Emergence of quantum mechanics from classical statistics

International Nuclear Information System (INIS)

Wetterich, C

2009-01-01

The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical interpretations to practical issues as quantum computing. In this note we demonstrate how quantum mechanics can emerge from classical statistical systems. We discuss conditions and circumstances for this to happen. Quantum systems describe isolated subsystems of classical statistical systems with infinitely many states. While infinitely many classical observables 'measure' properties of the subsystem and its environment, the state of the subsystem can be characterized by the expectation values of only a few probabilistic observables. They define a density matrix, and all the usual laws of quantum mechanics follow. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem.

Quantum-statistical kinetic equations

International Nuclear Information System (INIS)

Loss, D.; Schoeller, H.

1989-01-01

Considering a homogeneous normal quantum fluid consisting of identical interacting fermions or bosons, the authors derive an exact quantum-statistical generalized kinetic equation with a collision operator given as explicit cluster series where exchange effects are included through renormalized Liouville operators. This new result is obtained by applying a recently developed superoperator formalism (Liouville operators, cluster expansions, symmetrized projectors, P q -rule, etc.) to nonequilibrium systems described by a density operator ρ(t) which obeys the von Neumann equation. By means of this formalism a factorization theorem is proven (being essential for obtaining closed equations), and partial resummations (leading to renormalized quantities) are performed. As an illustrative application, the quantum-statistical versions (including exchange effects due to Fermi-Dirac or Bose-Einstein statistics) of the homogeneous Boltzmann (binary collisions) and Choh-Uhlenbeck (triple collisions) equations are derived

Probabilistic and Statistical Aspects of Quantum Theory

CERN Document Server

Holevo, Alexander S

2011-01-01

This book is devoted to aspects of the foundations of quantum mechanics in which probabilistic and statistical concepts play an essential role. The main part of the book concerns the quantitative statistical theory of quantum measurement, based on the notion of positive operator-valued measures. During the past years there has been substantial progress in this direction, stimulated to a great extent by new applications such as Quantum Optics, Quantum Communication and high-precision experiments. The questions of statistical interpretation, quantum symmetries, theory of canonical commutation re

Carrier Statistics and Quantum Capacitance Models of Graphene Nanoscroll

Directory of Open Access Journals (Sweden)

M. Khaledian

2014-01-01

schematic perfect scroll-like Archimedes spiral. The DOS model was derived at first, while it was later applied to compute the carrier concentration and quantum capacitance model. Furthermore, the carrier concentration and quantum capacitance were modeled for both degenerate and nondegenerate regimes, along with examining the effect of structural parameters and chirality number on the density of state and carrier concentration. Latterly, the temperature effect on the quantum capacitance was studied too.

Eigenfunction statistics on quantum graphs

International Nuclear Information System (INIS)

Gnutzmann, S.; Keating, J.P.; Piotet, F.

2010-01-01

We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.

On quantum statistical inference

NARCIS (Netherlands)

Barndorff-Nielsen, O.E.; Gill, R.D.; Jupp, P.E.

2001-01-01

Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions addressed apart from those met classically in stochastics.

Quantum fields on manifolds: an interplay between quantum theory, statistical thermodynamics and general relativity

International Nuclear Information System (INIS)

Sewell, G.L.

1986-01-01

The author shows how the basic axioms of quantum field theory, general relativity and statistical thermodynamics lead, in a model-independent way, to a generalized Hawking-Unruh effect, whereby the gravitational fields carried by a class of space-time manifolds with event horizons thermalize ambient quantum fields. The author is concerned with a quantum field on a space-time x containing a submanifold X' bounded by event horizons. The objective is to show that, for a wide class of space-times, the global vacuum state of the field reduces, in X', to a thermal state, whose temperature depends on the geometry. The statistical thermodynaical, geometrical, and quantum field theoretical essential ingredients for the reduction of the vacuum state are discussed

Quantum mechanics and field theory with fractional spin and statistics

International Nuclear Information System (INIS)

Forte, S.

1992-01-01

Planar systems admit quantum states that are neither bosons nor fermions, i.e., whose angular momentum is neither integer nor half-integer. After a discussion of some examples of familiar models in which fractional spin may arise, the relevant (nonrelativistic) quantum mechanics is developed from first principles. The appropriate generalization of statistics is also discussed. Some physical effects of fractional spin and statistics are worked out explicitly. The group theory underlying relativistic models with fractional spin and statistics is then introduced and applied to relativistic particle mechanics and field theory. Field-theoretical models in 2+1 dimensions are presented which admit solitons that carry fractional statistics, and are discussed in a semiclassical approach, in the functional integral approach, and in the canonical approach. Finally, fundamental field theories whose Fock states carry fractional spin and statistics are discussed

On quantum statistical inference

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler; Gill, Richard D.; Jupp, Peter E.

Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions addressed apart from those met classically in stochastics....... Furthermore, concurrent advances in experimental techniques and in the theory of quantum computation have led to a strong interest in questions of quantum information, in particular in the sense of the amount of information about unknown parameters in given observational data or accessible through various...

Beyond quantum microcanonical statistics

International Nuclear Information System (INIS)

Fresch, Barbara; Moro, Giorgio J.

2011-01-01

Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e., the wavefunction, of an isolated system is determined to calculate molecular properties and their time evolution according to the unitary Schroedinger equation. On the other hand a mixed state, i.e., a statistical density matrix, is the standard formalism to account for thermal equilibrium, as postulated in the microcanonical quantum statistics. In the present paper an alternative treatment relying on a statistical analysis of the possible wavefunctions of an isolated system is presented. In analogy with the classical ergodic theory, the time evolution of the wavefunction determines the probability distribution in the phase space pertaining to an isolated system. However, this alone cannot account for a well defined thermodynamical description of the system in the macroscopic limit, unless a suitable probability distribution for the quantum constants of motion is introduced. We present a workable formalism assuring the emergence of typical values of thermodynamic functions, such as the internal energy and the entropy, in the large size limit of the system. This allows the identification of macroscopic properties independently of the specific realization of the quantum state. A description of material systems in agreement with equilibrium thermodynamics is then derived without constraints on the physical constituents and interactions of the system. Furthermore, the canonical statistics is recovered in all generality for the reduced density matrix of a subsystem.

Quantum Statistics and Entanglement Problems

OpenAIRE

Trainor, L. E. H.; Lumsden, Charles J.

2002-01-01

Interpretations of quantum measurement theory have been plagued by two questions, one concerning the role of observer consciousness and the other the entanglement phenomenon arising from the superposition of quantum states. We emphasize here the remarkable role of quantum statistics in describing the entanglement problem correctly and discuss the relationship to issues arising from current discussions of intelligent observers in entangled, decohering quantum worlds.

Lecture notes on quantum statistics

NARCIS (Netherlands)

Gill, R.D.

2000-01-01

These notes are meant to form the material for an introductory course on quantum statistics at the graduate level aimed at mathematical statisticians and probabilists No background in physics quantum or otherwise is required They are still far from complete

Semi-Poisson statistics in quantum chaos.

Science.gov (United States)

García-García, Antonio M; Wang, Jiao

2006-03-01

We investigate the quantum properties of a nonrandom Hamiltonian with a steplike singularity. It is shown that the eigenfunctions are multifractals and, in a certain range of parameters, the level statistics is described exactly by semi-Poisson statistics (SP) typical of pseudointegrable systems. It is also shown that our results are universal, namely, they depend exclusively on the presence of the steplike singularity and are not modified by smooth perturbations of the potential or the addition of a magnetic flux. Although the quantum properties of our system are similar to those of a disordered conductor at the Anderson transition, we report important quantitative differences in both the level statistics and the multifractal dimensions controlling the transition. Finally, the study of quantum transport properties suggests that the classical singularity induces quantum anomalous diffusion. We discuss how these findings may be experimentally corroborated by using ultracold atoms techniques.

On Quantum Statistical Inference, II

OpenAIRE

Barndorff-Nielsen, O. E.; Gill, R. D.; Jupp, P. E.

2003-01-01

Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems. Furthermore, theoretical developments in the theory of quantum measurements have brought the basic mathematical framework for the probability calculations much closer to that of classical probability theory. The present paper reviews this field and proposes and inte...

Quantum Entropy and Its Applications to Quantum Communication and Statistical Physics

Directory of Open Access Journals (Sweden)

Masanori Ohya

2010-05-01

Full Text Available Quantum entropy is a fundamental concept for quantum information recently developed in various directions. We will review the mathematical aspects of quantum entropy (entropies and discuss some applications to quantum communication, statistical physics. All topics taken here are somehow related to the quantum entropy that the present authors have been studied. Many other fields recently developed in quantum information theory, such as quantum algorithm, quantum teleportation, quantum cryptography, etc., are totally discussed in the book (reference number 60.

Quantum level statistics of pseudointegrable billiards

International Nuclear Information System (INIS)

Cheon, T.; Cohen, T.D.

1989-01-01

We study the spectral statistics of systems of two-dimensional pseudointegrable billiards. These systems are classically nonergodic, but nonseparable. It is found that such systems possess quantum spectra which are closely simulated by the Gaussian orthogonal ensemble. We discuss the implications of these results on the conjectured relation between classical chaos and quantum level statistics. We emphasize the importance of the semiclassical nature of any such relation

Quantum Statistical Operator and Classically Chaotic Hamiltonian ...

African Journals Online (AJOL)

Quantum Statistical Operator and Classically Chaotic Hamiltonian System. ... Journal of the Nigerian Association of Mathematical Physics ... In a Hamiltonian system von Neumann Statistical Operator is used to tease out the quantum consequence of (classical) chaos engendered by the nonlinear coupling of system to its ...

The Generalized Quantum Statistics

OpenAIRE

Hwang, WonYoung; Ji, Jeong-Young; Hong, Jongbae

1999-01-01

The concept of wavefunction reduction should be introduced to standard quantum mechanics in any physical processes where effective reduction of wavefunction occurs, as well as in the measurement processes. When the overlap is negligible, each particle obey Maxwell-Boltzmann statistics even if the particles are in principle described by totally symmetrized wavefunction [P.R.Holland, The Quantum Theory of Motion, Cambridge Unversity Press, 1993, p293]. We generalize the conjecture. That is, par...

Quantum mechanics as applied mathematical statistics

International Nuclear Information System (INIS)

Skala, L.; Cizek, J.; Kapsa, V.

2011-01-01

Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schroedinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.

QUANTUM MECHANICS WITHOUT STATISTICAL POSTULATES

International Nuclear Information System (INIS)

Geiger, G.

2000-01-01

The Bohmian formulation of quantum mechanics describes the measurement process in an intuitive way without a reduction postulate. Due to the chaotic motion of the hidden classical particle all statistical features of quantum mechanics during a sequence of repeated measurements can be derived in the framework of a deterministic single system theory

Quantum fermions and quantum field theory from classical statistics

International Nuclear Information System (INIS)

Wetterich, Christof

2012-01-01

An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory for Dirac particles in an external electromagnetic field. This yields in the non-relativistic one-particle limit the Schrödinger equation for a quantum particle in a potential. Interference or tunneling arise from classical probabilities.

Electron Energy Level Statistics in Graphene Quantum Dots

NARCIS (Netherlands)

De Raedt, H.; Katsnellson, M. I.; Katsnelson, M.I.

2008-01-01

Motivated by recent experimental observations of size quantization of electron energy levels in graphene quantum dots [7] we investigate the level statistics in the simplest tight-binding model for different dot shapes by computer simulation. The results are in a reasonable agreement with the

Quantum Statistical Mechanics on a Quantum Computer

NARCIS (Netherlands)

Raedt, H. De; Hams, A.H.; Michielsen, K.; Miyashita, S.; Saito, K.; Saito, E.

2000-01-01

We describe a simulation method for a quantum spin model of a generic, general purpose quantum computer. The use of this quantum computer simulator is illustrated through several implementations of Grover’s database search algorithm. Some preliminary results on the stability of quantum algorithms

Hidden Statistics Approach to Quantum Simulations

Science.gov (United States)

Zak, Michail

2010-01-01

Recent advances in quantum information theory have inspired an explosion of interest in new quantum algorithms for solving hard computational (quantum and non-quantum) problems. The basic principle of quantum computation is that the quantum properties can be used to represent structure data, and that quantum mechanisms can be devised and built to perform operations with this data. Three basic non-classical properties of quantum mechanics superposition, entanglement, and direct-product decomposability were main reasons for optimism about capabilities of quantum computers that promised simultaneous processing of large massifs of highly correlated data. Unfortunately, these advantages of quantum mechanics came with a high price. One major problem is keeping the components of the computer in a coherent state, as the slightest interaction with the external world would cause the system to decohere. That is why the hardware implementation of a quantum computer is still unsolved. The basic idea of this work is to create a new kind of dynamical system that would preserve the main three properties of quantum physics superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. In other words, such a system would reinforce the advantages and minimize limitations of both quantum and classical aspects. Based upon a concept of hidden statistics, a new kind of dynamical system for simulation of Schroedinger equation is proposed. The system represents a modified Madelung version of Schroedinger equation. It preserves superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. Such an optimal combination of characteristics is a perfect match for simulating quantum systems. The model includes a transitional component of quantum potential (that has been overlooked in previous treatment of the Madelung equation). The role of the

Intermediate statistics in quantum maps

Energy Technology Data Exchange (ETDEWEB)

Giraud, Olivier [H H Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL (United Kingdom); Marklof, Jens [School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW (United Kingdom); O' Keefe, Stephen [School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW (United Kingdom)

2004-07-16

We present a one-parameter family of quantum maps whose spectral statistics are of the same intermediate type as observed in polygonal quantum billiards. Our central result is the evaluation of the spectral two-point correlation form factor at small argument, which in turn yields the asymptotic level compressibility for macroscopic correlation lengths. (letter to the editor)

Statistical ensembles in quantum mechanics

International Nuclear Information System (INIS)

Blokhintsev, D.

