, these obey a fluctuation relation, called the heat engine fluctuation relation, which implies the Carnot bound: no machine can have an efficiency larger than Carnot's efficiency. The stochastic thermodynamics of a quantum heat engine (including the joint statistics of heat and work and the statistics of efficiency) is illustrated by means of an optimal two-qubit heat engine, where each qubit is coupled to a thermal bath and a two-qubit gate determines energy exchanges between the two qubits. We discuss possible solid state implementations with Cooper pair boxes and flux qubits, quantum gate operations, and fast calorimetric on-chip measurements of single stochastic events.
Xavier Busch
2014-11-06T23:59:59.000Z
The two main predictions of quantum field theory in curved space-time, namely Hawking radiation and cosmological pair production, have not been directly tested and involve ultra high energy configurations. As a consequence, they should be considered with caution. Using the analogy with condensed matter systems, their analogue versions could be tested in the lab. Moreover, the high energy behavior of these systems is known and involves dispersion and dissipation, which regulate the theory at short distances. When considering experiments which aim to test the above predictions, there will also be a competition between the stimulated emission from thermal noise and the spontaneous emission out of vacuum. In order to measure these effects, one should thus compute the consequences of UV dispersion and dissipation, and identify observables able to establish that the spontaneous emission took place. In this thesis, we first analyze the effects of dispersion and dissipation on both Hawking radiation and pair particle production. To get explicit results, we work in the context of de Sitter space. Using the extended symmetries of the theory in such a background, exact results are obtained. These are then transposed to the context of black holes using the correspondence between de Sitter space and the black hole near horizon region. To introduce dissipation, we consider an exactly solvable model producing any decay rate. We also study the quantum entanglement of the particles so produced. In a second part, we consider explicit condensed matter systems, namely Bose Einstein condensates and exciton-polariton systems. We analyze the effects of dissipation on entanglement produced by the dynamical Casimir effect. As a final step, we study the entanglement of Hawking radiation in the presence of dispersion for a generic analogue system.
Quantum Control: Approach based on Scattering Theory for Non-commutative Markov
Gohm, Rolf
this fits in with the modern view point that control is essentially interconnection of systems. See the book Introduction Modern control theory has frequently used concepts and results from abstract mathematics. The aim of control theory [Ki,Za], i.e. the descrip- tion of the system by an internal state space with in- put
Beylkin, Gregory
Multiresolution quantum chemistry in multiwavelet bases: Analytic derivatives for Hartree An efficient and accurate analytic gradient method is presented for HartreeFock and density functional differential equations. In this paper, we extend the approach to include computation of analytic derivatives
Anderson, Paul R.
space Paul R. Anderson* Department of Physics, Wake Forest University, Winston-Salem, North Carolina the validity of the approximation used, provided the profile of the flow varies smoothly on scales compared fluctuations are converted into real on shell quanta. One quantum (the positive energy one) is emitted outside
Can we advance macroscopic quantum systems outside the framework of complex decoherence theory?
Mark E. Brezinski; Maria Rupnick
2013-12-30T23:59:59.000Z
Macroscopic quantum systems (MQS) are macroscopic systems driven by quantum rather than classical mechanics, a long studied area with minimal success till recently. Harnessing the benefits of quantum mechanics on a macroscopic level would revolutionize fields ranging from telecommunication to biology, the latter focused on here for reasons discussed. Contrary to misconceptions, there are no known physical laws that prevent the development of MQS. Instead, they are generally believed universally lost in complex systems from environmental entanglements (decoherence). But we argue success is achievable MQS with decoherence compensation developed, naturally or artificially, from top-down rather current reductionist approaches. This paper advances the MQS field by a complex systems approach to decoherence. First, why complex system decoherence approaches (top-down) are needed is discussed. Specifically, complex adaptive systems (CAS) are not amenable to reductionist models (and their master equations) because of emergent behavior, approximation failures, not accounting for quantum compensator mechanisms, ignoring path integrals, and the subentity problem. In addition, since MQS must exist within the context of the classical world, rapid decoherence and prolonged coherence are both needed. Nature has already demonstrated this for quantum subsystems such as photosynthesis and magnetoreception. Second, we perform a preliminary study that illustrates a top-down approach to potential MQS. In summary, reductionist arguments against MQS are not justifiable. It is more likely they are not easily detectable in large intact classical systems or has been destroyed by reductionist experimental set-ups. This complex systems decoherence approach, using top down investigations, is critical to paradigm shifts in MQS research both in biological and non-biological systems.
CONSERVATION LAWS AND THE QUANTUM THEORY OF TRANSPORT: THE EARLY DAYS
Gardel, Margaret
systems: superconductivity, and with Roy Glauber as well, writing a second thesis, Acceleration's interest in the problem arose from the question of how to write the BCS theory of superconductivity
Ooi, C. H. Raymond; Scully, Marlan O.; Sun, Qingqing; Zubairy, M. Suhail
2007-01-01T23:59:59.000Z
We present a largely analytical theory for two-photon correlations G((2)) between Stokes (s) and anti-Stokes (a) photon pairs from an extended medium (amplifier) composed of double-Lambda atoms in counterpropagating geometry. We generalize...
A String Theory Explanation for Quantum Chaos in the Hadronic Spectrum
Leopoldo A. Pando Zayas; Dori Reichmann
2013-03-27T23:59:59.000Z
In the 1950's Wigner and collaborators provided an explanation for the spectrum of hadronic excitations in terms of Random Matrix Theory. In the 1980's it was understood that some hadronic spectral properties were generic to systems whose classical limit is chaotic. We use string theory to demonstrate explicitly how, under very general conditions, recent holographic models of strong interactions have a spectrum compatible with Wigner's conjecture.
A String Theory Explanation for Quantum Chaos in the Hadronic Spectrum
Zayas, Leopoldo A Pando
2012-01-01T23:59:59.000Z
In the 1950's Wigner and collaborators provided an explanation for the spectrum of hadronic excitations in terms of Random Matrix Theory. In the 1980's it was understood that some hadronic spectral properties were generic to systems whose classical limit is chaotic. We use string theory to demonstrate explicitly how, under very general conditions, recent holographic models of strong interactions have a spectrum compatible with Wigner's conjecture.
M. Lapert; R. Tehini; G. Turinici; D. Sugny
2009-05-29T23:59:59.000Z
We consider the optimal control of quantum systems interacting non-linearly with an electromagnetic field. We propose new monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured by a non-standard choice of the cost which is not quadratic in the field. These algorithms can be constructed for pure and mixed-state quantum systems. The efficiency of the method is shown numerically on molecular orientation with a non-linearity of order 3 in the field. Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well-approximated by pulses that could be implemented experimentally.
Thellamurege, Nandun M.; Si, Dejun; Cui, Fengchao; Li, Hui, E-mail: hli4@unl.edu [Department of Chemistry, University of Nebraska-Lincoln, Lincoln, Nebraska 68588 (United States)] [Department of Chemistry, University of Nebraska-Lincoln, Lincoln, Nebraska 68588 (United States)
2014-05-07T23:59:59.000Z
A combined quantum mechanical/molecular mechanical/continuum (QM/MM/C) style second order Mřller-Plesset perturbation theory (MP2) method that incorporates induced dipole polarizable force field and induced surface charge continuum solvation model is established. The Z-vector method is modified to include induced dipoles and induced surface charges to determine the MP2 response density matrix, which can be used to evaluate MP2 properties. In particular, analytic nuclear gradient is derived and implemented for this method. Using the Assisted Model Building with Energy Refinement induced dipole polarizable protein force field, the QM/MM/C style MP2 method is used to study the hydrogen bonding distances and strengths of the photoactive yellow protein chromopore in the wild type and the Glu46Gln mutant.
Iyengar, Srinivasan S.
of obtaining these measurements is basically a dot product. The dot product can also be interpreted as a proAtomic and Molecular Quantum Theory Course Number: C561 C A Measurement is a Projection or a "dot" product (or inner product)!! 1. Lets go back and consider the Stern Gerlach experiment that we studied
-state-NMR and quasi-elastic neutron scattering are consistent with wave-like, rather than particle-like protons. We is essentially the case for solid-state NMR or quasi-elastic neutron scattering (QENS);6,15 (iii) theoreticalA neutron diffraction study from 6 to 293 K and a macroscopic-scale quantum theory of the hydrogen
Quantum correlations; quantum probability approach
W. A. Majewski
2015-05-21T23:59:59.000Z
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical and quantum), mathematical structures, and their consequences. These include the canonical form of classical correlation functionals, general definitions of separable (entangled) states, definition and analysis of quantumness of correlations, description of entanglement of formation, and PPT states. This work is intended both for physicists interested not only in collection of results but also in the mathematical methods justifying them, and mathematicians looking for an application of quantum probability to concrete new problems of quantum theory.
DFT Investigation of Osmium Terpyridinyl Complexes as Potential Optical Limiting Materials
Alok, Shashwat
2015-01-01T23:59:59.000Z
The development of optical power limiting materials is important to protect individuals or materials from intense laser irradiation. The photophysical behavior of Os(II) polypyridinyl complexes having aromatic hydrocarbon terpyridyl ligands has received considerable attention as systems exhibiting intramolecular energy transfer to yield a long excited states lifetime. Here we present a focused discussion to illustrate the photophysical behavior of transition metal complexes with modified terpyridyl ligands, utilizing density functional theory. Our DFT studies of the excited state behavior of Os(II) complexes containing pyrene-vinylene derived terpyridine (pyr-v-tpy) ligands can be applied to the development of optical limiting materials controlling the laser power at longer wavelength range.
Desnavi, Sameerah, E-mail: sameerah-desnavi@zhcet.ac.in [Department of Electronic Engineering, ZHCET, Aligarh Muslim University, Aligarh-202002 (India); Chakraborty, Brahmananda; Ramaniah, Lavanya M. [High Pressure and Synchrotron Radiation Physics Division, Bhabha Atomic Research Centre, Mumbai-400085 (India)
2014-04-24T23:59:59.000Z
The electronic structure and hydrogen storage capability of Yttrium-doped grapheme has been theoretically investigated using first principles density functional theory (DFT). Yttrium atom prefers the hollow site of the hexagonal ring with a binding energy of 1.40 eV. Doping by Y makes the system metallic and magnetic with a magnetic moment of 2.11 ?{sub B}. Y decorated graphene can adsorb up to four hydrogen molecules with an average binding energy of 0.415 eV. All the hydrogen atoms are physisorbed with an average desorption temperature of 530.44 K. The Y atoms can be placed only in alternate hexagons, which imply a wt% of 6.17, close to the DoE criterion for hydrogen storage materials. Thus, this system is potential hydrogen storage medium with 100% recycling capability.
The spacetime of double field theory: Review, remarks, and outlook
Hohm, Olaf
We review double field theory (DFT) with emphasis on the doubled spacetime and its generalized coordinate transformations, which unify diffeomorphisms and b-field gauge transformations. We illustrate how the composition ...
Alternative evaluation of a ln tan integral arising in quantum field theory
Mark W. Coffey
2008-11-15T23:59:59.000Z
A certain dilogarithmic integral I_7 turns up in a number of contexts including Feynman diagram calculations, volumes of tetrahedra in hyperbolic geometry, knot theory, and conjectured relations in analytic number theory. We provide an alternative explicit evaluation of a parameterized family of integrals containing this particular case. By invoking the Bloch-Wigner form of the dilogarithm function, we produce an equivalent result, giving a third evaluation of I_7. We also alternatively formulate some conjectures which we pose in terms of values of the specific Clausen function Cl_2.
Weakly relativistic quantum kinetic theory for electrostatic wave modes in magnetized plasmas
Hussain, Azhar [Department of Physics, GC University Lahore, 54000 Lahore (Pakistan)] [Department of Physics, GC University Lahore, 54000 Lahore (Pakistan); Stefan, Martin; Brodin, Gert [Department of Physics, Umeĺ University, SE-901 87 Umeĺ (Sweden)] [Department of Physics, Umeĺ University, SE-901 87 Umeĺ (Sweden)
2014-03-15T23:59:59.000Z
We have derived the electrostatic dispersion relation in a magnetized plasma using a recently developed quantum kinetic model based on the Dirac equation. The model contains weakly relativistic spin effects such as Thomas precession, the polarization currents associated with the spin and the spin-orbit coupling. It turns out that for strictly electrostatic perturbations the non-relativistic spin effects vanish, and the modification of the classical dispersion relation is solely associated with the relativistic terms. Several new wave modes appear due the electron spin effects, and an example for astrophysical plasmas are given.
Unified theory of exactly and quasiexactly solvable ''discrete'' quantum mechanics. I. Formalism
Odake, Satoru [Department of Physics, Shinshu University, Matsumoto 390-8621 (Japan); Sasaki, Ryu [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2010-08-15T23:59:59.000Z
We present a simple recipe to construct exactly and quasiexactly solvable Hamiltonians in one-dimensional ''discrete'' quantum mechanics, in which the Schroedinger equation is a difference equation. It reproduces all the known ones whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. The recipe also predicts several new ones. An essential role is played by the sinusoidal coordinate, which generates the closure relation and the Askey-Wilson algebra together with the Hamiltonian. The relationship between the closure relation and the Askey-Wilson algebra is clarified.
Theory of Linear Optical Absorption in Diamond Shaped Graphene Quantum Dots
Basak, Tista; Shukla, Alok
2015-01-01T23:59:59.000Z
In this paper, optical and electronic properties of diamond shaped graphene quantum dots (DQDs) have been studied by employing large-scale electron-correlated calculations. The computations have been performed using the $\\pi$-electron Pariser-Parr-Pople model Hamiltonian, which incorporates long-range Coulomb interactions. The influence of electron-correlation effects on the ground and excited states has been included by means of the configuration-interaction approach, used at various levels. Our calculations have revealed that the absorption spectra are red-shifted with the increasing sizes of quantum dots. It has been observed that the first peak of the linear optical absorption, which represents the optical gap, is not the most intense peak. This result is in excellent agreement with the experimental data, but in stark contrast to the predictions of the tight-binding model, according to which the first peak is the most intense peak, pointing to the importance of electron-correlation effects. Furthermore, a...
Collective multipole expansions and the perturbation theory in the quantum three-body problem
A. V. Meremianin
2008-03-10T23:59:59.000Z
The perturbation theory with respect to the potential energy of three particles is considered. The first-order correction to the continuum wave function of three free particles is derived. It is shown that the use of the collective multipole expansion of the free three-body Green function over the set of Wigner $D$-functions can reduce the dimensionality of perturbative matrix elements from twelve to six. The explicit expressions for the coefficients of the collective multipole expansion of the free Green function are derived. It is found that the $S$-wave multipole coefficient depends only upon three variables instead of six as higher multipoles do. The possible applications of the developed theory to the three-body molecular break-up processes are discussed.
Tahir, M. [PSE Division, KAUST, Thuwal 23955-6900 (Saudi Arabia); Department of Physics, University of Sargodha, Sargodha 40100 (Pakistan); Sabeeh, K. [Department of Physics, Quaid-i-Azam University, Islamabad 45320 (Pakistan); Shaukat, A. [Department of Physics, University of Sargodha, Sargodha 40100 (Pakistan); Schwingenschlögl, U., E-mail: Udo.Schwingenschlogl@kaust.edu.sa [PSE Division, KAUST, Thuwal 23955-6900 (Saudi Arabia)
2013-12-14T23:59:59.000Z
Since the discovery of graphene, a lot of interest has been attracted by the zeroth Landau level, which has no analog in the conventional two dimensional electron gas. Recently, lifting of the spin and valley degeneracies has been confirmed experimentally by capacitance measurements, while in transport experiments, this is difficult due to the scattering in the device. In this context, we model interaction effects on the quantum capacitance of graphene in the presence of a perpendicular magnetic field, finding good agreement with experiments. We demonstrate that the valley degeneracy is lifted by the substrate and by Kekule distortion, whereas the spin degeneracy is lifted by Zeeman interaction. The two cases can be distinguished by capacitance measurements.