1976-01-01

The interpretation of quantum mechanics presented in this paper is based on the concept of quantum ensembles. This concept differs essentially from the canonical one by that the interference of the observer into the state of a microscopic system is of no greater importance than in any other field of physics. Owing to this fact, the laws established by quantum mechanics are not of less objective character than the laws governing classical statistical mechanics. The paradoxical nature of some statements of quantum mechanics which result from the interpretation of the wave functions as the observer's notebook greatly stimulated the development of the idea presented. (Auth.)

A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.

Science.gov (United States)

Sinitskiy, Anton V; Voth, Gregory A

2015-09-07

Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman's imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.

A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals

International Nuclear Information System (INIS)

Sinitskiy, Anton V.; Voth, Gregory A.

2015-01-01

Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments

Introduction to quantum statistical mechanics

International Nuclear Information System (INIS)

Bogolyubov, N.N.; Bogolyubov, N.N.

1980-01-01

In a set of lectures, which has been delivered at the Physical Department of Moscow State University as a special course for students represented are some basic ideas of quantum statistical mechanics. Considered are in particular, the Liouville equations in classical and quantum mechanics, canonical distribution and thermodynamical functions, two-time correlation functions and Green's functions in the theory of thermal equilibrium

Quantum Statistical Entropy of Five-Dimensional Black Hole

Institute of Scientific and Technical Information of China (English)

ZHAO Ren; WU Yue-Qin; ZHANG Sheng-Li

2006-01-01

The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole.By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole's entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.

Quantum Statistical Entropy of Five-Dimensional Black Hole

International Nuclear Information System (INIS)

Zhao Ren; Zhang Shengli; Wu Yueqin

2006-01-01

The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole's entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.

Statistical physics of black holes as quantum-mechanical systems

OpenAIRE

Giddings, Steven B.

2013-01-01

Some basic features of black-hole statistical mechanics are investigated, assuming that black holes respect the principles of quantum mechanics. Care is needed in defining an entropy S_bh corresponding to the number of microstates of a black hole, given that the black hole interacts with its surroundings. An open question is then the relationship between this entropy and the Bekenstein-Hawking entropy S_BH. For a wide class of models with interactions needed to ensure unitary quantum evolutio...

Statistical algebraic approach to quantum mechanics

International Nuclear Information System (INIS)

Slavnov, D.A.

2001-01-01

The scheme for plotting the quantum theory with application of the statistical algebraic approach is proposed. The noncommutative algebra elements (observed ones) and nonlinear functionals on this algebra (physical state) are used as the primary constituents. The latter ones are associated with the single-unit measurement results. Certain physical state groups are proposed to consider as quantum states of the standard quantum mechanics. It is shown that the mathematical apparatus of the standard quantum mechanics may be reproduced in such a scheme in full volume [ru

Quantum physics and statistical physics. 5. ed.

International Nuclear Information System (INIS)

Alonso, Marcelo; Finn, Edward J.

2012-01-01

By logical and uniform presentation this recognized introduction in modern physics treats both the experimental and theoretical aspects. The first part of the book deals with quantum mechanics and their application to atoms, molecules, nuclei, solids, and elementary particles. The statistical physics with classical statistics, thermodynamics, and quantum statistics is theme of the second part. Alsonso and Finn avoid complicated mathematical developments; by numerous sketches and diagrams as well as many problems and examples they make the reader early and above all easily understandably familiar with the formations of concepts of modern physics.

Quantum models of classical systems

International Nuclear Information System (INIS)

Hájíček, P

2015-01-01

Quantum statistical methods that are commonly used for the derivation of classical thermodynamic properties are extended to classical mechanical properties. The usual assumption that every real motion of a classical mechanical system is represented by a sharp trajectory is not testable and is replaced by a class of fuzzy models, the so-called maximum entropy (ME) packets. The fuzzier are the compared classical and quantum ME packets, the better seems to be the match between their dynamical trajectories. Classical and quantum models of a stiff rod will be constructed to illustrate the resulting unified quantum theory of thermodynamic and mechanical properties. (paper)

Quantum Statistical Mechanics on a Quantum Computer

OpenAIRE

De Raedt, H.; Hams, A. H.; Michielsen, K.; Miyashita, S.; Saito, K.

1999-01-01

We describe a quantum algorithm to compute the density of states and thermal equilibrium properties of quantum many-body systems. We present results obtained by running this algorithm on a software implementation of a 21-qubit quantum computer for the case of an antiferromagnetic Heisenberg model on triangular lattices of different size.

Quantum field theory and statistical mechanics

International Nuclear Information System (INIS)

Jegerlehner, F.

1975-01-01

At first a heuristic understanding is given how the relation between quantum field theory and statistical mechanics near phase transitions comes about. A long range scale invariant theory is constructed, critical indices are calculated and the relations among them are proved, field theoretical Kadanoff-scale transformations are formulated and scaling corrections calculated. A precise meaning to many of Kadanoffs considerations and a model matching Wegners phenomenological scheme is given. It is shown, that soft parametrization is most transparent for the discussion of scaling behaviour. (BJ) [de

Is quantum theory a form of statistical mechanics?

Science.gov (United States)

Adler, S. L.

2007-05-01

We give a review of the basic themes of my recent book: Adler S L 2004 Quantum Theory as an Emergent Phenomenon (Cambridge: Cambridge University Press). We first give motivations for considering the possibility that quantum mechanics is not exact, but is instead an accurate asymptotic approximation to a deeper level theory. For this deeper level, we propose a non-commutative generalization of classical mechanics, that we call "trace dynamics", and we give a brief survey of how it works, considering for simplicity only the bosonic case. We then discuss the statistical mechanics of trace dynamics and give our argument that with suitable approximations, the Ward identities for trace dynamics imply that ensemble averages in the canonical ensemble correspond to Wightman functions in quantum field theory. Thus, quantum theory emerges as the statistical thermodynamics of trace dynamics. Finally, we argue that Brownian motion corrections to this thermodynamics lead to stochastic corrections to the Schrödinger equation, of the type that have been much studied in the "continuous spontaneous localization" model of objective state vector reduction. In appendices to the talk, we give details of the existence of a conserved operator in trace dynamics that encodes the structure of the canonical algebra, of the derivation of the Ward identities, and of the proof that the stochastically-modified Schrödinger equation leads to state vector reduction with Born rule probabilities.

Constructions of quantum fields with anyonic statistics

International Nuclear Information System (INIS)

Plaschke, M.

2015-01-01

From the principles of algebraic quantum field theory it follows that in low dimensions particles are not necessarily bosons or fermions, but their statistics can in general be governed by the braid group. Such particles are called anyons and their possible statistics is intimately related to their localization properties and their covariance with respect to rotations. This work is concerned with the explicit construction of quantum fields with anyonic statistics which are localized in various different regions on two- and three-dimensional Minkowski space, and we will analyze the connection between localization, statistics and spin. The reason why this is considerably more difficult than for bosons or fermions is the no-go theorem regarding free cone-localized anyons in d=2+1. This problem is approached in this work from different directions leaving out some of the underlying assumptions one makes in the abstract algebraic quantum field theory. Despite a similar no-go theorem for free local anyons, it is in two dimensions possible to construct compactly localized quantum field nets with anyonic commutation relations for every mass m ≥ 0 and every statistics parameter by using the theory of loop groups and implementable Bogoliubov transformations. This does not work in higher dimensions so in d=2+1 we will first construct polarization free generators, which are only wedge-local, using a recent work about multiplicative deformations of free quantum fields on the Fock space. By generalizing this procedure to the charged case it is possible to extend the set of admissible deformations and end up with fields satisfying anyonic commutation relations, which are covariant w.r.t a Poincaré group representation with arbitrary real-valued spin. Another approach, which further demonstrates the connection between localization, statistics and spin of quantum field nets, is to focus first only on the rotational degrees of freedom and construct field operators on the circle

The quantum Rabi model: solution and dynamics

International Nuclear Information System (INIS)

Xie, Qiongtao; Zhong, Honghua; Lee, Chaohong; Batchelor, Murray T

2017-01-01

This article presents a review of recent developments on various aspects of the quantum Rabi model. Particular emphasis is given on the exact analytic solution obtained in terms of confluent Heun functions. The analytic solutions for various generalisations of the quantum Rabi model are also discussed. Results are also reviewed on the level statistics and the dynamics of the quantum Rabi model. The article concludes with an introductory overview of several experimental realisations of the quantum Rabi model. An outlook towards future developments is also given. (topical review)

Statistical approach to quantum field theory. An introduction

International Nuclear Information System (INIS)

Wipf, Andreas

2013-01-01

Based on course-tested notes and pedagogical in style. Authored by a leading researcher in the field. Contains end-of-chapter problems and listings of short, useful computer programs. Authored by a leading researcher in the field. Contains end-of-chapter problems and listings of short, useful computer programs. Contains end-of-chapter problems and listings of short, useful computer programs. Over the past few decades the powerful methods of statistical physics and Euclidean quantum field theory have moved closer together, with common tools based on the use of path integrals. The interpretation of Euclidean field theories as particular systems of statistical physics has opened up new avenues for understanding strongly coupled quantum systems or quantum field theories at zero or finite temperatures. Accordingly, the first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an ''experimental'' tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems with discrete and continuous spins, where the ubiquitous Ising model serves as an ideal guide for introducing the fascinating area of phase transitions. As an alternative to the lattice formulation of quantum field theories, variants of the flexible renormalization group methods are discussed in detail. Since, according to our present-day knowledge, all fundamental interactions in nature are described by gauge theories, the remaining chapters of the book deal with gauge theories without and with matter. This text is based on course-tested notes for graduate students and, as

Quantum-Like Bayesian Networks for Modeling Decision Making

Directory of Open Access Journals (Sweden)

Catarina eMoreira

2016-01-01

Full Text Available In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences to accommodate the paradoxical findings of the Sure Thing Principle. We propose a Quantum-Like Bayesian Network, which consists in replacing classical probabilities by quantum probability amplitudes. However, since this approach suffers from the problem of exponential growth of quantum parameters, we also propose a similarity heuristic that automatically fits quantum parameters through vector similarities. This makes the proposed model general and predictive in contrast to the current state of the art models, which cannot be generalized for more complex decision scenarios and that only provide an explanatory nature for the observed paradoxes. In the end, the model that we propose consists in a nonparametric method for estimating inference effects from a statistical point of view. It is a statistical model that is simpler than the previous quantum dynamic and quantum-like models proposed in the literature. We tested the proposed network with several empirical data from the literature, mainly from the Prisoner's Dilemma game and the Two Stage Gambling game. The results obtained show that the proposed quantum Bayesian Network is a general method that can accommodate violations of the laws of classical probability theory and make accurate predictions regarding human decision-making in these scenarios.

[Establishment of the mathematic model of total quantum statistical moment standard similarity for application to medical theoretical research].

Science.gov (United States)

He, Fu-yuan; Deng, Kai-wen; Huang, Sheng; Liu, Wen-long; Shi, Ji-lian

2013-09-01

The paper aims to elucidate and establish a new mathematic model: the total quantum statistical moment standard similarity (TQSMSS) on the base of the original total quantum statistical moment model and to illustrate the application of the model to medical theoretical research. The model was established combined with the statistical moment principle and the normal distribution probability density function properties, then validated and illustrated by the pharmacokinetics of three ingredients in Buyanghuanwu decoction and of three data analytical method for them, and by analysis of chromatographic fingerprint for various extracts with different solubility parameter solvents dissolving the Buyanghanwu-decoction extract. The established model consists of four mainly parameters: (1) total quantum statistical moment similarity as ST, an overlapped area by two normal distribution probability density curves in conversion of the two TQSM parameters; (2) total variability as DT, a confidence limit of standard normal accumulation probability which is equal to the absolute difference value between the two normal accumulation probabilities within integration of their curve nodical; (3) total variable probability as 1-Ss, standard normal distribution probability within interval of D(T); (4) total variable probability (1-beta)alpha and (5) stable confident probability beta(1-alpha): the correct probability to make positive and negative conclusions under confident coefficient alpha. With the model, we had analyzed the TQSMS similarities of pharmacokinetics of three ingredients in Buyanghuanwu decoction and of three data analytical methods for them were at range of 0.3852-0.9875 that illuminated different pharmacokinetic behaviors of each other; and the TQSMS similarities (ST) of chromatographic fingerprint for various extracts with different solubility parameter solvents dissolving Buyanghuanwu-decoction-extract were at range of 0.6842-0.999 2 that showed different constituents

Integrable lattice models and quantum groups

International Nuclear Information System (INIS)

Saleur, H.; Zuber, J.B.