Neutrinos Meet Supersymmetry: Quantum Aspects of of Neutrinophysics in Supersymmetric Theories
Hollik, Wolfgang Gregor
2015-01-01T23:59:59.000Z
We address the influence of quantum corrections to neutrino masses and mixings and discuss the possibilities to completely generate the flavor mixing irrespective of any tree-level flavor model. Furthermore, we describe a new class of vacua with a new minimum appearing in the standard Higgs direction. The results hint towards a charge and color breaking global minimum and therefore extend existing bounds at tree-level. Finally, we combine the discussion of vacuum stability in the MSSM with the right-handed neutrino extension. The supersymmetric version of the seesaw mechanism rescues the potential and also does not induce further instabilities neither at the SUSY scale nor at the scale of heavy neutrinos, as long as both scales are well separated. Moreover, we resolve a degeneracy in name space.
Multi-channel conduction in redox-based resistive switch modelled using quantum point contact theory
Miranda, E., E-mail: enrique.miranda@uab.cat; Suńé, J. [Departament d'Enginyeria Electrňnica, Universitat Autňnoma de Barcelona, 08193 Cerdanyola del Vallés, Barcelona (Spain)] [Departament d'Enginyeria Electrňnica, Universitat Autňnoma de Barcelona, 08193 Cerdanyola del Vallés, Barcelona (Spain); Mehonic, A.; Kenyon, A. J. [Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE (United Kingdom)] [Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE (United Kingdom)
2013-11-25T23:59:59.000Z
A simple analytic model for the electron transport through filamentary-type structures in Si-rich silica (SiO{sub x})-based resistive switches is proposed. The model is based on a mesoscopic description and is able to account for the linear and nonlinear components of conductance that arise from both fully and partially formed conductive channels spanning the dielectric film. Channels are represented by arrays of identical scatterers whose number and quantum transmission properties determine the current magnitude in the low and high resistance states. We show that the proposed model not only reproduces the experimental current-voltage (I-V) characteristics but also the normalized differential conductance (dln(I)/dln(V)-V) curves of devices under test.
Nash equilibrium in quantum superpositions
Faisal Shah Khan; Simon. J. D. Phoenix
2011-06-15T23:59:59.000Z
A working definition of the term \\quantum game" is developed in an attempt to gain insights into aspects of quantum mechanics via game theory.
Khan, Shabbir A
2013-01-01T23:59:59.000Z
Quantum plasma physics is a rapidly evolving research field with a very inter-disciplinary scope of potential applications, ranging from nano-scale science in condensed matter to the vast scales of astrophysical objects. The theoretical description of quantum plasmas relies on various approaches, microscopic or macroscopic, some of which have obvious relation to classical plasma models. The appropriate model should, in principle, incorporate the quantum mechanical effects such as diffraction, spin statistics and correlations, operative on the relevant scales. However, first-principle approaches such as quantum Monte Carlo and density functional theory or quantum-statistical methods such as quantum kinetic theory or non-equilibrium Green's functions require substantial theoretical and computational efforts. Therefore, for selected problems, alternative simpler methods have been put forward. In particular, the collective behavior of many-body systems is usually described within a self-consistent scheme of parti...
Recent Progress in the Physics of Open Quantum Systems: Theory and Experiment
Rotter, I
2015-01-01T23:59:59.000Z
This Report explores recent advances in our understanding of the physics of open quantum systems (OQSs) which consist of some localized region that is coupled to an external environment. Examples of such systems may be found in numerous areas of physics including mesoscopic physics that provides the main focus of this review. We provide a detailed discussion of the behavior of OQSs in terms of the projection-operator formalism, according to which the system under study is considered to be comprised of a localized region ($Q$), embedded into a well-defined environment ($P$) of scattering wavefunctions (with $Q+P=1$). The $Q$ subspace must be treated using the concepts of non-Hermitian physics, and of particular interest here is: the capacity of the environment to mediate a coupling between the different states of $Q$; the role played by the presence of exceptional points (EPs) in the spectra of OQSs; the influence of EPs on the rigidity of the wavefunction phases, and; the ability of EPs to initiate a dynamica...
Quantum theory of collective strong coupling of molecular vibrations with a microcavity mode
Javier del Pino; Johannes Feist; Francisco J. Garcia-Vidal
2015-02-27T23:59:59.000Z
We develop a quantum mechanical formalism to treat the strong coupling between an electromagnetic mode and a vibrational excitation of an ensemble of organic molecules. By employing a Bloch-Redfield-Wangsness approach, we show that the influence of dephasing-type interactions, i.e., elastic collisions with a background bath of phonons, critically depends on the nature of the bath modes. In particular, for long-range phonons corresponding to a common bath, the dynamics of the "bright state" (the collective superposition of molecular vibrations coupling to the cavity mode) is effectively decoupled from other system eigenstates. For the case of independent baths (or short-range phonons), incoherent energy transfer occurs between the bright state and the uncoupled dark states. However, these processes are suppressed when the Rabi splitting is larger than the frequency range of the bath modes, as achieved in a recent experiment [Shalabney et al., Nat. Commun. 6, 5981 (2015)]. In both cases, the dynamics can thus be described through a single collective oscillator coupled to a photonic mode, making this system an ideal candidate to explore cavity optomechanics at room temperature.
J. Wurm; K. Richter; I. Adagideli
2011-11-14T23:59:59.000Z
We investigate the effect of different edge types on the statistical properties of both the energy spectrum of closed graphene billiards and the conductance of open graphene cavities in the semiclassical limit. To this end, we use the semiclassical Green's function for ballistic graphene flakes that we have derived in Reference 1. First we study the spectral two point correlation function, or more precisely its Fourier transform the spectral form factor, starting from the graphene version of Gutzwiller's trace formula for the oscillating part of the density of states. We calculate the two leading order contributions to the spectral form factor, paying particular attention to the influence of the edge characteristics of the system. Then we consider transport properties of open graphene cavities. We derive generic analytical expressions for the classical conductance, the weak localization correction, the size of the universal conductance fluctuations and the shot noise power of a ballistic graphene cavity. Again we focus on the effects of the edge structure. For both, the conductance and the spectral form factor, we find that edge induced pseudospin interference affects the results significantly. In particular intervalley coupling mediated through scattering from armchair edges is the key mechanism that governs the coherent quantum interference effects in ballistic graphene cavities.
High energy cosmic rays experiments inspired by noncommutative quantum field theory
Josip Trampetic
2012-10-19T23:59:59.000Z
Phenomenological analysis of the covariant theta-exact noncommutative (NC) gauge field theory (GFT), inspired by high energy cosmic rays experiments, is performed in the framework of the inelastic neutrino-nucleon scatterings, plasmon and $Z$-boson decays into neutrino pair, the Big Bang Nucleosynthesis (BBN) and the Reheating Phase After Inflation (RPAI), respectively. Next we have have found neutrino two-point function and shows a closed form decoupling of the hard ultraviolet (UV) divergent term from softened ultraviolet/infrared (UV/IR) mixing term and from the finite terms as well. For a certain choice of the noncommutative parameter theta which preserves unitarity, problematic UV divergent and UV/IR mixing terms vanish. Non-perturbative modifications of the neutrino dispersion relations are assymptotically independent of the scale of noncommutativity in both the low and high energy limits and may allow superluminal propagation.
Josip Trampetic
2013-02-04T23:59:59.000Z
Analysis of the covariant theta-exact noncommutative (NC) gauge field theory (GFT), inspired by high energy cosmic rays experiments, is performed in the framework of the inelastic neutrino-nucleon scatterings. Next we have have found neutrino two-point function and shows a closed form decoupled from the hard ultraviolet (UV) divergent term, from softened ultraviolet/infrared (UV/IR) mixing term, and from the finite terms as well. For a certain choice of the noncommutative parameter theta which preserves unitarity, problematic UV divergent and UV/IR mixing terms vanish. Non-perturbative modifications of the neutrino dispersion relations are assymptotically independent of the scale of noncommutativity in both, the low and high energy limits and may allow superluminal propagation.