1990-01-01

These lectures aim at introducing some basic algebraic concepts on lattice integrable models, in particular quantum groups, and to discuss some connections with knot theory and conformal field theories. The list of contents is: Vertex models and Yang-Baxter equation; Quantum sl(2) algebra and the Yang-Baxter equation; U q sl(2) as a symmetry of statistical mechanical models; Face models; Face models attached to graphs; Yang-Baxter equation, braid group and link polynomials

QInfer: Statistical inference software for quantum applications

Directory of Open Access Journals (Sweden)

Christopher Granade

2017-04-01

Full Text Available Characterizing quantum systems through experimental data is critical to applications as diverse as metrology and quantum computing. Analyzing this experimental data in a robust and reproducible manner is made challenging, however, by the lack of readily-available software for performing principled statistical analysis. We improve the robustness and reproducibility of characterization by introducing an open-source library, QInfer, to address this need. Our library makes it easy to analyze data from tomography, randomized benchmarking, and Hamiltonian learning experiments either in post-processing, or online as data is acquired. QInfer also provides functionality for predicting the performance of proposed experimental protocols from simulated runs. By delivering easy-to-use characterization tools based on principled statistical analysis, QInfer helps address many outstanding challenges facing quantum technology.

Satyendranath Bose: Co-Founder of Quantum Statistics

Science.gov (United States)

Blanpied, William A.

1972-01-01

Satyendranath Bose was first to prove Planck's Law by using ideal quantum gas. Einstein credited Bose for this first step in the development of quantum statistical mechanics. Bose did not realize the importance of his work, perhaps because of peculiar academic settings in India under British rule. (PS)

Quantum entanglement and teleportation using statistical correlations

Indian Academy of Sciences (India)

Administrator

Abstract. A study of quantum teleportation using two and three-particle correlated density matrix is presented. A criterion based on standard quantum statistical correlations employed in the many-body virial expansion is used to determine the extent of entanglement for a 2N-particle system. A relation between the probability ...

Unifying quantum heat transfer in a nonequilibrium spin-boson model with full counting statistics

Science.gov (United States)

Wang, Chen; Ren, Jie; Cao, Jianshu

2017-02-01

To study the full counting statistics of quantum heat transfer in a driven nonequilibrium spin-boson model, we develop a generalized nonequilibrium polaron-transformed Redfield equation with an auxiliary counting field. This enables us to study the impact of qubit-bath coupling ranging from weak to strong regimes. Without external modulations, we observe maximal values of both steady-state heat flux and noise power in moderate coupling regimes, below which we find that these two transport quantities are enhanced by the finite-qubit-energy bias. With external modulations, the geometric-phase-induced heat flux shows a monotonic decrease upon increasing the qubit-bath coupling at zero qubit energy bias (without bias). While under the finite-qubit-energy bias (with bias), the geometric-phase-induced heat flux exhibits an interesting reversal behavior in the strong coupling regime. Our results unify the seemingly contradictory results in weak and strong qubit-bath coupling regimes and provide detailed dissections for the quantum fluctuation of nonequilibrium heat transfer.

Classical model of intermediate statistics

International Nuclear Information System (INIS)

Kaniadakis, G.

1994-01-01

In this work we present a classical kinetic model of intermediate statistics. In the case of Brownian particles we show that the Fermi-Dirac (FD) and Bose-Einstein (BE) distributions can be obtained, just as the Maxwell-Boltzmann (MD) distribution, as steady states of a classical kinetic equation that intrinsically takes into account an exclusion-inclusion principle. In our model the intermediate statistics are obtained as steady states of a system of coupled nonlinear kinetic equations, where the coupling constants are the transmutational potentials η κκ' . We show that, besides the FD-BE intermediate statistics extensively studied from the quantum point of view, we can also study the MB-FD and MB-BE ones. Moreover, our model allows us to treat the three-state mixing FD-MB-BE intermediate statistics. For boson and fermion mixing in a D-dimensional space, we obtain a family of FD-BE intermediate statistics by varying the transmutational potential η BF . This family contains, as a particular case when η BF =0, the quantum statistics recently proposed by L. Wu, Z. Wu, and J. Sun [Phys. Lett. A 170, 280 (1992)]. When we consider the two-dimensional FD-BE statistics, we derive an analytic expression of the fraction of fermions. When the temperature T→∞, the system is composed by an equal number of bosons and fermions, regardless of the value of η BF . On the contrary, when T=0, η BF becomes important and, according to its value, the system can be completely bosonic or fermionic, or composed both by bosons and fermions

Reversibility in Quantum Models of Stochastic Processes

Science.gov (United States)

Gier, David; Crutchfield, James; Mahoney, John; James, Ryan

Natural phenomena such as time series of neural firing, orientation of layers in crystal stacking and successive measurements in spin-systems are inherently probabilistic. The provably minimal classical models of such stochastic processes are ɛ-machines, which consist of internal states, transition probabilities between states and output values. The topological properties of the ɛ-machine for a given process characterize the structure, memory and patterns of that process. However ɛ-machines are often not ideal because their statistical complexity (Cμ) is demonstrably greater than the excess entropy (E) of the processes they represent. Quantum models (q-machines) of the same processes can do better in that their statistical complexity (Cq) obeys the relation Cμ >= Cq >= E. q-machines can be constructed to consider longer lengths of strings, resulting in greater compression. With code-words of sufficiently long length, the statistical complexity becomes time-symmetric - a feature apparently novel to this quantum representation. This result has ramifications for compression of classical information in quantum computing and quantum communication technology.

Interaction of a quantum well with squeezed light: Quantum-statistical properties

International Nuclear Information System (INIS)

Sete, Eyob A.; Eleuch, H.

2010-01-01

We investigate the quantum statistical properties of the light emitted by a quantum well interacting with squeezed light from a degenerate subthreshold optical parametric oscillator. We obtain analytical solutions for the pertinent quantum Langevin equations in the strong-coupling and low-excitation regimes. Using these solutions we calculate the intensity spectrum, autocorrelation function, and quadrature squeezing for the fluorescent light. We show that the fluorescent light exhibits bunching and quadrature squeezing. We also show that the squeezed light leads to narrowing of the width of the spectrum of the fluorescent light.

Quantum statistics of many-particle systems

International Nuclear Information System (INIS)

Kraeft, W.D.; Ebeling, W.; Kremp, D.; Ropke, G.

1986-01-01

This paper presents the elements of quantum statistics and discusses the quantum mechanics of many-particle systems. The method of second quantization is discussed and the Bogolyubov hierarchy is examined. The general properties of the correlation function and one-particle Green's function are examined. The paper presents dynamical and thermodynamical information contained in the spectral function. An equation of motion is given for the one-particle Green's function. T-matrix and thermodynamic properties in binary collision approximation are discussed

The scientifiv way of thinking in statistics, statistical physics and quantum mechanics

OpenAIRE

Săvoiu, Gheorghe

2008-01-01

This paper focuses on the way of thinking in both classical and modern Physics and Statistics, Statistical Mechanics or Statistical Physics and Quantum Mechanics. These different statistical ways of thinking and their specific methods have generated new fields for new activities and new scientific disciplines, like Econophysics (between Economics and Physics), Sociophysics (between Sociology and Physics), Mediaphysics (between all media and comunication sciences), etc. After describing some r...

The scientific way of thinking in statistics, statistical physics and quantum mechanics

OpenAIRE

Săvoiu, Gheorghe

2008-01-01

This paper focuses on the way of thinking in both classical and modern Physics and Statistics, Statistical Mechanics or Statistical Physics and Quantum Mechanics. These different statistical ways of thinking and their specific methods have generated new fields for new activities and new scientific disciplines, like Econophysics (between Economics and Physics), Sociophysics (between Sociology and Physics), Mediaphysics (between all media and comunication sciences), etc. After describing some r...

Applications of quantum entropy to statistics

International Nuclear Information System (INIS)

Silver, R.N.; Martz, H.F.

1994-01-01

This paper develops two generalizations of the maximum entropy (ME) principle. First, Shannon classical entropy is replaced by von Neumann quantum entropy to yield a broader class of information divergences (or penalty functions) for statistics applications. Negative relative quantum entropy enforces convexity, positivity, non-local extensivity and prior correlations such as smoothness. This enables the extension of ME methods from their traditional domain of ill-posed in-verse problems to new applications such as non-parametric density estimation. Second, given a choice of information divergence, a combination of ME and Bayes rule is used to assign both prior and posterior probabilities. Hyperparameters are interpreted as Lagrange multipliers enforcing constraints. Conservation principles are proposed to act statistical regularization and other hyperparameters, such as conservation of information and smoothness. ME provides an alternative to heirarchical Bayes methods

Energy-level statistics and time relaxation in quantum systems

International Nuclear Information System (INIS)

Gruver, J.L.; Cerdeira, H.A.; Aliaga, J.; Mello, P.A.; Proto, A.N.

1997-05-01

We study a quantum-mechanical system, prepared, at t = 0, in a model state, that subsequently decays into a sea of other states whose energy levels form a discrete spectrum with given statistical properties. An important quantity is the survival probability P(t), defined as the probability, at time t, to find the system in the original model state. Our main purpose is to analyze the influence of the discreteness and statistical properties of the spectrum on the behavior of P(t). Since P(t) itself is a statistical quantity, we restrict our attention to its ensemble average , which is calculated analytically using random-matrix techniques, within certain approximations discussed in the text. We find, for , an exponential decay, followed by a revival, governed by the two-point structure of the statistical spectrum, thus giving a nonzero asymptotic value for large t's. The analytic result compares well with a number of computer simulations, over a time range discussed in the text. (author). 17 refs, 1 fig

Quantum statistical entropy corresponding to cosmic horizon in five-dimensional spacetime

Institute of Scientific and Technical Information of China (English)

2008-01-01

The generalized uncertainty relation is introduced to calculate the quantum statis-tical entropy corresponding to cosmic horizon. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is no divergent logarithmic term in the original brick-wall method. And it is obtained that the quantum statistical en-tropy corresponding to cosmic horizon is proportional to the area of the horizon. Further it is shown that the entropy corresponding to cosmic horizon is the entropy of quantum state on the surface of horizon. The black hole’s entropy is the intrinsic property of the black hole. The entropy is a quantum effect. In our calculation, by using the quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of five-dimensional spacetime. We provide a way to study the quantum statistical entropy corresponding to cosmic horizon in the higher-dimensional spacetime.

Quantum theory as an emergent phenomenon the statistical mechanics of matrix models as the precursor of quantum field theory

CERN Document Server

Adler, Stephen L

2004-01-01

Quantum mechanics is our most successful physical theory. However, it raises conceptual issues that have perplexed physicists and philosophers of science for decades. This 2004 book develops an approach, based on the proposal that quantum theory is not a complete, final theory, but is in fact an emergent phenomenon arising from a deeper level of dynamics. The dynamics at this deeper level are taken to be an extension of classical dynamics to non-commuting matrix variables, with cyclic permutation inside a trace used as the basic calculational tool. With plausible assumptions, quantum theory is shown to emerge as the statistical thermodynamics of this underlying theory, with the canonical commutation/anticommutation relations derived from a generalized equipartition theorem. Brownian motion corrections to this thermodynamics are argued to lead to state vector reduction and to the probabilistic interpretation of quantum theory, making contact with phenomenological proposals for stochastic modifications to Schr�...

Quantum versus classical statistical dynamics of an ultracold Bose gas

International Nuclear Information System (INIS)

Berges, Juergen; Gasenzer, Thomas

2007-01-01

We investigate the conditions under which quantum fluctuations are relevant for the quantitative interpretation of experiments with ultracold Bose gases. This requires to go beyond the description in terms of the Gross-Pitaevskii and Hartree-Fock-Bogoliubov mean-field theories, which can be obtained as classical (statistical) field-theory approximations of the quantum many-body problem. We employ functional-integral techniques based on the two-particle irreducible (2PI) effective action. The role of quantum fluctuations is studied within the nonperturbative 2PI 1/N expansion to next-to-leading order. At this accuracy level memory integrals enter the dynamic equations, which differ for quantum and classical statistical descriptions. This can be used to obtain a classicality condition for the many-body dynamics. We exemplify this condition by studying the nonequilibrium evolution of a one-dimensional Bose gas of sodium atoms, and discuss some distinctive properties of quantum versus classical statistical dynamics

Sub-Poissonian statistics of quantum jumps in single molecule or atomic ion

International Nuclear Information System (INIS)

Osad'ko, I.S.; Gus'kov, D.N.

2007-01-01

A theory for statistics of quantum jumps in single molecule or ion driven by continues wave laser field is developed. These quantum jumps can relate to nonradiative singlet-triplet transitions in a molecule or to on → off jumps in a single ion with shelving processes. Distribution function w N (T) of quantum jumps in time interval T is found. Computer simulation of quantum jumps is realized. Statistical treatment of simulated jumps reveals sub-Poissonian statistics of quantum jumps. The theoretical distribution function w N (T) fits well the distribution of jumps found from simulated data. Experimental data on quantum jumps found in experiments with single Hg + ion are described by the function w N (T) well

Analogies between classical statistical mechanics and quantum mechanics

International Nuclear Information System (INIS)

Uehara, M.