John H. Schwarz
1998-09-01T23:59:59.000Z
Superstring theory, and a recent extension called M theory, are leading candidates for a quantum theory that unifies gravity with the other forces. As such, they are certainly not ordinary quantum field theories. However, recent duality conjectures suggest that a more complete definition of these theories can be provided by the large N limits of suitably chosen U(N) gauge theories associated to the asymptotic boundary of spacetime.
Kirrander, Adam [Laboratoire Aime Cotton du CNRS, Universite de Paris-Sud, Batiment 505, F-91405 Orsay (France); Shalashilin, Dmitrii V. [School of Chemistry, University of Leeds, Leeds LS2 9JT (United Kingdom)
2011-09-15T23:59:59.000Z
We present an alternate version of the coupled-coherent-state method, specifically adapted for solving the time-dependent Schroedinger equation for multielectron dynamics in atoms and molecules. This theory takes explicit account of the exchange symmetry of fermion particles, and it uses fermion molecular dynamics to propagate trajectories. As a demonstration, calculations in the He atom are performed using the full Hamiltonian and accurate experimental parameters. Single- and double-ionization yields by 160-fs and 780-nm laser pulses are calculated as a function of field intensity in the range 10{sup 14}-10{sup 16} W/cm{sup 2}, and good agreement with experiments by Walker et al. is obtained. Since this method is trajectory based, mechanistic analysis of the dynamics is straightforward. We also calculate semiclassical momentum distributions for double ionization following 25-fs and 795-nm pulses at 1.5x10{sup 15} W/cm{sup 2}, in order to compare them with the detailed experiments by Rudenko et al. For this more challenging task, full convergence is not achieved. However, major effects such as the fingerlike structures in the momentum distribution are reproduced.
S. Kun; Y. Li; M. H. Zhao; M. R. Huang
2013-07-17T23:59:59.000Z
The idea of a thermalized non-equilibrated state of matter offers a conceptually new understanding of the strong angular asymmetry. In this compact review we present some clarifications, corrections and further developments of the approach, and provide a brief account of results previously discussed but not reported in the literature. The cross symmetry compound nucleus $S$-matrix correlations are obtained (i) starting from the unitary $S$-matrix representation, (ii) by explicitly taking into account a process of energy equilibration, and (iii) without taking the thermodynamic limit of an infinite number of particles in the thermalized system. It is conjectured that the long phase memory is due to the exponentially small total spin off-diagonal resonance intensity correlations. This manifestly implies that the strong angular asymmetry intimately relates to extremely small deviations of the eigenfunction distribution from Gaussian law. The spin diagonal resonance intensity correlations determine a new time/energy scale for a validity of random matrix theory. Its definition does not involve overlaps of the many-body interacting configurations with shell model non-interacting states and thus is conceptually different from the physical meaning (inverse energy relaxation time) of the spreading widths introduced by Wigner. Exact Gaussian distribution of the resonance wave functions corresponds to the instantaneous phase relaxation. We invite the nuclear reaction community for the competition to describe, as the first challenge, the strong forward peaking in the typically evaporation part of the proton spectra. This is necessary to initiate revealing long-term misconduct in the heavily cross-disciplinary field, also important for nuclear industry applications.
DFT --Das Future Tool ``Das Future Tool'' was the title of the group T-shirt1 that we
Ziegler, Tom
TRIBUTE DFT -- Das Future Tool ``Das Future Tool'' was the title of the group T-shirt1 that we had and considered it just another semi-empirical method.2 Tom, however, realized that DFT was ``Das Future Tool
Quantum state discrimination with bosonic channels and Gaussian states
Tan, Si Hui, Ph. D. Massachusetts Institute of Technology
2010-01-01T23:59:59.000Z
Discriminating between quantum states is an indispensable part of quantum information theory. This thesis investigates state discrimination of continuous quantum variables, focusing on bosonic communication channels and ...
Mexican contributions to Noncommutative Theories
Vergara, J. David [Instituto de Ciencias Nucleares, UNAM, A. Postal 70-543, Mexico, D.F. Mexico (Mexico); Garcia-Compean, H. [Centro de Investigacion y de Estudios Avanzados del IPN, Unidad Monterrey, Cerro de las Mitras 2565, Col. Obispado, Monterrey N.L. 64060 (Mexico); Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN, Apdo. Postal 14-740, Mexico D.F. 07000 (Mexico)
2006-09-25T23:59:59.000Z
In this paper we summarize the Mexican contributions to the subject of Noncommutative theories. These contributions span several areas: Quantum Groups, Noncommutative Field Theories, Hopf algebra of renormalization, Deformation Quantization, Noncommutative Gravity, and Noncommutative Quantum Mechanics.
Sai Vinjanampathy; Janet Anders
2015-08-25T23:59:59.000Z
Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit, in non-equilibrium situations, and with the full inclusion of quantum effects. Fuelled by experimental advances and the potential of future nanoscale applications this research effort is pursued by scientists with different backgrounds, including statistical physics, many-body theory, mesoscopic physics and quantum information theory, who bring various tools and methods to the field. A multitude of theoretical questions are being addressed ranging from issues of thermalisation of quantum systems and various definitions of "work", to the efficiency and power of quantum engines. This overview provides a perspective on a selection of these current trends accessible to postgraduate students and researchers alike.
Field Theory and Standard Model
W. Buchmüller; C. Lüdeling
2006-09-18T23:59:59.000Z
This is a short introduction to the Standard Model and the underlying concepts of quantum field theory.
Jae-Suk Park; John Terilla; Thomas Tradler
2009-09-21T23:59:59.000Z
We introduce the concept of a quantum background and a functor QFT. In the case that the QFT moduli space is smooth formal, we construct a flat quantum superconnection on a bundle over QFT which defines algebraic structures relevant to correlation functions in quantum field theory. We go further and identify chain level generalizations of correlation functions which should be present in all quantum field theories.
-point motion in a d-wave superconductor. The vortex is treated as a point flux tube, carrying fluxElectronic states near a quantum fluctuating point vortex in a d-wave superconductor: Dirac fermion model of the low-energy electronic states in the vicinity of a vortex undergoing quantum zero
Ye, Jingyun; Liu, Changjun; Mei, Donghai; Ge, Qingfeng
2014-08-01T23:59:59.000Z
Methanol synthesis from CO2 hydrogenation on Pd4/In2O3 has been investigated using density functional theory (DFT) and microkinetic modeling. In this study, three possible routes in the reaction network of CO2 + H2 ? CH3OH + H2O have been examined. Our DFT results show that the HCOO route competes with the RWGS route whereas a high activation barrier kinetically blocks the HCOOH route. DFT results also suggest that H2COO* + H* ? H2CO* +OH* and cis-COOH* + H* ?CO* + H2O* are the rate limiting steps in the HCOO route and the RWGS route, respectively. Microkinetic modeling results demonstrate that the HCOO route is the dominant reaction route for methanol synthesis from CO2 hydrogenation. We found that the activation of H adatom on the small Pd cluster and the presence of H2O on the In2O3 substrate play important roles in promoting the methanol synthesis. The hydroxyl adsorbed at the interface of Pd4/In2O3 induces the transformation of the supported Pd4 cluster from a butterfly structure into a tetrahedron structure. This important structure change not only indicates the dynamical nature of the supported nanoparticle catalyst structure during the reaction but also shifts the final hydrogenation step from H2COH to CH3O.
Optimal Transportation Theory with Repulsive Costs
Simone Di Marino; Augusto Gerolin; Luca Nenna
2015-06-15T23:59:59.000Z
This paper intents to present the state of art and recent developments of the optimal transportation theory with many marginals for a class of repulsive cost functions. We introduce some aspects of the Density Functional Theory (DFT) from a mathematical point of view, and revisit the theory of optimal transport from its perspective. Moreover, in the last three sections, we describe some recent and new theoretical and numerical results obtained for the Coulomb cost, the repulsive harmonic cost and the determinant cost.
Functionalized Graphene Nanoroads for Quantum Well Device. |...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Nanoroads for Quantum Well Device. Functionalized Graphene Nanoroads for Quantum Well Device. Abstract: Using density functional theory, a series of calculations of structural and...
On the Quantum Aspects of Geophysics
F. Darabi
2004-10-10T23:59:59.000Z
We introduce a simple quantum mechanical justification for the formation of folded mountains. It is very appealing to develop this idea to a theory of {\\it Quantum Geophysics}
The Spacetime of Double Field Theory: Review, Remarks, and Outlook
Olaf Hohm; Dieter Lust; Barton Zwiebach
2014-10-30T23:59:59.000Z
We review double field theory (DFT) with emphasis on the doubled spacetime and its generalized coordinate transformations, which unify diffeomorphisms and b-field gauge transformations. We illustrate how the composition of generalized coordinate transformations fails to associate. Moreover, in dimensional reduction, the O(d,d) T-duality transformations of fields can be obtained as generalized diffeomorphisms. Restricted to a half-dimensional subspace, DFT includes `generalized geometry', but is more general in that local patches of the doubled space may be glued together with generalized coordinate transformations. Indeed, we show that for certain T-fold backgrounds with non-geometric fluxes, there are generalized coordinate transformations that induce, as gauge symmetries of DFT, the requisite O(d,d;Z) monodromy transformations. Finally we review recent results on the \\alpha' extension of DFT which, reduced to the half-dimensional subspace, yields intriguing modifications of the basic structures of generalized geometry.
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
Models of quantum computation and quantum programming languages
J. A. Miszczak
2011-12-03T23:59:59.000Z
The goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory. We review various models of quantum Turing machine, quantum circuits and quantum random access machine (QRAM) along with their classical counterparts. We also provide an introduction to quantum programming languages, which are developed using the QRAM model. We review the syntax of several existing quantum programming languages and discuss their features and limitations.
Jussi Ilmari Lindgren
2013-02-13T23:59:59.000Z
This paper defines an equation for causality. This equation is then combined with the postulates of quantum mechanics and mass-energy equivalence to produce a quantum mechanical telegrapher's equation and to reproduce the Schrodinger and Klein-Gordon equations. The incompressible Navier-Stokes equations and dynamic general equilibrium in economics (with an interpretation of a Nash equilibrium) are obtained when the equation of causality refers to itself, i.e. when the cause is its own effect. As it is shown that the Klein-Gordon equation is obtained by Wick rotating the cause vector with de Broglie angular frequency, this paper postulates an equation for Quantum Gravity, which relates the Navier-Stokes equations to the Einstein Field Equations of General Relativity.
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.
Frydman, Lucio
Fast radio-frequency amplitude modulation in multiple-quantum magic-angle-spinning nuclear magnetic of this experiment has been the poor efficiency of the radio-frequency pulses used in converting multiple-modulated radio-frequency pulses, and which can yield substantial signal and even resolution enhancements over
Introduction Classical Field Theory
Baer, Christian
Introduction Classical Field Theory Locally Covariant Quantum Field Theory Renormalization Time evolution Conclusions and outlook Locality and Algebraic Structures in Field Theory Klaus Fredenhagen IIÂ¨utsch and Pedro Lauridsen Ribeiro) Klaus Fredenhagen Locality and Algebraic Structures in Field Theory #12
Rabani, Eran
Communication: Embedded fragment stochastic density functional theory Daniel Neuhauser, Roi Baer (2014) Communication: Embedded fragment stochastic density functional theory Daniel Neuhauser,1,a) RoiÂ18 Recently, we formulated KS-DFT as a statistical theory in which the electron density is determined from
Moreira, E. [Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN (Brazil); Henriques, J.M. [Centro de Educacao e Saude, Universidade Federal de Campina Grande, Campus Cuite, 58175-000 Cuite-PB (Brazil); Azevedo, D.L. [Departamento de Fisica, Universidade Federal do Maranhao, Centro de Ciencias Exatas e Tecnologia, 65085-580 Sao Luis-MA (Brazil); Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN (Brazil); Caetano, E.W.S., E-mail: ewcaetano@gmail.co [Instituto Federal de Educacao, Ciencia e Tecnologia do Ceara, Av. 13 de Maio, 2081, Benfica, 60040-531 Fortaleza-CE (Brazil); Freire, V.N. [Departamento de Fisica, Universidade Federal do Ceara, Centro de Ciencias, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza-CE (Brazil); Albuquerque, E.L. [Departamento de Biofisica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN (Brazil)
2011-04-15T23:59:59.000Z
Orthorhombic SrSnO{sub 3} was investigated using density functional theory (DFT) considering both the local density and generalized gradient approximations, LDA and GGA, respectively. The electronic band structure, density of states, complex dielectric function, optical absorption, and the infrared and Raman spectra were computed. Calculated lattice parameters are close to the experimental measurements, and an indirect band gap E(S{yields}{Gamma})=1.97eV (2.27 eV) was obtained within the GGA (LDA) level of calculation. Effective masses for holes and electrons were estimated, being very anisotropic in comparison with similar results for orthorhombic CaSnO{sub 3}. The complex dielectric function and the optical absorption of SrSnO{sub 3} were shown to be sensitive to the plane of polarization of the incident light. The infrared spectrum between 100 and 600 cm{sup -1} was obtained, with its main peaks being assigned, and a nice agreement between experimental and theoretical peaks of the Raman spectrum of orthorhombic SrSnO{sub 3} was achieved. -- Graphical abstract: Orthorhombic SrSnO{sub 3}: a view of the unit cell (left) and plots showing the calculated and experimental Raman spectra (right). Display Omitted Research highlights: {yields} We have performed DFT calculations on orthorhombic SrSnO{sub 3} crystals, obtaining their structural, electronical and optical properties. {yields} An indirect band gap was obtained, and anisotropic effective masses were found for both electrons and holes. {yields} The complex dielectric function and the optical absorption of SrSnO{sub 3} were shown to be very sensitive to the plane of polarization of the incident light. {yields} The infrared spectrum between 100 and 600 cm{sup -1} was obtained, with its main peaks being assigned, and a nice agreement between experimental and theoretical peaks of the Raman spectrum was achieved.
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.
LATTICE GAUGE THEORY 1 Lattice Gauge Theory
Creutz, Michael
a crucial tool for the quantum field the- orist. Applied to the formalism of lattice gauge theory, numerical simulations are providing fundamental quantitative information about the interactions of quarksLATTICE GAUGE THEORY 1 Lattice Gauge Theory Michael Creutz Supercomputers have recently become
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.
H. De Raedt; M. I. Katsnelson; H. C. Donker; K. Michielsen
2015-06-10T23:59:59.000Z
We propose and develop the thesis that the quantum theoretical description of experiments emerges from the desire to organize experimental data such that the description of the system under scrutiny and the one used to acquire the data are separated as much as possible. Application to the Stern-Gerlach and Einstein-Podolsky-Rosen-Bohm experiments are shown to support this thesis. General principles of logical inference which have been shown to lead to the Schr\\"odinger and Pauli equation and the probabilistic descriptions of the Stern-Gerlach and Einstein-Podolsky-Rosen-Bohm experiments, are used to demonstrate that the condition for the separation procedure to yield the quantum theoretical description is intimately related to the assumptions that the observed events are independent and that the data generated by these experiments is robust with respect to small changes of the conditions under which the experiment is carried out.
Washington Taylor
2006-06-28T23:59:59.000Z
This elementary introduction to string field theory highlights the features and the limitations of this approach to quantum gravity as it is currently understood. String field theory is a formulation of string theory as a field theory in space-time with an infinite number of massive fields. Although existing constructions of string field theory require expanding around a fixed choice of space-time background, the theory is in principle background-independent, in the sense that different backgrounds can be realized as different field configurations in the theory. String field theory is the only string formalism developed so far which, in principle, has the potential to systematically address questions involving multiple asymptotically distinct string backgrounds. Thus, although it is not yet well defined as a quantum theory, string field theory may eventually be helpful for understanding questions related to cosmology in string theory.
Nikolai N. Bogolubov, Jr.; Anatoliy K. Prykarpatsky
2008-10-21T23:59:59.000Z
The main fundamental principles characterizing the vacuum field structure are formulated and the modeling of the related vacuum medium and charged point particle dynamics by means of devised field theoretic tools are analyzed. The work is devoted to studying the vacuum structure, special relativity, electrodynamics of interacting charged point particles and quantum mechanics, and is a continuation of \\cite{BPT,BRT1}. Based on the vacuum field theory no-geometry approach, the Lagrangian and Hamiltonian reformulation of some alternative classical electrodynamics models is devised. The Dirac type quantization procedure, based on the canonical Hamiltonian formulation, is developed for some alternative electrodynamics models. Within an approach developed a possibility of the combined description both of electrodynamics and gravity is analyzed.