1986-01-01

Some analogies between nonequilibrium classical statistical mechanics and quantum mechanics, at the level of the Liouville equation and at the kinetic level, are commented on. A theorem, related to the Vlasov equation applied to a plasma, is proved. The theorem presents an analogy with Ehrenfest's theorem of quantum mechanics. An analogy between the plasma kinetic theory and Bohm's quantum theory with 'hidden variables' is also shown. (Author) [pt

Statistical separability and the impossibility of the superluminal quantum communication

International Nuclear Information System (INIS)

Zhang Qiren

2004-01-01

The authors analyse the relation and the difference between the quantum correlation of two points in space and the communication between them. The statistical separability of two points in the space is defined and proven. From this statistical separability, authors prove that the superluminal quantum communication between different points is impossible. To emphasis the compatibility between the quantum theory and the relativity, authors write the von Neumann equation of density operator evolution in the multi-time form. (author)

Quantum-like model of unconscious–conscious dynamics

Science.gov (United States)

Khrennikov, Andrei

2015-01-01

We present a quantum-like model of sensation–perception dynamics (originated in Helmholtz theory of unconscious inference) based on the theory of quantum apparatuses and instruments. We illustrate our approach with the model of bistable perception of a particular ambiguous figure, the Schröder stair. This is a concrete model for unconscious and conscious processing of information and their interaction. The starting point of our quantum-like journey was the observation that perception dynamics is essentially contextual which implies impossibility of (straightforward) embedding of experimental statistical data in the classical (Kolmogorov, 1933) framework of probability theory. This motivates application of nonclassical probabilistic schemes. And the quantum formalism provides a variety of the well-approved and mathematically elegant probabilistic schemes to handle results of measurements. The theory of quantum apparatuses and instruments is the most general quantum scheme describing measurements and it is natural to explore it to model the sensation–perception dynamics. In particular, this theory provides the scheme of indirect quantum measurements which we apply to model unconscious inference leading to transition from sensations to perceptions. PMID:26283979

Derivation of quantum statistics from Gauss's principle and the second law

International Nuclear Information System (INIS)

Lavenda, B.H.

1988-01-01

Quantum statistical laws are derived from bona fide stationary probability distributions of physical stochastic processes. These distributions are shown to be the laws of error for which the average occupation numbers are the most probable values. They determine uniquely the statistical entropy functions and the second law gives the quantum statistical distributions

Fisher information and quantum potential well model for finance

Energy Technology Data Exchange (ETDEWEB)

Nastasiuk, V.A., E-mail: nasa@i.ua

2015-09-25

The probability distribution function (PDF) for prices on financial markets is derived by extremization of Fisher information. It is shown how on that basis the quantum-like description for financial markets arises and different financial market models are mapped by quantum mechanical ones. - Highlights: • The financial Schrödinger equation is derived using the principle of minimum Fisher information. • Statistical models for price variation are mapped by the quantum models of coupled particle. • The model of quantum particle in parabolic potential well corresponds to Efficient market.

Fisher information and quantum potential well model for finance

International Nuclear Information System (INIS)

Nastasiuk, V.A.

2015-01-01

The probability distribution function (PDF) for prices on financial markets is derived by extremization of Fisher information. It is shown how on that basis the quantum-like description for financial markets arises and different financial market models are mapped by quantum mechanical ones. - Highlights: • The financial Schrödinger equation is derived using the principle of minimum Fisher information. • Statistical models for price variation are mapped by the quantum models of coupled particle. • The model of quantum particle in parabolic potential well corresponds to Efficient market

Infinite Random Graphs as Statistical Mechanical Models

DEFF Research Database (Denmark)

Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria

2011-01-01

We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe a ...

Quantum statistics and liquid helium 3 - helum 4 mixtures

International Nuclear Information System (INIS)

Cohen, E.G.D.

1979-01-01

The behaviour of liquid helium 3-helium 4 mixtures is considered from the point of view of manifestation of quantum statistics effects in macrophysics. The Boze=Einstein statistics is shown to be of great importance for understanding superfluid helium-4 properties whereas the Fermi-Dirac statistics is of importance for understanding helium-3 properties. Without taking into consideration the interaction between the helium atoms it is impossible to understand the basic properties of liquid helium 33 - helium 4 mixtures at constant pressure. Proposed is a simple model of the liquid helium 3-helium 4 mixture, namely the binary mixture consisting of solid spheres of two types subjecting to the Fermi-Dirac and Bose-Einstein statistics relatively. This model predicts correctly the most surprising peculiarities of phase diagrams of concentration dependence on temperature for helium solutions. In particular, the helium 4 Bose-Einstein statistics is responsible for the phase lamination of helium solutions at low temperatures. It starts in the peculiar critical point. The helium 4 Fermi-Dirac statistics results in incomplete phase lamination close to the absolute zero temperatures, that permits operation of a powerful cooling facility, namely refrigerating machine on helium solution

Quantum mean-field approximation for lattice quantum models: Truncating quantum correlations and retaining classical ones

Science.gov (United States)

Malpetti, Daniele; Roscilde, Tommaso

2017-02-01

The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical

Statistical and stochastic aspects of the delocalization problem in quantum mechanics

International Nuclear Information System (INIS)

Claverie, P.; Diner, S.

1976-01-01

The space-time behaviour of electrons in atoms and molecules is reviewed. The wave conception of the electron is criticized and the poverty of the non-reductionist attitude is underlined. Further, the two main interpretations of quantum mechanics are recalled: the Copenhagen and the Statistical Interpretations. The meaning and the successes of the Statistical Interpretation are explained and it is shown that it does not solve all problems because quantum mechanics is irreducible to a classical statistical theory. The fluctuation of the particle number and its relationship to loge theory, delocalization and correlation is studied. Finally, different stochastic models for microphysics are reviewed. The markovian Fenyes-Nelson process allows an interpretation of the original heuristic considerations of Schroedinger. Non-markov processes with Schroedinger time evolution are shown to be equivalent to the base state analysis of Feynmann but they are unsatisfactory from a probabilistic point of view. Stochastic electrodynamics is presented as the most satisfactory conception nowadays

Statistical properties of quantum entanglement and information entropy

International Nuclear Information System (INIS)

Abdel-Aty, M.M.A.

2007-03-01

Key words: entropy, entanglement, atom-field interaction, trapped ions, cold atoms, information entropy. Objects of research: Pure state entanglement, entropy squeezing mazer. The aim of the work: Study of the new entanglement features and new measures for both pure-state and mixed state of particle-field interaction. Also, the impact of the information entropy on the quantum information theory. Method of investigation: Methods of theoretical physics and applied mathematics (statistical physics, quantum optics) are used. Results obtained and their novelty are: All the results of the dissertation are new and many new features have been discovered. Particularly: the most general case of the pure state entanglement has been introduced. Although various special aspects of the quantum entropy have been investigated previously, the general features of the dynamics, when a multi-level system and a common environment are considered, have not been treated before and our work therefore, field a gap in the literature. Specifically: 1) A new entanglement measure due to quantum mutual entropy (mixed-state entanglement) we called it DEM, has been introduced, 2) A new treatment of the atomic information entropy in higher level systems has been presented. The problem has been completely solved in the case of three-level system, 3) A new solution of the interaction between the ultra cold atoms and cavity field has been discovered, 4) Some new models of the atom-field interaction have been adopted. Practical value: The subject carries out theoretic character. Application region: Results can be used in quantum computer developments. Also, the presented results can be used for further developments of the quantum information and quantum communications. (author)

Multiparticle quantum mechanics obeying fractional statistics

International Nuclear Information System (INIS)

Wu, Y.

1984-01-01

We obtain the rule governing many-body wave functions for particles obeying fractional statistics in two (space) dimensions. It generalizes and continuously interpolates the usual symmetrization and antisymmetrization. Quantum mechanics of more than two particles is discussed and some new features are found

A quantum hydrodynamic model for multicomponent quantum magnetoplasma with Jeans term

International Nuclear Information System (INIS)

Masood, W.; Salimullah, M.; Shah, H.A.

2008-01-01

The effect of Jeans term in a multicomponent self-gravitating quantum magnetoplasma is investigated employing the quantum hydrodynamic (QHD) model. The effects of quantum Bohm potential and statistical terms as well as the ambient magnetic field are also investigated on both dust and ion dynamics driven waves in this Letter. We state the conditions that can drive the system unstable in the presence of Jeans term. The limiting cases are also presented. The present work may have relevance in the dense astrophysical environments where the self-gravitating effects are expected to play a pivotal role

Mathematical methods in quantum and statistical mechanics

International Nuclear Information System (INIS)

Fishman, L.

1977-01-01

The mathematical structure and closed-form solutions pertaining to several physical problems in quantum and statistical mechanics are examined in some detail. The J-matrix method, introduced previously for s-wave scattering and based upon well-established Hilbert Space theory and related generalized integral transformation techniques, is extended to treat the lth partial wave kinetic energy and Coulomb Hamiltonians within the context of square integrable (L 2 ), Laguerre (Slater), and oscillator (Gaussian) basis sets. The theory of relaxation in statistical mechanics within the context of the theory of linear integro-differential equations of the Master Equation type and their corresponding Markov processes is examined. Several topics of a mathematical nature concerning various computational aspects of the L 2 approach to quantum scattering theory are discussed

Quantum - statistical equation of state

International Nuclear Information System (INIS)

Kalitkin, N.N.; Kuz'mina, L.V.

1976-01-01

An atom model is considered which allows uniform description of the equation of an equilibrium plasma state in the range of densities from gas to superhigh ones and in the temperature range from 1-5 eV to a ten of keV. Quantum and exchange corrections to the Thomas-Fermi thermodynamic functions at non zero temperatures have been calculated. The calculated values have been compared with experimental data and with calculations performed by more accurate models. The differences result from the fact that a quantum approach does not allow for shell effects. The evaluation of these differences makes it possible to indicate the limits of applicability of the Thomas-Fermi model with quantum and exchange corrections. It turns out that if at zero temperature the model may be applied only for high compressions, at the temperature more than 1 eV it well describes the behaviour of plasma in a very wide range of densities and agrees satisfactorily with experiment even for non-ideal plasma

Quantum probability, choice in large worlds, and the statistical structure of reality.

Science.gov (United States)

Ross, Don; Ladyman, James

2013-06-01

Classical probability models of incentive response are inadequate in "large worlds," where the dimensions of relative risk and the dimensions of similarity in outcome comparisons typically differ. Quantum probability models for choice in large worlds may be motivated pragmatically - there is no third theory - or metaphysically: statistical processing in the brain adapts to the true scale-relative structure of the universe.

Quantum statistical theory of solid plasma (Com.1)

International Nuclear Information System (INIS)

Kim Yon Il

1986-01-01

In order to obtain the Hamiltonian of the electron system in solid plasma, the self-consistent electromagnetic field formed by the electron system is quantalized. In this process the longitudinal vector potential is introduced through the relation. The obtained Hamiltonian is expressed by the collective coordinate, consistent with D. Pines' result. Various quantum statistical expressions, the dispersion relation and sum rules of the transverse dielectric function are derived using the fact that the collectived cooredinates are connected with the electromagnetic field in the method in this paper. In additon, various quantum statistical expressions for the longitudinal dielectric function convenient for practical calculations are obtained besides the Nozieres-Pines' expression. (author)

Sanov and central limit theorems for output statistics of quantum Markov chains

Energy Technology Data Exchange (ETDEWEB)

Horssen, Merlijn van, E-mail: merlijn.vanhorssen@nottingham.ac.uk [School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD (United Kingdom); Guţă, Mădălin, E-mail: madalin.guta@nottingham.ac.uk [School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD (United Kingdom)

2015-02-15

In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Such higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not.

Machine learning Z2 quantum spin liquids with quasiparticle statistics

Science.gov (United States)

Zhang, Yi; Melko, Roger G.; Kim, Eun-Ah

2017-12-01

After decades of progress and effort, obtaining a phase diagram for a strongly correlated topological system still remains a challenge. Although in principle one could turn to Wilson loops and long-range entanglement, evaluating these nonlocal observables at many points in phase space can be prohibitively costly. With growing excitement over topological quantum computation comes the need for an efficient approach for obtaining topological phase diagrams. Here we turn to machine learning using quantum loop topography (QLT), a notion we have recently introduced. Specifically, we propose a construction of QLT that is sensitive to quasiparticle statistics. We then use mutual statistics between the spinons and visons to detect a Z2 quantum spin liquid in a multiparameter phase space. We successfully obtain the quantum phase boundary between the topological and trivial phases using a simple feed-forward neural network. Furthermore, we demonstrate advantages of our approach for the evaluation of phase diagrams relating to speed and storage. Such statistics-based machine learning of topological phases opens new efficient routes to studying topological phase diagrams in strongly correlated systems.

The spin-statistics connection in quantum gravity

International Nuclear Information System (INIS)

Balachandran, A.P.; Batista, E.; Costa e Silva, I.P.; Teotonio-Sobrinho, P.

2000-01-01

It is well known that in spite of sharing some properties with conventional particles, topological geons in general violate the spin-statistics theorem. On the other hand, it is generally believed that in quantum gravity theories allowing for topology change, using pair creation and annihilation of geons, one should be able to recover this theorem. In this paper, we take an alternative route, and use an algebraic formalism developed in previous work. We give a description of topological geons where an algebra of 'observables' is identified and quantized. Different irreducible representations of this algebra correspond to different kinds of geons, and are labeled by a non-abelian 'charge' and 'magnetic flux'. We then find that the usual spin-statistics theorem is indeed violated, but a new spin-statistics relation arises, when we assume that the fluxes are superselected. This assumption can be proved if all observables are local, as is generally the case in physical theories. Finally, we also discuss how our approach fits into conventional formulations of quantum gravity

Full Counting Statistics for Interacting Fermions with Determinantal Quantum Monte Carlo Simulations.

Science.gov (United States)

Humeniuk, Stephan; Büchler, Hans Peter

2017-12-08

We present a method for computing the full probability distribution function of quadratic observables such as particle number or magnetization for the Fermi-Hubbard model within the framework of determinantal quantum Monte Carlo calculations. Especially in cold atom experiments with single-site resolution, such a full counting statistics can be obtained from repeated projective measurements. We demonstrate that the full counting statistics can provide important information on the size of preformed pairs. Furthermore, we compute the full counting statistics of the staggered magnetization in the repulsive Hubbard model at half filling and find excellent agreement with recent experimental results. We show that current experiments are capable of probing the difference between the Hubbard model and the limiting Heisenberg model.

Higher-Order Statistical Correlations and Mutual Information Among Particles in a Quantum Well

Science.gov (United States)

Yépez, V. S.; Sagar, R. P.; Laguna, H. G.

2017-12-01

The influence of wave function symmetry on statistical correlation is studied for the case of three non-interacting spin-free quantum particles in a unidimensional box, in position and in momentum space. Higher-order statistical correlations occurring among the three particles in this quantum system is quantified via higher-order mutual information and compared to the correlation between pairs of variables in this model, and to the correlation in the two-particle system. The results for the higher-order mutual information show that there are states where the symmetric wave functions are more correlated than the antisymmetric ones with same quantum numbers. This holds in position as well as in momentum space. This behavior is opposite to that observed for the correlation between pairs of variables in this model, and the two-particle system, where the antisymmetric wave functions are in general more correlated. These results are also consistent with those observed in a system of three uncoupled oscillators. The use of higher-order mutual information as a correlation measure, is monitored and examined by considering a superposition of states or systems with two Slater determinants.

Higher-Order Statistical Correlations and Mutual Information Among Particles in a Quantum Well

International Nuclear Information System (INIS)

Yépez, V. S.; Sagar, R. P.; Laguna, H. G.

2017-01-01

The influence of wave function symmetry on statistical correlation is studied for the case of three non-interacting spin-free quantum particles in a unidimensional box, in position and in momentum space. Higher-order statistical correlations occurring among the three particles in this quantum system is quantified via higher-order mutual information and compared to the correlation between pairs of variables in this model, and to the correlation in the two-particle system. The results for the higher-order mutual information show that there are states where the symmetric wave functions are more correlated than the antisymmetric ones with same quantum numbers. This holds in position as well as in momentum space. This behavior is opposite to that observed for the correlation between pairs of variables in this model, and the two-particle system, where the antisymmetric wave functions are in general more correlated. These results are also consistent with those observed in a system of three uncoupled oscillators. The use of higher-order mutual information as a correlation measure, is monitored and examined by considering a superposition of states or systems with two Slater determinants. (author)

A quantum relativistic integrable model as the continuous limit of the six-vertex model

International Nuclear Information System (INIS)

Zhou, Y.K.

1992-01-01

The six-vertex model in two-dimensional statistical mechanics is used to construct the L-matrix of a one-dimensional quantum relativistic integrable model through a continuous limit. This is the first step to extend the method used earlier by the author to construct quantum completely integrable systems from other well-known two-dimensional vertex models. (orig.)

Incorporation of quantum statistical features in molecular dynamics

International Nuclear Information System (INIS)

Ohnishi, Akira; Randrup, J.

1995-01-01

We formulate a method for incorporating quantum fluctuations into molecular-dynamics simulations of many-body systems, such as those employed for energetic nuclear collision processes. Based on Fermi's Golden Rule, we allow spontaneous transitions to occur between the wave packets which are not energy eigenstates. The ensuing diffusive evolution in the space of the wave packet parameters exhibits appealing physical properties, including relaxation towards quantum-statistical equilibrium. (author)

Analysis of proton-induced fragment production cross sections by the Quantum Molecular Dynamics plus Statistical Decay Model

Energy Technology Data Exchange (ETDEWEB)

Chiba, Satoshi; Iwamoto, Osamu; Fukahori, Tokio; Niita, Koji; Maruyama, Toshiki; Maruyama, Tomoyuki; Iwamoto, Akira [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment

1997-03-01

The production cross sections of various fragments from proton-induced reactions on {sup 56}Fe and {sup 27}Al have been analyzed by the Quantum Molecular Dynamics (QMD) plus Statistical Decay Model (SDM). It was found that the mass and charge distributions calculated with and without the statistical decay have very different shapes. These results also depend strongly on the impact parameter, showing an importance of the dynamical treatment as realized by the QMD approach. The calculated results were compared with experimental data in the energy region from 50 MeV to 5 GeV. The QMD+SDM calculation could reproduce the production cross sections of the light clusters and intermediate-mass to heavy fragments in a good accuracy. The production cross section of {sup 7}Be was, however, underpredicted by approximately 2 orders of magnitude, showing the necessity of another reaction mechanism not taken into account in the present model. (author)

Statistical Characterization of Dispersed Single-Wall Carbon Nanotube Quantum Dots

International Nuclear Information System (INIS)

Shimizu, M; Moriyama, S; Suzuki, M; Fuse, T; Homma, Y; Ishibashi, K

2006-01-01

Quantum dots have been fabricated in single-wall carbon nanotubes (SWCNTs) simply by depositing metallic contacts on top of them. The fabricated quantum dots show different characteristics from sample to sample, which are even different in samples fabricated in the same chip. In this report, we study the statistical variations of the quantum dots fabricated with our method, and suggest their possible origin

Experimental statistical signature of many-body quantum interference

Science.gov (United States)

Giordani, Taira; Flamini, Fulvio; Pompili, Matteo; Viggianiello, Niko; Spagnolo, Nicolò; Crespi, Andrea; Osellame, Roberto; Wiebe, Nathan; Walschaers, Mattia; Buchleitner, Andreas; Sciarrino, Fabio

2018-03-01

Multi-particle interference is an essential ingredient for fundamental quantum mechanics phenomena and for quantum information processing to provide a computational advantage, as recently emphasized by boson sampling experiments. Hence, developing a reliable and efficient technique to witness its presence is pivotal in achieving the practical implementation of quantum technologies. Here, we experimentally identify genuine many-body quantum interference via a recent efficient protocol, which exploits statistical signatures at the output of a multimode quantum device. We successfully apply the test to validate three-photon experiments in an integrated photonic circuit, providing an extensive analysis on the resources required to perform it. Moreover, drawing upon established techniques of machine learning, we show how such tools help to identify the—a priori unknown—optimal features to witness these signatures. Our results provide evidence on the efficacy and feasibility of the method, paving the way for its adoption in large-scale implementations.

Critical examination of logical formulations in quantum theory. Statistical inference and Hilbertian distance between quantum states

International Nuclear Information System (INIS)

Hadjisawas, Nicolas.

1982-01-01

After a critical study of the logical quantum mechanics formulations of Jauch and Piron, classical and quantum versions of statistical inference are studied. In order to do this, the significance of the Jaynes and Kulback principles (maximum likelihood, least squares principles) is revealed from the theorems established. In the quantum mechanics inference problem, a ''distance'' between states is defined. This concept is used to solve the quantum equivalent of the classical problem studied by Kulback. The ''projection postulate'' proposition is subsequently deduced [fr

Semiclassical quantum gravity: statistics of combinatorial Riemannian geometries

International Nuclear Information System (INIS)

Bombelli, L.; Corichi, A.; Winkler, O.

2005-01-01

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at ''quantum scales'' and continuum, classical geometries at large scales. Such a correspondence can be meaningfully established when one has a ''semiclassical'' state in the underlying quantum gravity theory, and the uncertainties in the correspondence arise both from quantum fluctuations in this state and from the kinematical procedure of matching a smooth geometry to a discrete one. We focus on the latter type of uncertainty, and suggest the use of statistical geometry as a way to quantify it. With a cell complex as an example of discrete structure, we discuss how to construct quantities that define a smooth geometry, and how to estimate the associated uncertainties. We also comment briefly on how to combine our results with uncertainties in the underlying quantum state, and on their use when considering phenomenological aspects of quantum gravity. (Abstract Copyright [2005], Wiley Periodicals, Inc.)

Annotations to quantum statistical mechanics

CERN Document Server

Kim, In-Gee

2018-01-01

This book is a rewritten and annotated version of Leo P. Kadanoff and Gordon Baym’s lectures that were presented in the book Quantum Statistical Mechanics: Green’s Function Methods in Equilibrium and Nonequilibrium Problems. The lectures were devoted to a discussion on the use of thermodynamic Green’s functions in describing the properties of many-particle systems. The functions provided a method for discussing finite-temperature problems with no more conceptual difficulty than ground-state problems, and the method was equally applicable to boson and fermion systems and equilibrium and nonequilibrium problems. The lectures also explained nonequilibrium statistical physics in a systematic way and contained essential concepts on statistical physics in terms of Green’s functions with sufficient and rigorous details. In-Gee Kim thoroughly studied the lectures during one of his research projects but found that the unspecialized method used to present them in the form of a book reduced their readability. He st...

Solvable model of quantum microcanonical states

International Nuclear Information System (INIS)

Bender, Carl M; Brody, Dorje C; Hook, Daniel W

2005-01-01

This letter examines the consequences of a recently proposed modification of the postulate of equal a priori probability in quantum statistical mechanics. This modification, called the quantum microcanonical postulate (QMP), asserts that for a system in microcanonical equilibrium all pure quantum states having the same energy expectation value are realized with equal probability. A simple model of a quantum system that obeys the QMP and that has a nondegenerate spectrum with equally spaced energy eigenvalues is studied. This model admits a closed-form expression for the density of states in terms of the energy eigenvalues. It is shown that in the limit as the number of energy levels approaches infinity, the expression for the density of states converges to a δ function centred at the intermediate value (E max + E min )/2 of the energy. Determining this limit requires an elaborate asymptotic study of an infinite sum whose terms alternate in sign. (letter to the editor)

Some connections between relativistic classical mechanics, statistical mechanics, and quantum field theory

International Nuclear Information System (INIS)

Remler, E.A.

1977-01-01

A gauge-invariant version of the Wigner representation is used to relate relativistic mechanics, statistical mechanics, and quantum field theory in the context of the electrodynamics of scalar particles. A unified formulation of quantum field theory and statistical mechanics is developed which clarifies the physics interpretation of the single-particle Wigner function. A covariant form of Ehrenfest's theorem is derived. Classical electrodynamics is derived from quantum field theory after making a random-phase approximation. The validity of this approximation is discussed

Quantum Oscillator in the Thermostat as a Model in the Thermodynamics of Open Quantum Systems

OpenAIRE

Sukhanov, Aleksander

2005-01-01

The quantum oscillator in the thermostat is considered as the model of an open quantum system. Our analysis will be heavily founded on the use of the Schroedinger generalized uncertainties relations (SUR). Our first aim is to demonstrate that for the quantum oscillator the state of thermal equilibrium belongs to the correlated coherent states (CCS), which imply the saturation of SUR at any temperature. The obtained results open the perspective for the search of some statistical theory, which ...

Agents with left and right dominant hemispheres and quantum statistics

Science.gov (United States)

Ezhov, Alexandr A.; Khrennikov, Andrei Yu.

2005-01-01

We present a multiagent model illustrating the emergence of two different quantum statistics, Bose-Einstein and Fermi-Dirac, in a friendly population of individuals with the right-brain dominance and in a competitive population of individuals with the left-brain hemisphere dominance, correspondingly. Doing so, we adduce the arguments that Lefebvre’s “algebra of conscience” can be used in a natural way to describe decision-making strategies of agents simulating people with different brain dominance. One can suggest that the emergence of the two principal statistical distributions is able to illustrate different types of society organization and also to be used in order to simulate market phenomena and psychic disorders, when a switching of hemisphere dominance is involved.

Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

Science.gov (United States)

Williams Colin P.

1999-01-01

Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

Spectral deformation techniques applied to the study of quantum statistical irreversible processes

International Nuclear Information System (INIS)

Courbage, M.

1978-01-01

A procedure of analytic continuation of the resolvent of Liouville operators for quantum statistical systems is discussed. When applied to the theory of irreversible processes of the Brussels School, this method supports the idea that the restriction to a class of initial conditions is necessary to obtain an irreversible behaviour. The general results are tested on the Friedrichs model. (Auth.)

On the Effect of Dipole-Dipole Interactions on the Quantum Statistics of Surface Plasmons in Multiparticle Spaser Systems

Science.gov (United States)

Shesterikov, A. V.; Gubin, M. Yu.; Karpov, S. N.; Prokhorov, A. V.

2018-04-01

The problem of controlling the quantum dynamics of localized plasmons has been considered in the model of a four-particle spaser composed of metallic nanoparticles and semiconductor quantum dots. Conditions for the observation of stable steady-state regimes of the formation of surface plasmons in this model have been determined in the mean-field approximation. It has been shown that the presence of strong dipole-dipole interactions between metallic nanoparticles of the spaser system leads to a considerable change in the quantum statistics of plasmons generated on the nanoparticles.

Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems.

Science.gov (United States)

Gogolin, Christian; Eisert, Jens

2016-05-01

We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.