Solovyeva, Alisa [Gorlaeus Laboratories, Leiden Institute of Chemistry, Leiden University, P.O. Box 9502, 2300 RA Leiden (Netherlands); Technical University Braunschweig, Institute for Physical and Theoretical Chemistry, Hans-Sommer-Str. 10, 38106 Braunschweig (Germany); Pavanello, Michele [Gorlaeus Laboratories, Leiden Institute of Chemistry, Leiden University, P.O. Box 9502, 2300 RA Leiden (Netherlands); Neugebauer, Johannes [Technical University Braunschweig, Institute for Physical and Theoretical Chemistry, Hans-Sommer-Str. 10, 38106 Braunschweig (Germany)
2012-05-21T23:59:59.000Z
Subsystem density-functional theory (DFT) is a powerful and efficient alternative to Kohn-Sham DFT for large systems composed of several weakly interacting subunits. Here, we provide a systematic investigation of the spin-density distributions obtained in subsystem DFT calculations for radicals in explicit environments. This includes a small radical in a solvent shell, a {pi}-stacked guanine-thymine radical cation, and a benchmark application to a model for the special pair radical cation, which is a dimer of bacteriochlorophyll pigments, from the photosynthetic reaction center of purple bacteria. We investigate the differences in the spin densities resulting from subsystem DFT and Kohn-Sham DFT calculations. In these comparisons, we focus on the problem of overdelocalization of spin densities due to the self-interaction error in DFT. It is demonstrated that subsystem DFT can reduce this problem, while it still allows to describe spin-polarization effects crossing the boundaries of the subsystems. In practical calculations of spin densities for radicals in a given environment, it may thus be a pragmatic alternative to Kohn-Sham DFT calculations. In our calculation on the special pair radical cation, we show that the coordinating histidine residues reduce the spin-density asymmetry between the two halves of this system, while inclusion of a larger binding pocket model increases this asymmetry. The unidirectional energy transfer in photosynthetic reaction centers is related to the asymmetry introduced by the protein environment.
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.
STATISTICAL MECHANICS AND FIELD THEORY
Samuel, S.A.
2010-01-01T23:59:59.000Z
1. L. 1. Schiff, Quantum Mechanics, third edition (McGraw-two-dimensional quantum mechanics problem vith a potential,Theory Methods to Statistical Mechanics Chapter I The Use of
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
Time-dependent Internal DFT formalism and Kohn-Sham scheme
J. Messud
2009-11-05T23:59:59.000Z
We generalize to the time-dependent case the stationary Internal DFT / Kohn-Sham formalism presented in Ref. [14]. We prove that, in the time-dependent case, the internal properties of a self-bound system (as an atomic nuclei) are all defined by the internal one-body density and the initial state. We set-up a time-dependent Internal Kohn-Sham scheme as a practical way to compute the internal density. The main difference with the traditional DFT / Kohn-Sham formalism is the inclusion of the center-of-mass correlations in the functional.
Makrlik, Emanuel [Czech University of Life Sciences, Prague, Kamy´cká; Toman, Petr [Institute of Macromolecular Chemistry, Prague; Vanura, Petr [Institute of Chemical Technology, Prague, Czech Republic; Moyer, Bruce A [ORNL
2013-01-01T23:59:59.000Z
From extraction experiments and c-activity measurements, the extraction constant corresponding to the equilibrium Cs+ (aq) + I (aq) + 1 (org),1Cs+ (org) + I (org) taking place in the two-phase water-phenyltrifluoromethyl sulfone (abbrev. FS 13) system (1 = calix[4]arene-bis(t-octylbenzo-18-crown-6); aq = aqueous phase, org = FS 13 phase) was evaluated as logKex (1Cs+, I) = 2.1 0.1. Further, the stability constant of the 1Cs+ complex in FS 13 saturated with water was calculated for a temperature of 25 C: log borg (1Cs+) = 9.9 0.1. Finally, by using quantum mechanical DFT calculations, the most probable structure of the cationic complex species 1Cs+ was derived. In the resulting 1Cs+ complex, the central cation Cs+ is bound by eight bond interactions to six oxygen atoms of the respective 18-crown-6 moiety and to two carbons of the corresponding two benzene rings of the parent ligand 1 via cation p interaction.
Quantum Vacuum Structure and Cosmology
Johann Rafelski; Lance Labun; Yaron Hadad; Pisin Chen
2009-09-16T23:59:59.000Z
Short review of riddles that lie at the intersection of quantum theory, particle physics and cosmology; dark energy as false vacuum; discussion of a possible detection experiment.
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.
TjT^f'Dft Ris#-R-442 Department of Reactor
Tf tf 4 otgiooRfc ©TjT^f'Dft Ris#-R-442 iK Department of Reactor Technology Annual Progress Report-R-442 DEPARTMENT OF REACTOR TECHNOLOGY ANNUAL PROGRESS REPORT 1 January - 31 December 1980 Abstract. The activities of the Department of Reactor Tech- nology at Riso during 1980 are described. The work is presented
Oeiras, R. Y.; Silva, E. Z. da [Institute of Physics “Gleb Wataghin”, University of Campinas-Unicamp, 13083-859 Campinas, SP (Brazil)] [Institute of Physics “Gleb Wataghin”, University of Campinas-Unicamp, 13083-859 Campinas, SP (Brazil)
2014-04-07T23:59:59.000Z
Carbon linear atomic chains attached to graphene have experimentally been produced. Motivated by these results, we study the nature of the carbon bonds in these nanowires and how it affects their electrical properties. In the present study we investigate chains with different numbers of atoms and we observe that nanowires with odd number of atoms present a distinct behavior than the ones with even numbers. Using graphene nanoribbons as leads, we identify differences in the quantum transport of the chains with the consequence that even and odd numbered chains have low and high electrical conduction, respectively. We also noted a dependence of current with the wire size. We study this unexpected behavior using a combination of first principles calculations and simple models based on chemical bond theory. From our studies, the electrons of carbon nanowires present a quasi-free electron behavior and this explains qualitatively the high electrical conduction and the bond lengths with unexpected values for the case of odd nanowires. Our study also allows the understanding of the electric conduction dependence with the number of atoms and their parity in the chain. In the case of odd number chains a proposed ?-bond (MpB) model describes unsaturated carbons that introduce a mobile ?-bond that changes dramatically the structure and transport properties of these wires. Our results indicate that the nature of bonds plays the main role in the oscillation of quantum electrical conduction for chains with even and odd number of atoms and also that nanowires bonded to graphene nanoribbons behave as a quasi-free electron system, suggesting that this behavior is general and it could also remain if the chains are bonded to other materials.
Stapp, Henry P
2011-01-01T23:59:59.000Z
Robert Griffiths has recently addressed, within the framework of a 'consistent quantum theory' that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues that the putative proofs of this property that involve hidden variables include in their premises some essentially classical-physics-type assumptions that are fundamentally incompatible with the precepts of quantum physics. One cannot logically prove properties of a system by establishing, instead, properties of a system modified by adding properties alien to the original system. Hence Griffiths' rejection of hidden-variable-based proofs is logically warranted. Griffiths mentions the existence of a certain alternative proof that does not involve hidden variables, and that uses only macroscopically described observable properties. He notes that he had examined in his book proofs of this general kind, and concluded that they provide no evidence...
On the theory of superconductivity
Cheng, Kai-Chia
The phenomenon of superconductivity has so for defied all attempts of explanation since it was first discovered in 1911. Although two phenomenological theories have been put forward and proved very successful, yet no atomic theories based on quantum...
CLASSICAL FIELD THEORY WITH Z (3) SYMMETRY
Ruck, H.M.
2010-01-01T23:59:59.000Z
and H.M. Ruck, Quantum field theory Potts model, J. Math.in cyclic symmetry field theories, Nucl. Phys. B167 M.J.waves in nonlinear field theories, Phys. Rev. Lett. 32. R.