Quantum-like microeconomics: Statistical model of distribution of investments and production

Science.gov (United States)

Khrennikov, Andrei

2008-10-01

In this paper we demonstrate that the probabilistic quantum-like (QL) behavior-the Born’s rule, interference of probabilities, violation of Bell’s inequality, representation of variables by in general noncommutative self-adjoint operators, Schrödinger’s dynamics-can be exhibited not only by processes in the micro world, but also in economics. In our approach the QL-behavior is induced not by properties of systems. Here systems (commodities) are macroscopic. They could not be superpositions of two different states. In our approach the QL-behavior of economical statistics is a consequence of the organization of the process of production as well as investments. In particular, Hamiltonian (“financial energy”) is determined by rate of return.

Path integral molecular dynamics for exact quantum statistics of multi-electronic-state systems.

Science.gov (United States)

Liu, Xinzijian; Liu, Jian

2018-03-14

An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD), Liu et al. [J. Chem. Phys. 145, 024103 (2016)] and Zhang et al. [J. Chem. Phys. 147, 034109 (2017)], for quantum statistical mechanics when a single potential energy surface is involved. We first define an effective potential function that is numerically favorable for MES-PIMD and then derive corresponding estimators in MES-PIMD for evaluating various physical properties. Its application to several representative one-dimensional and multi-dimensional models demonstrates that MES-PIMD in principle offers a practical tool in either of the diabatic and adiabatic representations for studying exact quantum statistics of complex/large MES systems when the Born-Oppenheimer approximation, Condon approximation, and harmonic bath approximation are broken.

Statistical distribution of the local purity in a large quantum system

International Nuclear Information System (INIS)

De Pasquale, A; Pascazio, S; Facchi, P; Giovannetti, V; Parisi, G; Scardicchio, A

2012-01-01

The local purity of large many-body quantum systems can be studied by following a statistical mechanical approach based on a random matrix model. Restricting the analysis to the case of global pure states, this method proved to be successful, and a full characterization of the statistical properties of the local purity was obtained by computing the partition function of the problem. Here we generalize these techniques to the case of global mixed states. In this context, by uniformly sampling the phase space of states with assigned global mixedness, we determine the exact expression of the first two moments of the local purity and a general expression for the moments of higher order. This generalizes previous results obtained for globally pure configurations. Furthermore, through the introduction of a partition function for a suitable canonical ensemble, we compute the approximate expression of the first moment of the marginal purity in the high-temperature regime. In the process, we establish a formal connection with the theory of quantum twirling maps that provides an alternative, possibly fruitful, way of performing the calculation. (paper)

Introduction to nonequilibrium statistical mechanics with quantum field theory

International Nuclear Information System (INIS)

Kita, Takafumi

2010-01-01

In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson's equation. The aims are threefold: (1) to explain the fundamentals of nonequilibrium quantum field theory as simple as possible on the basis of the knowledge of the equilibrium counterpart; (2) to elucidate the hierarchy in describing nonequilibrium systems from Dyson's equation on the Keldysh contour to the Navier-Stokes equation in fluid mechanics via quantum transport equations and the Boltzmann equation; (3) to derive an expression of nonequilibrium entropy that evolves with time. In stage (1), we introduce nonequilibrium Green's function and the self-energy uniquely on the round-trip Keldysh contour, thereby avoiding possible confusions that may arise from defining multiple Green's functions at the very beginning. We try to present the Feynman rules for the perturbation expansion as simple as possible. In particular, we focus on the self-consistent perturbation expansion with the Luttinger-Ward thermodynamic functional, i.e., Baym's Φ-derivable approximation, which has a crucial property for nonequilibrium systems of obeying various conservation laws automatically. We also show how the two-particle correlations can be calculated within the Φ-derivable approximation, i.e., an issue of how to handle the 'Bogoliubov-Born-Green-Kirkwood-Yvons (BBGKY) hierarchy'. Aim (2) is performed through successive reductions of relevant variables with the Wigner transformation, the gradient expansion based on the Groenewold-Moyal product, and Enskog's expansion from local equilibrium. This part may be helpful for convincing readers that nonequilibrium systems can be handled microscopically with

Geometric Approach to Quantum Statistical Mechanics and Application to Casimir Energy and Friction Properties

International Nuclear Information System (INIS)

Ichinose, Shoichi

2010-01-01

A geometric approach to general quantum statistical systems (including the harmonic oscillator) is presented. It is applied to Casimir energy and the dissipative system with friction. We regard the (N+1)-dimensional Euclidean coordinate system (X i ,τ) as the quantum statistical system of N quantum (statistical) variables (X τ ) and one Euclidean time variable (t). Introducing paths (lines or hypersurfaces) in this space (X τ ,t), we adopt the path-integral method to quantize the mechanical system. This is a new view of (statistical) quantization of the mechanical system. The system Hamiltonian appears as the area. We show quantization is realized by the minimal area principle in the present geometric approach. When we take a line as the path, the path-integral expressions of the free energy are shown to be the ordinary ones (such as N harmonic oscillators) or their simple variation. When we take a hyper-surface as the path, the system Hamiltonian is given by the area of the hyper-surface which is defined as a closed-string configuration in the bulk space. In this case, the system becomes a O(N) non-linear model. We show the recently-proposed 5 dimensional Casimir energy (ArXiv:0801.3064,0812.1263) is valid. We apply this approach to the visco-elastic system, and present a new method using the path-integral for the calculation of the dissipative properties.

Quantum-like Modeling of Cognition

Science.gov (United States)

Khrennikov, Andrei

2015-09-01

This paper begins with a historical review of the mutual influence of physics and psychology, from Freud's invention of psychic energy inspired by von Boltzmann' thermodynamics to the enrichment quantum physics gained from the side of psychology by the notion of complementarity (the invention of Niels Bohr who was inspired by William James), besides we consider the resonance of the correspondence between Wolfgang Pauli and Carl Jung in both physics and psychology. Then we turn to the problem of development of mathematical models for laws of thought starting with Boolean logic and progressing towards foundations of classical probability theory. Interestingly, the laws of classical logic and probability are routinely violated not only by quantum statistical phenomena but by cognitive phenomena as well. This is yet another common feature between quantum physics and psychology. In particular, cognitive data can exhibit a kind of the probabilistic interference effect. This similarity with quantum physics convinced a multi-disciplinary group of scientists (physicists, psychologists, economists, sociologists) to apply the mathematical apparatus of quantum mechanics to modeling of cognition. We illustrate this activity by considering a few concrete phenomena: the order and disjunction effects, recognition of ambiguous figures, categorization-decision making. In Appendix 1 we briefly present essentials of theory of contextual probability and a method of representations of contextual probabilities by complex probability amplitudes (solution of the ``inverse Born's problem'') based on a quantum-like representation algorithm (QLRA).

Quantum-like Modeling of Cognition

Directory of Open Access Journals (Sweden)

Andrei eKhrennikov

2015-09-01

Full Text Available This paper begins with a historical review of the mutual influence of physics and psychology, from Freud's invention of psychic energy inspired by von Boltzmann' thermodynamics to the enrichment quantum physics gained from the side of psychology by the notion of complementarity (the invention of Niels Bohr who was inspired by William James, besides we consider the resonance of the correspondence between Wolfgang Pauli and Carl Jung in both physics and psychology. Then we turn to the problem of development of mathematical models for laws of thought starting with Boolean logic and progressing towards foundations of classical probability theory. Interestingly, the laws of classical logic and probability are routinely violated not only by quantum statistical phenomena but by cognitive phenomena as well. This is yet another common feature between quantum physics and psychology.In particular, cognitive data can exhibit a kind of the probabilistic interference effect. This similarity with quantum physics convinced a multi-disciplinary group of scientists (physicists, psychologists, economists, sociologists to apply the mathematical apparatus of quantum mechanics to modeling of cognition. We illustrate this activity by considering a few concrete phenomena: the order and disjunction effects, recognition of ambiguous figures, categorization-decision making.In Appendix 1 we briefly present essentials of theory of contextual probability and a method of representations of contextual probabilities by complex probability amplitudes(solution of the ``inverse Born's problem'' based on a quantum-like representation algorithm (QLRA.

Quantum statistical Monte Carlo methods and applications to spin systems

International Nuclear Information System (INIS)

Suzuki, M.

1986-01-01

A short review is given concerning the quantum statistical Monte Carlo method based on the equivalence theorem that d-dimensional quantum systems are mapped onto (d+1)-dimensional classical systems. The convergence property of this approximate tansformation is discussed in detail. Some applications of this general appoach to quantum spin systems are reviewed. A new Monte Carlo method, ''thermo field Monte Carlo method,'' is presented, which is an extension of the projection Monte Carlo method at zero temperature to that at finite temperatures

Quantum statistical field theory an introduction to Schwinger's variational method with Green's function nanoapplications, graphene and superconductivity

CERN Document Server

Morgenstern Horing, Norman J

2017-01-01

This book provides an introduction to the methods of coupled quantum statistical field theory and Green's functions. The methods of coupled quantum field theory have played a major role in the extensive development of nonrelativistic quantum many-particle theory and condensed matter physics. This introduction to the subject is intended to facilitate delivery of the material in an easily digestible form to advanced undergraduate physics majors at a relatively early stage of their scientific development. The main mechanism to accomplish this is the early introduction of variational calculus and the Schwinger Action Principle, accompanied by Green's functions. Important achievements of the theory in condensed matter and quantum statistical physics are reviewed in detail to help develop research capability. These include the derivation of coupled field Green's function equations-of-motion for a model electron-hole-phonon system, extensive discussions of retarded, thermodynamic and nonequilibrium Green's functions...

Statistical benchmarking for orthogonal electrostatic quantum dot qubit devices

Science.gov (United States)

Gamble, John; Frees, Adam; Friesen, Mark; Coppersmith, S. N.

2014-03-01

Quantum dots in semiconductor systems have emerged as attractive candidates for the implementation of quantum information processors because of the promise of scalability, manipulability, and integration with existing classical electronics. A limitation in current devices is that the electrostatic gates used for qubit manipulation exhibit strong cross-capacitance, presenting a barrier for practical scale-up. Here, we introduce a statistical framework for making precise the notion of orthogonality. We apply our method to analyze recently implemented designs at the University of Wisconsin-Madison that exhibit much increased orthogonal control than was previously possible. We then use our statistical modeling to future device designs, providing practical guidelines for devices to have robust control properties. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy Nuclear Security Administration under contract DE-AC04-94AL85000. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressly or implied, of the US Government. This work was supported in part by the Laboratory Directed Research and Development program at Sandia National Laboratories, by ARO (W911NF-12-0607), and by the United States Department of Defense.

Lie-superalgebraical aspects of quantum statistics

International Nuclear Information System (INIS)

Palev, T.D.

1978-01-01

The Lie-superalgebraical properties of the ordinary quantum statistics are discussed with the aim of possible generalization in quantum theory and in theoretical physics. It is indicated that the algebra generated by n pairs of Fermi or paraFermi operators is isomorphic to the classical simple Lie algebra Bsub(n) of the SO(2n+1) orthogonal group, whereas n pairs of Bose or paraBose operators generate the simple orthosympletic superalgebra B(O,n). The transition to infinite number of creation and annihilation operators (n → infinity) does not change a superalgebraic structure. Hence, ordinary Bose and Fermi quantization can be considered as quantization over definite irreducible representations of two simple Lie superalgebras. The idea is given of how one can introduce creation and annihilation operators that satisfy the second quantization postulates and generate other simple Lie superalgebras

Counting statistics of many-particle quantum walks

Science.gov (United States)

Mayer, Klaus; Tichy, Malte C.; Mintert, Florian; Konrad, Thomas; Buchleitner, Andreas

2011-06-01

We study quantum walks of many noninteracting particles on a beam splitter array as a paradigmatic testing ground for the competition of single- and many-particle interference in a multimode system. We derive a general expression for multimode particle-number correlation functions, valid for bosons and fermions, and infer pronounced signatures of many-particle interferences in the counting statistics.

Counting statistics of many-particle quantum walks

International Nuclear Information System (INIS)

Mayer, Klaus; Tichy, Malte C.; Buchleitner, Andreas; Mintert, Florian; Konrad, Thomas

2011-01-01

We study quantum walks of many noninteracting particles on a beam splitter array as a paradigmatic testing ground for the competition of single- and many-particle interference in a multimode system. We derive a general expression for multimode particle-number correlation functions, valid for bosons and fermions, and infer pronounced signatures of many-particle interferences in the counting statistics.

Introduction to modern theoretical physics. Volume II. Quantum theory and statistical physics

International Nuclear Information System (INIS)

Harris, E.G.

1975-01-01

The topics discussed include the history and principles, some solvable problems, and symmetry in quantum mechanics, interference phenomena, approximation methods, some applications of nonrelativistic quantum mechanics, relativistic wave equations, quantum theory of radiation, second quantization, elementary particles and their interactions, thermodynamics, equilibrium statistical mechanics and its applications, the kinetic theory of gases, and collective phenomena

On the geometry of the spin-statistics connection in quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Reyes, A.

2006-07-01

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishability and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be

Quantum random oracle model for quantum digital signature

Science.gov (United States)

Shang, Tao; Lei, Qi; Liu, Jianwei

2016-10-01

The goal of this work is to provide a general security analysis tool, namely, the quantum random oracle (QRO), for facilitating the security analysis of quantum cryptographic protocols, especially protocols based on quantum one-way function. QRO is used to model quantum one-way function and different queries to QRO are used to model quantum attacks. A typical application of quantum one-way function is the quantum digital signature, whose progress has been hampered by the slow pace of the experimental realization. Alternatively, we use the QRO model to analyze the provable security of a quantum digital signature scheme and elaborate the analysis procedure. The QRO model differs from the prior quantum-accessible random oracle in that it can output quantum states as public keys and give responses to different queries. This tool can be a test bed for the cryptanalysis of more quantum cryptographic protocols based on the quantum one-way function.

Quantum Theory for the Binomial Model in Finance Thoery

OpenAIRE

Chen, Zeqian

2001-01-01

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 statist...

Statistics of decay dynamics of quantum emitters in disordered photonic-crystal waveguides

DEFF Research Database (Denmark)

Javadi, Alisa; Garcia-Fernandez, Pedro David; Sapienza, Luca

2014-01-01

We present a statistical analysis of the spontaneous emission of quantum dots coupled to Anderson-localized cavities in disordered photonic-crystal waveguides.We observe an average Purcell factor of ∼ 5 with a maximum value of 24.......We present a statistical analysis of the spontaneous emission of quantum dots coupled to Anderson-localized cavities in disordered photonic-crystal waveguides.We observe an average Purcell factor of ∼ 5 with a maximum value of 24....

Quantum statistical effects in the mass transport of interstitial solutes in a crystalline solid

Science.gov (United States)

Woo, C. H.; Wen, Haohua

2017-09-01

The impact of quantum statistics on the many-body dynamics of a crystalline solid at finite temperatures containing an interstitial solute atom (ISA) is investigated. The Mori-Zwanzig theory allows the many-body dynamics of the crystal to be formulated and solved analytically within a pseudo-one-particle approach using the Langevin equation with a quantum fluctuation-dissipation relation (FDR) based on the Debye model. At the same time, the many-body dynamics is also directly solved numerically via the molecular dynamics approach with a Langevin heat bath based on the quantum FDR. Both the analytical and numerical results consistently show that below the Debye temperature of the host lattice, quantum statistics significantly impacts the ISA transport properties, resulting in major departures from both the Arrhenius law of diffusion and the Einstein-Smoluchowski relation between the mobility and diffusivity. Indeed, we found that below one-third of the Debye temperature, effects of vibrations on the quantum mobility and diffusivity are both orders-of-magnitude larger and practically temperature independent. We have shown that both effects have their physical origin in the athermal lattice vibrations derived from the phonon ground state. The foregoing theory is tested in quantum molecular dynamics calculation of mobility and diffusivity of interstitial helium in bcc W. In this case, the Arrhenius law is only valid in a narrow range between ˜300 and ˜700 K. The diffusivity becomes temperature independent on the low-temperature side while increasing linearly with temperature on the high-temperature side.

Quantum chaos: Statistical relaxation in discrete spectrum

International Nuclear Information System (INIS)

Chirikov, B.V.

1991-01-01

The controversial phenomenon of quantum chaos is discussed using the quantized standard map, or the kicked rotator, as a simple model. The relation to the classical dynamical chaos is tracked down on the basis of the correspondence principle. Various mechanisms of the quantum suppression of classical chaos are considered with an application to the excitation and ionization of Rydberg atoms in a microwave field. Several definitions of the quantum chaos are discussed. (author). 27 refs

Quantum statistics of dense gases and nonideal plasmas

CERN Document Server

Ebeling, Werner; Filinov, Vladimir

2017-01-01

The aim of this book is the pedagogical exploration of the basic principles of quantum-statistical thermodynamics as applied to various states of matter – ranging from rare gases to astrophysical matter with high-energy density. The reader will learn in this work that thermodynamics and quantum statistics are still the concepts on which even the most advanced research is operating - despite of a flood of modern concepts, classical entities like temperature, pressure, energy and entropy are shown to remain fundamental. The physics of gases, plasmas and high-energy density matter is still a growing field and even though solids and liquids dominate our daily life, more than 99 percent of the visible Universe is in the state of gases and plasmas and the overwhelming part of matter exists at extreme conditions connected with very large energy densities, such as in the interior of stars. This text, combining material from lectures and advanced seminars given by the authors over many decades, is a must-have intr...

Two-dimensional models in statistical mechanics and field theory

International Nuclear Information System (INIS)

Koberle, R.

1980-01-01

Several features of two-dimensional models in statistical mechanics and Field theory, such as, lattice quantum chromodynamics, Z(N), Gross-Neveu and CP N-1 are discussed. The problems of confinement and dynamical mass generation are also analyzed. (L.C.) [pt

Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels

Directory of Open Access Journals (Sweden)

Benoît Collins

2010-06-01

Full Text Available Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models of relevance for the recent counterexamples to the minimum output entropy additivity problems. Our main result is a classification of regimes for which the von Neumann entropy is lower on average than the elementary bounds that can be obtained with linear algebra techniques.

Local box-counting dimensions of discrete quantum eigenvalue spectra: Analytical connection to quantum spectral statistics

Science.gov (United States)

Sakhr, Jamal; Nieminen, John M.

2018-03-01

Two decades ago, Wang and Ong, [Phys. Rev. A 55, 1522 (1997)], 10.1103/PhysRevA.55.1522 hypothesized that the local box-counting dimension of a discrete quantum spectrum should depend exclusively on the nearest-neighbor spacing distribution (NNSD) of the spectrum. In this Rapid Communication, we validate their hypothesis by deriving an explicit formula for the local box-counting dimension of a countably-infinite discrete quantum spectrum. This formula expresses the local box-counting dimension of a spectrum in terms of single and double integrals of the NNSD of the spectrum. As applications, we derive an analytical formula for Poisson spectra and closed-form approximations to the local box-counting dimension for spectra having Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE), and Gaussian symplectic ensemble (GSE) spacing statistics. In the Poisson and GOE cases, we compare our theoretical formulas with the published numerical data of Wang and Ong and observe excellent agreement between their data and our theory. We also study numerically the local box-counting dimensions of the Riemann zeta function zeros and the alternate levels of GOE spectra, which are often used as numerical models of spectra possessing GUE and GSE spacing statistics, respectively. In each case, the corresponding theoretical formula is found to accurately describe the numerically computed local box-counting dimension.

Shell model in large spaces and statistical spectroscopy

International Nuclear Information System (INIS)

Kota, V.K.B.

1996-01-01

For many nuclear structure problems of current interest it is essential to deal with shell model in large spaces. For this, three different approaches are now in use and two of them are: (i) the conventional shell model diagonalization approach but taking into account new advances in computer technology; (ii) the shell model Monte Carlo method. A brief overview of these two methods is given. Large space shell model studies raise fundamental questions regarding the information content of the shell model spectrum of complex nuclei. This led to the third approach- the statistical spectroscopy methods. The principles of statistical spectroscopy have their basis in nuclear quantum chaos and they are described (which are substantiated by large scale shell model calculations) in some detail. (author)

Bohm's mysterious 'quantum force' and 'active information': alternative interpretation and statistical properties

International Nuclear Information System (INIS)

Lan, B.L.

2001-01-01

An alternative interpretation to Bohm's 'quantum force' and 'active information' is proposed. Numerical evidence is presented, which suggests that the time series of Bohm's 'quantum force' evaluated at the Bohmian position for non-stationary quantum states are typically non-Gaussian stable distributed with a flat power spectrum in classically chaotic Hamiltonian systems. An important implication of these statistical properties is briefly mentioned. (orig.)

Negative values of quasidistributions and quantum wave and number statistics

Science.gov (United States)

Peřina, J.; Křepelka, J.

2018-04-01

We consider nonclassical wave and number quantum statistics, and perform a decomposition of quasidistributions for nonlinear optical down-conversion processes using Bessel functions. We show that negative values of the quasidistribution do not directly represent probabilities; however, they directly influence measurable number statistics. Negative terms in the decomposition related to the nonclassical behavior with negative amplitudes of probability can be interpreted as positive amplitudes of probability in the negative orthogonal Bessel basis, whereas positive amplitudes of probability in the positive basis describe classical cases. However, probabilities are positive in all cases, including negative values of quasidistributions. Negative and positive contributions of decompositions to quasidistributions are estimated. The approach can be adapted to quantum coherence functions.

Quantum chaos: statistical relaxation in discrete spectrum

International Nuclear Information System (INIS)

Chirikov, B.V.

1990-01-01

The controversial phenomenon of quantum chaos is discussed using the quantized standard map, or the kicked rotator, as a simple model. The relation to the classical dynamical chaos is tracked down on the basis of the correspondence principle. Several definitions of the quantum chaos are discussed. 27 refs

Quantum Link Models and Quantum Simulation of Gauge Theories

International Nuclear Information System (INIS)

Wiese, U.J.

2015-01-01

This lecture is about Quantum Link Models and Quantum Simulation of Gauge Theories. The lecture consists out of 4 parts. The first part gives a brief history of Computing and Pioneers of Quantum Computing and Quantum Simulations of Quantum Spin Systems are introduced. The 2nd lecture is about High-Temperature Superconductors versus QCD, Wilson’s Lattice QCD and Abelian Quantum Link Models. The 3rd lecture deals with Quantum Simulators for Abelian Lattice Gauge Theories and Non-Abelian Quantum Link Models. The last part of the lecture discusses Quantum Simulators mimicking ‘Nuclear’ physics and the continuum limit of D-Theorie models. (nowak)

Algebraic methods in statistical mechanics and quantum field theory

CERN Document Server

Emch, Dr Gérard G

2009-01-01

This systematic algebraic approach concerns problems involving a large number of degrees of freedom. It extends the traditional formalism of quantum mechanics, and it eliminates conceptual and mathematical difficulties common to the development of statistical mechanics and quantum field theory. Further, the approach is linked to research in applied and pure mathematics, offering a reflection of the interplay between formulation of physical motivations and self-contained descriptions of the mathematical methods.The four-part treatment begins with a survey of algebraic approaches to certain phys

Statistical analysis of time-resolved emission from ensembles of semiconductor quantum dots: interpretations of exponantial decay models

NARCIS (Netherlands)

van Driel, A.F.; Nikolaev, I.; Vergeer, P.; Lodahl, P.; Vanmaekelbergh, D.; Vos, Willem L.

2007-01-01

We present a statistical analysis of time-resolved spontaneous emission decay curves from ensembles of emitters, such as semiconductor quantum dots, with the aim of interpreting ubiquitous non-single-exponential decay. Contrary to what is widely assumed, the density of excited emitters and the

Nonlinear unitary quantum collapse model with self-generated noise

Science.gov (United States)

Geszti, Tamás

2018-04-01

Collapse models including some external noise of unknown origin are routinely used to describe phenomena on the quantum-classical border; in particular, quantum measurement. Although containing nonlinear dynamics and thereby exposed to the possibility of superluminal signaling in individual events, such models are widely accepted on the basis of fully reproducing the non-signaling statistical predictions of quantum mechanics. Here we present a deterministic nonlinear model without any external noise, in which randomness—instead of being universally present—emerges in the measurement process, from deterministic irregular dynamics of the detectors. The treatment is based on a minimally nonlinear von Neumann equation for a Stern–Gerlach or Bell-type measuring setup, containing coordinate and momentum operators in a self-adjoint skew-symmetric, split scalar product structure over the configuration space. The microscopic states of the detectors act as a nonlocal set of hidden parameters, controlling individual outcomes. The model is shown to display pumping of weights between setup-defined basis states, with a single winner randomly selected and the rest collapsing to zero. Environmental decoherence has no role in the scenario. Through stochastic modelling, based on Pearle’s ‘gambler’s ruin’ scheme, outcome probabilities are shown to obey Born’s rule under a no-drift or ‘fair-game’ condition. This fully reproduces quantum statistical predictions, implying that the proposed non-linear deterministic model satisfies the non-signaling requirement. Our treatment is still vulnerable to hidden signaling in individual events, which remains to be handled by future research.

A stochastic model for quantum measurement

International Nuclear Information System (INIS)

Budiyono, Agung

2013-01-01

We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic process with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary action. We apply the statistical model to stochastically modify a classical mechanical model for the measurement of physical quantities reproducing the prediction of quantum mechanics. The system+apparatus always has a definite configuration at all times, as in classical mechanics, fluctuating randomly following a continuous trajectory. On the other hand, the wavefunction and quantum mechanical Hermitian operator corresponding to the physical quantity arise formally as artificial mathematical constructs. During a single measurement, the wavefunction of the whole system+apparatus evolves according to a Schrödinger equation and the configuration of the apparatus acts as the pointer of the measurement so that there is no wavefunction collapse. We will also show that while the outcome of each single measurement event does not reveal the actual value of the physical quantity prior to measurement, its average in an ensemble of identical measurements is equal to the average of the actual value of the physical quantity prior to measurement over the distribution of the configuration of the system. (paper)

A quantum probability model of causal reasoning

Directory of Open Access Journals (Sweden)

Jennifer S Trueblood

2012-05-01

Full Text Available People can often outperform statistical methods and machine learning algorithms in situations that involve making inferences about the relationship between causes and effects. While people are remarkably good at causal reasoning in many situations, there are several instances where they deviate from expected responses. This paper examines three situations where judgments related to causal inference problems produce unexpected results and describes a quantum inference model based on the axiomatic principles of quantum probability theory that can explain these effects. Two of the three phenomena arise from the comparison of predictive judgments (i.e., the conditional probability of an effect given a cause with diagnostic judgments (i.e., the conditional probability of a cause given an effect. The third phenomenon is a new finding examining order effects in predictive causal judgments. The quantum inference model uses the notion of incompatibility among different causes to account for all three phenomena. Psychologically, the model assumes that individuals adopt different points of view when thinking about different causes. The model provides good fits to the data and offers a coherent account for all three causal reasoning effects thus proving to be a viable new candidate for modeling human judgment.