A Review of Noncommutative Field Theories
Victor O. Rivelles
2011-01-27T23:59:59.000Z
We present a brief review of selected topics in noncommutative field theories ranging from its revival in string theory, its influence on quantum field theories, its possible experimental signatures and ending with some applications in gravity and emergent gravity.
P. H. -L. Sit; Matteo Cococcioni; Nicola Marzari
2007-01-12T23:59:59.000Z
We implemented a rotationally-invariant Hubbard U extension to density-functional theory in the Car-Parrinello molecular dynamics framework, with the goal of bringing the accuracy of the DFT+U approach to finite-temperature simulations, especially for liquids or solids containing transition-metal ions. First, we studied the effects on the Hubbard U on the static equilibrium structure of the hexa-aqua ferrous and ferric ions, and the inner-sphere reorganization energy for the electron-transfer reaction between aqueous ferrous and ferric ions. It is found that the reorganization energy is increased, mostly as a result of the Fe-O distance elongation in the hexa-aqua ferrous ion. Second, we performed a first-principles molecular dynamics study of the solvation structure of the two aqueous ferrous and ferric ions. The Hubbard term is found to change the Fe-O radial distribution function for the ferrous ion, while having a negligible effect on the aqueous ferric ion. Moreover, the frequencies of vibrations between Fe and oxygen atoms in the first-solvation shell are shown to be unaffected by the Hubbard corrections for both ferrous and ferric ions.
Gerold Doyen; Deiana Drakova
2014-08-12T23:59:59.000Z
We construct a world model consisting of a matter field living in 4 dimensional spacetime and a gravitational field living in 11 dimensional spacetime. The seven hidden dimensions are compactified within a radius estimated by reproducing the particle - wave characteristic of diffraction experiments. In the presence of matter fields the gravitational field develops localized modes with elementary excitations called gravonons which are induced by the sources (massive particles). The final world model treated here contains only gravonons and a scalar matter field. The solution of the Schroedinger equation for the world model yields matter fields which are localized in the 4 dimensional subspace. The localization has the following properties: (i) There is a chooser mechanism for the selection of the localization site. (ii) The chooser selects one site on the basis of minor energy differences and differences in the gravonon structure between the sites, which appear statistical. (iii) The changes from one localization site to a neighbouring one take place in a telegraph-signal like manner. (iv) The times at which telegraph like jumps occur dependent on subtleties of the gravonon structure which appear statistical. (v) The fact that the dynamical law acts in the configuration space of fields living in 11 dimensional spacetime lets the events observed in 4 dimensional spacetime appear non-local. In this way the phenomenology of Copenhagen quantum mechanics is obtained without the need of introducing the process of collapse and a probabilistic interpretation of the wave function. Operators defining observables need not be introduced. All experimental findings are explained in a deterministic way as a consequence of the time development of the wave function in configuration space according to Schroedinger's equation.
Effect of Ligands on Characteristics of (CdSe)13 Quantum Dot
Gao, Yang; Zhou, Bo; Kang, Seung-gu; Xin, Minsi; Yang, Ping; Dai, Xing; Wang, Zhigang; Zhou, Ruhong
2014-01-01T23:59:59.000Z
The widespread applications of quantum dots (QDs) have spurred an increasing interest in the study of their coating ligands, which can not only protect the electronic structures of the central QDs, but also control their permeability through biological membranes with both size and shape. In this work, we have used density functional theory (DFT) to investigate the electronic structures of (CdSe)13 passivated by OPMe2(CH2)nMe ligands with different lengths and various numbers of branches (Me=methyl group, n = 0, 1-3). Our results show that the absorption peak in the ultraviolet-visible (UV-vis) spectra displays a clear blue-shift, on the scale of ~100 nm, upon the binding of ligands. Once the total number of ligands bound with (CdSe)13 reached a saturated number (9 or 10), no more blue-shift occurred in the absorption peak in the UV-vis spectra. On the other hand, the aliphatic chain length of ligands has a negligible effect on the optical properties of the QD core. Analyses of the bonding characteristics confirm that optical transitions are dominantly governed by the central QD core rather than the organic passivation. Interestingly, the density of states (DOS) share similar characteristics as vibrational spectra, even though there is no coordination vibration mode between the ligands and the central QD. These findings might provide insights on the material design for the passivation of quantum dots for biomedical applications.
Pastore, S. [University of South Carolina; Wiringa, Robert B. [ANL; Pieper, Steven C. [ANL; Schiavilla, Rocco [Old Dominion U., JLAB
2014-08-01T23:59:59.000Z
We report quantum Monte Carlo calculations of electromagnetic transitions in $^8$Be. The realistic Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon potentials are used to generate the ground state and nine excited states, with energies that are in excellent agreement with experiment. A dozen $M1$ and eight $E2$ transition matrix elements between these states are then evaluated. The $E2$ matrix elements are computed only in impulse approximation, with those transitions from broad resonant states requiring special treatment. The $M1$ matrix elements include two-body meson-exchange currents derived from chiral effective field theory, which typically contribute 20--30\\% of the total expectation value. Many of the transitions are between isospin-mixed states; the calculations are performed for isospin-pure states and then combined with the empirical mixing coefficients to compare to experiment. In general, we find that transitions between states that have the same dominant spatial symmetry are in decent agreement with experiment, but those transitions between different spatial symmetries are often significantly underpredicted.
Alessandro Sergi
2009-07-11T23:59:59.000Z
A critical assessment of the recent developments of molecular biology is presented. The thesis that they do not lead to a conceptual understanding of life and biological systems is defended. Maturana and Varela's concept of autopoiesis is briefly sketched and its logical circularity avoided by postulating the existence of underlying {\\it living processes}, entailing amplification from the microscopic to the macroscopic scale, with increasing complexity in the passage from one scale to the other. Following such a line of thought, the currently accepted model of condensed matter, which is based on electrostatics and short-ranged forces, is criticized. It is suggested that the correct interpretation of quantum dispersion forces (van der Waals, hydrogen bonding, and so on) as quantum coherence effects hints at the necessity of including long-ranged forces (or mechanisms for them) in condensed matter theories of biological processes. Some quantum effects in biology are reviewed and quantum mechanics is acknowledged as conceptually important to biology since without it most (if not all) of the biological structures and signalling processes would not even exist. Moreover, it is suggested that long-range quantum coherent dynamics, including electron polarization, may be invoked to explain signal amplification process in biological systems in general.
Noncommutative Supergeometry and Quantum Supergroups
Axel de Goursac
2015-01-26T23:59:59.000Z
This is a review of concepts of noncommutative supergeometry - namely Hilbert superspace, C*-superalgebra, quantum supergroup - and corresponding results. In particular, we present applications of noncommutative supergeometry in harmonic analysis of Lie supergroups, non-formal deformation quantization of supermanifolds, quantum field theory on noncommutative spaces; and we give explicit examples such as deformation of flat superspaces, noncommutative supertori, solvable topological quantum supergroups.
M-Theory and Maximally Supersymmetric Gauge Theories
Neil Lambert
2012-05-21T23:59:59.000Z
In this informal review for non-specalists we discuss the construction of maximally supersymmetric gauge theories that arise on the worldvolumes branes in String Theory and M-Theory. Particular focus is made on the relatively recent construction of M2-brane worldvolume theories. In a formal sense, the existence of these quantum field theories can be viewed as predictions of M-Theory. Their construction is therefore a reinforcement of the ideas underlying String Theory and M-Theory. We also briefly discuss the six-dimensional conformal field theory that is expected to arise on M5-branes. The construction of this theory is not only an important open problem for M-Theory but also a significant challenge to our current understanding of quantum field theory more generally.
Quantum Gravito-Optics: A Light Route from Semiclassical Gravity to Quantum Gravity
Unnikrishnan, C S
2015-01-01T23:59:59.000Z
Quantum gravity remains an elusive theory, in spite of our thorough understanding of the quantum theory and the general theory of relativity separately, presumably due to the lack of any observational clues. We argue that the theory of quantum gravity has a strong constraining anchor in the sector of gravitational radiation ensuring reliable physical clues, albeit in a limited observable form. In particular, all types of gravitational waves expected to be observable in LIGO-like advanced detectors are fully quantum mechanical states of radiation. Exact equivalence of the full quantum gravity theory with the familiar semiclassical theory is ensured in the radiation sector, in most real situations where the relevant quantum operator functions are normal ordered, by the analogue of the optical equivalence theorem in quantum optics. We show that this is indeed the case for detection of the waves from a massive binary system, a single gravitational atom, that emits coherent radiation. The idea of quantum-gravitati...
John H. Schwarz
1998-08-16T23:59:59.000Z
In the strong coupling limit type IIA superstring theory develops an eleventh dimension that is not apparent in perturbation theory. This suggests the existence of a consistent 11d quantum theory, called M theory, which is approximated by 11d supergravity at low energies. In this review we describe some of the evidence for this picture and some of its implications.
Molecular simulations studies of gas adsorption in metal–organic frameworks
Chen, Linjiang
2014-06-30T23:59:59.000Z
Using computational tools ranging from molecular simulations – including both Monte Carlo and molecular dynamics methods – to quantum mechanical (QM) calculations (primarily at density functional theory (DFT) level), ...
Gautam, P.; Gautam, D.; Chaudhary, R. P., E-mail: rpchaudhary65@gmail.com [Sant Longowal Institute of Engineering and Technology, Department of Chemistry (India)
2013-12-15T23:59:59.000Z
The title compound N-(4-acetyl-5,5-dimethyl-4,5-dihydro-1,3,4-thiadiazol-2-yl)acetamide (III) was obtained from the reaction of 2-(propan-2-ylidene)hydrazinecarbothioamide (II) with acetic anhydride instead of formation of the desired thiosemcarbazide derivative of Meldrum acid. The structures of II and III were established by elemental analysis, IR, NMR, Mass and X-ray crystallographic studies. II crystallizes in triclinic system, sp. gr. P-bar1 Z = 2; III crystallizes in the monoclinic system, sp. gr. P2{sub 1}/c, Z = 8. Density functional theory (DFT) calculations have been carried out for III. {sup 1}H and {sup 13}C NMR of III has been calculated and correlated with experimental results.
Revisiting HgCl2: A Solution- and Solid-State 199Hg NMR and ZORA-DFT Computational Study
Taylor, Robert E; Carver, Colin T; Larsen, Ross E; Dmitrenko, Olga; Bai, Shi; Dybowski, Cecil
2009-01-01T23:59:59.000Z
7 (1997), 333-336. [26] R. E. Taylor, Concepts Magn. Reson.DFT Computational Study R. E. Taylor 1 *, Colin T. Carver2522 USA *Corresponding author: R. E. Taylor Email address:
DFT-MD approach to TiO2/liquid interface systems for photocatalysis and dye-sensitised solar cell
Katsumoto, Shingo
DFT-MD approach to TiO2/liquid interface systems for photocatalysis and dye-sensitised solar cell- namics (MD) analysis of TiO2/solution in- terfaces related to photocatalysis and dye- sensitized solar
Stern-Gerlach Experiments and Complex Numbers in Quantum Physics
S. Sivakumar
2012-07-09T23:59:59.000Z
It is often stated that complex numbers are essential in quantum theory. In this article, the need for complex numbers in quantum theory is motivated using the results of tandem Stern-Gerlach experiments
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, ...
Efficiency and formalism of quantum games
Chiu Fan Lee; Neil Johnson
2008-09-19T23:59:59.000Z
We pursue a general theory of quantum games. We show that quantum games are more efficient than classical games, and provide a saturated upper bound for this efficiency. We demonstrate that the set of finite classical games is a strict subset of the set of finite quantum games. We also deduce the quantum version of the Minimax Theorem and the Nash Equilibrium Theorem.
Intrinsic Time Quantum Geometrodynamics
Ita, Eyo Eyo; Yu, Hoi-Lai
2015-01-01T23:59:59.000Z
Quantum Geometrodynamics with intrinsic time development and momentric variables is presented. An underlying SU(3) group structure at each spatial point regulates the theory. The intrinsic time behavior of the theory is analyzed, together with its ground state and primordial quantum fluctuations. Cotton-York potential dominates at early times when the universe was small; the ground state naturally resolves Penrose's Weyl Curvature Hypothesis, and thermodynamic and gravitational `arrows of time' point in the same direction. Ricci scalar potential corresponding to Einstein's General Relativity emerges as a zero-point energy contribution. A new set of fundamental canonical commutation relations without Planck's constant emerges from the unification of Gravitation and Quantum Mechanics.
Intrinsic Time Quantum Geometrodynamics
Eyo Eyo Ita III; Chopin Soo; Hoi-Lai Yu
2015-02-06T23:59:59.000Z
Quantum Geometrodynamics with intrinsic time development and momentric variables is presented. An underlying SU(3) group structure at each spatial point regulates the theory. The intrinsic time behavior of the theory is analyzed, together with its ground state and primordial quantum fluctuations. Cotton-York potential dominates at early times when the universe was small; the ground state naturally resolves Penrose's Weyl Curvature Hypothesis, and thermodynamic and gravitational `arrows of time' point in the same direction. Ricci scalar potential corresponding to Einstein's General Relativity emerges as a zero-point energy contribution. A new set of fundamental commutation relations without Planck's constant emerges from the unification of Gravitation and Quantum Mechanics.
Progress at the interface of wave-function and density-functional theories
Gidopoulos, Nikitas I. [ISIS, Rutherford Appleton Laboratory, STFC, Didcot, OX11 0QX, Oxon (United Kingdom)
2011-04-15T23:59:59.000Z
The Kohn-Sham (KS) potential of density-functional theory (DFT) emerges as the minimizing effective potential in a variational scheme that does not involve fixing the unknown single-electron density. Using Rayleigh Schroedinger (RS) perturbation theory (PT), we construct ab initio approximations for the energy difference, the minimization of which determines the KS potential directly - thereby bypassing DFT's traditional algorithm to search for the density that minimizes the total energy. From second-order RS PT, we obtain variationally stable energy differences to be minimized, solving the severe problem of variational collapse of orbital-dependent exchange-correlation functionals based on second-order RS PT.
Quantum algorithms for algebraic problems
Andrew M. Childs; Wim van Dam
2008-12-02T23:59:59.000Z
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article reviews the current state of quantum algorithms, focusing on algorithms with superpolynomial speedup over classical computation, and in particular, on problems with an algebraic flavor.
Lucien Hardy
2012-06-14T23:59:59.000Z
In this paper we consider theories in which reality is described by some underlying variables. Each value these variables can take represents an ontic state (a particular state of reality). The preparation of a quantum state corresponds to a distribution over the ontic states. If we make three basic assumptions, we can show that the distributions over ontic states corresponding to distinct pure states are non-overlapping. This means that we can deduce the quantum state from a knowledge of the ontic state. Hence, if these assumptions are correct, we can claim that the quantum state is a real thing (it is written into the underlying variables that describe reality). The key assumption we use in this proof is ontic indifference - that quantum transformations that do not affect a given pure quantum state can be implemented in such a way that they do not affect the ontic states in the support of that state. In fact this assumption is violated in the Spekkens toy model (which captures many aspects of quantum theory and in which different pure states of the model have overlapping distributions over ontic states). This paper proves that ontic indifference must be violated in any model reproducing quantum theory in which the quantum state is not a real thing. The argument presented in this paper is different from that given in a recent paper by Pusey, Barrett, and Rudolph. It uses a different key assumption and it pertains to a single copy of the system in question.
Quantum evolution across singularities
Ben Craps; Oleg Evnin
2008-01-21T23:59:59.000Z
Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular time-dependent backgounds and free quantum fields on the two-dimensional compactified Milne universe. Due to the presence of the singularities in the time dependence, the conventional quantum-mechanical evolution is not well-defined for such systems. We propose a natural way, mathematically analogous to renormalization in conventional quantum field theory, to construct unitary quantum evolution across the singularity. We carry out this procedure explicitly for free fields on the compactified Milne universe and compare our results with the matching conditions considered in earlier work (which were based on the covering Minkowski space).