A model of quantum communication device for quantum hashing

International Nuclear Information System (INIS)

Vasiliev, A

2016-01-01

In this paper we consider a model of quantum communications between classical computers aided with quantum processors, connected by a classical and a quantum channel. This type of communications implying both classical and quantum messages with moderate use of quantum processing is implicitly used in many quantum protocols, such as quantum key distribution or quantum digital signature. We show that using the model of a quantum processor on multiatomic ensembles in the common QED cavity we can speed up quantum hashing, which can be the basis of quantum digital signature and other communication protocols. (paper)

Statistical thermodynamics

International Nuclear Information System (INIS)

Lim, Gyeong Hui

2008-03-01

This book consists of 15 chapters, which are basic conception and meaning of statistical thermodynamics, Maxwell-Boltzmann's statistics, ensemble, thermodynamics function and fluctuation, statistical dynamics with independent particle system, ideal molecular system, chemical equilibrium and chemical reaction rate in ideal gas mixture, classical statistical thermodynamics, ideal lattice model, lattice statistics and nonideal lattice model, imperfect gas theory on liquid, theory on solution, statistical thermodynamics of interface, statistical thermodynamics of a high molecule system and quantum statistics

Thermodynamics of ideal quantum gas with fractional statistics in D dimensions.

Science.gov (United States)

Potter, Geoffrey G; Müller, Gerhard; Karbach, Michael

2007-06-01

We present exact and explicit results for the thermodynamic properties (isochores, isotherms, isobars, response functions, velocity of sound) of a quantum gas in dimensions D > or = 1 and with fractional exclusion statistics 0 < or = g < or =1 connecting bosons (g=0) and fermions (g=1) . In D=1 the results are equivalent to those of the Calogero-Sutherland model. Emphasis is given to the crossover between bosonlike and fermionlike features, caused by aspects of the statistical interaction that mimic long-range attraction and short-range repulsion. A phase transition along the isobar occurs at a nonzero temperature in all dimensions. The T dependence of the velocity of sound is in simple relation to isochores and isobars. The effects of soft container walls are accounted for rigorously for the case of a pure power-law potential.

Are Quantum Models for Order Effects Quantum?

Science.gov (United States)

Moreira, Catarina; Wichert, Andreas

2017-12-01

The application of principles of Quantum Mechanics in areas outside of physics has been getting increasing attention in the scientific community in an emergent disciplined called Quantum Cognition. These principles have been applied to explain paradoxical situations that cannot be easily explained through classical theory. In quantum probability, events are characterised by a superposition state, which is represented by a state vector in a N-dimensional vector space. The probability of an event is given by the squared magnitude of the projection of this superposition state into the desired subspace. This geometric approach is very useful to explain paradoxical findings that involve order effects, but do we really need quantum principles for models that only involve projections? This work has two main goals. First, it is still not clear in the literature if a quantum projection model has any advantage towards a classical projection. We compared both models and concluded that the Quantum Projection model achieves the same results as its classical counterpart, because the quantum interference effects play no role in the computation of the probabilities. Second, it intends to propose an alternative relativistic interpretation for rotation parameters that are involved in both classical and quantum models. In the end, instead of interpreting these parameters as a similarity measure between questions, we propose that they emerge due to the lack of knowledge concerned with a personal basis state and also due to uncertainties towards the state of world and towards the context of the questions.

Understanding quantum measurement from the solution of dynamical models

Energy Technology Data Exchange (ETDEWEB)

Allahverdyan, Armen E. [Laboratoire de Physique Statistique et Systèmes Complexes, ISMANS, 44 Av. Bartholdi, 72000 Le Mans (France); Balian, Roger [Institut de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette cedex (France); Nieuwenhuizen, Theo M., E-mail: T.M.Nieuwenhuizen@uva.nl [Center for Cosmology and Particle Physics, New York University, 4 Washington Place, New York, NY 10003 (United States)

2013-04-15

The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum–classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie–Weiss magnet, including N≫1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrix D{sup -hat} (t). Its off-diagonal blocks in a basis selected by the spin–pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final state D{sup -hat} (t{sub f}) that involves correlations between the system and the indications of the pointer, thus ensuring registration. Although D{sup -hat} (t{sub f}) has the form expected for ideal measurements, it only describes a large set of

Quantum Monte Carlo tunneling from quantum chemistry to quantum annealing

Science.gov (United States)

Mazzola, Guglielmo; Smelyanskiy, Vadim N.; Troyer, Matthias

2017-10-01

Quantum tunneling is ubiquitous across different fields, from quantum chemical reactions and magnetic materials to quantum simulators and quantum computers. While simulating the real-time quantum dynamics of tunneling is infeasible for high-dimensional systems, quantum tunneling also shows up in quantum Monte Carlo (QMC) simulations, which aim to simulate quantum statistics with resources growing only polynomially with the system size. Here we extend the recent results obtained for quantum spin models [Phys. Rev. Lett. 117, 180402 (2016), 10.1103/PhysRevLett.117.180402], and we study continuous-variable models for proton transfer reactions. We demonstrate that QMC simulations efficiently recover the scaling of ground-state tunneling rates due to the existence of an instanton path, which always connects the reactant state with the product. We discuss the implications of our results in the context of quantum chemical reactions and quantum annealing, where quantum tunneling is expected to be a valuable resource for solving combinatorial optimization problems.

Quantum theoretical physics is statistical and relativistic

International Nuclear Information System (INIS)

Harding, C.

1980-01-01

A new theoretical framework for the quantum mechanism is presented. It is based on a strict deterministic behavior of single systems. The conventional QM equation, however, is found to describe statistical results of many classical systems. It will be seen, moreover, that a rigorous synthesis of our theory requires relativistic kinematics. So, QM is not only a classical statistical theory, it is, of necessity, a relativistic theory. The equation of the theory does not just duplicate QM, it indicates an inherent nonlinearity in QM which is subject to experimental verification. It is shown, therefore, that conventional QM is a corollary of classical deterministic principles. It is suggested that this concept of nature conflicts with that prevalent in modern physics. (author)

Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction.

Science.gov (United States)

Budiyono, Agung; Rohrlich, Daniel

2017-11-03

Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic framework, allowing an unambiguous account of how one theory is the limit of the other. Here we derive non-relativistic quantum mechanics and classical statistical mechanics within a common framework. The common axioms include conservation of average energy and conservation of probability current. But two axioms distinguish quantum mechanics from classical statistical mechanics: an "ontic extension" defines a nonseparable (global) random variable that generates physical correlations, and an "epistemic restriction" constrains allowed phase space distributions. The ontic extension and epistemic restriction, with strength on the order of Planck's constant, imply quantum entanglement and uncertainty relations. This framework suggests that the wave function is epistemic, yet it does not provide an ontic dynamics for individual systems.

Equilibrium statistical mechanics

CERN Document Server

Jackson, E Atlee

2000-01-01

Ideal as an elementary introduction to equilibrium statistical mechanics, this volume covers both classical and quantum methodology for open and closed systems. Introductory chapters familiarize readers with probability and microscopic models of systems, while additional chapters describe the general derivation of the fundamental statistical mechanics relationships. The final chapter contains 16 sections, each dealing with a different application, ordered according to complexity, from classical through degenerate quantum statistical mechanics. Key features include an elementary introduction t

Statistical quasi-particle theory for open quantum systems

Science.gov (United States)

Zhang, Hou-Dao; Xu, Rui-Xue; Zheng, Xiao; Yan, YiJing

2018-04-01

This paper presents a comprehensive account on the recently developed dissipaton-equation-of-motion (DEOM) theory. This is a statistical quasi-particle theory for quantum dissipative dynamics. It accurately describes the influence of bulk environments, with a few number of quasi-particles, the dissipatons. The novel dissipaton algebra is then followed, which readily bridges the Schrödinger equation to the DEOM theory. As a fundamental theory of quantum mechanics in open systems, DEOM characterizes both the stationary and dynamic properties of system-and-bath interferences. It treats not only the quantum dissipative systems of primary interest, but also the hybrid environment dynamics that could be experimentally measurable. Examples are the linear or nonlinear Fano interferences and the Herzberg-Teller vibronic couplings in optical spectroscopies. This review covers the DEOM construction, the underlying dissipaton algebra and theorems, the physical meanings of dynamical variables, the possible identifications of dissipatons, and some recent advancements in efficient DEOM evaluations on various problems. The relations of the present theory to other nonperturbative methods are also critically presented.

The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles

Science.gov (United States)

Plotnitsky, Arkady

2017-06-01

The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, helpful or even necessary there or in physics itself. I shall suggest one possible type of such models, singularized probabilistic, SP, models, some of which are time-dependent, TDSP-models. The

Statistical model of exotic rotational correlations in emergent space-time

Energy Technology Data Exchange (ETDEWEB)

Hogan, Craig; Kwon, Ohkyung; Richardson, Jonathan

2017-06-06

A statistical model is formulated to compute exotic rotational correlations that arise as inertial frames and causal structure emerge on large scales from entangled Planck scale quantum systems. Noncommutative quantum dynamics are represented by random transverse displacements that respect causal symmetry. Entanglement is represented by covariance of these displacements in Planck scale intervals defined by future null cones of events on an observer's world line. Light that propagates in a nonradial direction inherits a projected component of the exotic rotational correlation that accumulates as a random walk in phase. A calculation of the projection and accumulation leads to exact predictions for statistical properties of exotic Planck scale correlations in an interferometer of any configuration. The cross-covariance for two nearly co-located interferometers is shown to depart only slightly from the autocovariance. Specific examples are computed for configurations that approximate realistic experiments, and show that the model can be rigorously tested.

Quantum measurement as a driven phase transition: An exactly solvable model

NARCIS (Netherlands)

Allahverdyan, A.; Balian, R.

2001-01-01

A model of quantum measurement is proposed, which aims to describe statistical mechanical aspects of this phenomenon, starting from a purely Hamiltonian formulation. The macroscopic measurement apparatus is modeled as an ideal Bose gas, the order parameter of which, that is, the amplitude of the

On estimating perturbative coefficients in quantum field theory and statistical physics

International Nuclear Information System (INIS)

Samuel, M.A.; Stanford Univ., CA

1994-05-01

The authors present a method for estimating perturbative coefficients in quantum field theory and Statistical Physics. They are able to obtain reliable error-bars for each estimate. The results, in all cases, are excellent

Effects of quantum statistics of phonons on the thermal conductivity of silicon and germanium nanoribbons

Science.gov (United States)

Kosevich, Yuriy A.; Savin, Alexander V.; Cantarero, Andrés

2013-01-01

We present molecular dynamics simulation of phonon thermal conductivity of semiconductor nanoribbons with an account for phonon quantum statistics. In our semiquantum molecular dynamics simulation, dynamics of the system is described with the use of classical Newtonian equations of motion where the effect of phonon quantum statistics is introduced through random Langevin-like forces with a specific power spectral density (color noise). The color noise describes interaction of the molecular system with the thermostat. The thermal transport of silicon and germanium nanoribbons with atomically smooth (perfect) and rough (porous) edges are studied. We show that the existence of rough (porous) edges and the quantum statistics of phonon change drastically the low-temperature thermal conductivity of the nanoribbon in comparison with that of the perfect nanoribbon with atomically smooth edges and classical phonon dynamics and statistics. The rough-edge phonon scattering and weak anharmonicity of the considered lattice produce a weakly pronounced maximum of thermal conductivity of the nanoribbon at low temperature.

Hybrid quantum-classical modeling of quantum dot devices

Science.gov (United States)

Kantner, Markus; Mittnenzweig, Markus; Koprucki, Thomas

2017-11-01

The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the well-established fields of semiclassical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we introduce a new hybrid quantum-classical modeling approach, which provides a comprehensive description of quantum dot devices on multiple scales: it enables the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics. The feasibility of the approach is demonstrated by numerical simulations of an electrically driven single-photon source based on a single quantum dot in the stationary and transient operation regime.

A unified treatment of dynamics and scattering in classical and quantum statistical mechanics

International Nuclear Information System (INIS)

Prugovecki, E.

1978-01-01

The common formal features of classical and quantum statistical mechanics are investigated at three separate levels: at the level of L 2 spaces of wave-packets on GAMMA-space, of Liouville spaces B 2 consisting of density operators constructed from such wave-packets, and of phase-space representation spaces P of GAMMA distribution functions. It is shown that at the last level the formal similarities become so outstanding that all key quantities in P-space, such as Liouville operators, Hamiltonian functions, position and momentum observables, etc., are represented by expressions which to the zeroth order in (h/2π) coincide in the classical and quantum case, and in some instances coincide completely. Scattering theory on the B 2 Liouville spaces takes on the same formal appearance for classical and quantum statistical mechanics, and to the zeroth order in (h/2π) it coincides in both cases. This makes possible the formulation of a classical approximation to quantum scattering, and of a computational scheme for determining rhosup(out) from rhosup(in) for successive order of (h/2π). (Auth.)

A statistical model of structure functions and quantum chromodynamics

International Nuclear Information System (INIS)

Mac, E.; Ugaz, E.; Universidad Nacional de Ingenieria, Lima

1989-01-01

We consider a model for the x-dependence of the quark distributions in the proton. Within the context of simple statistical assumptions, we obtain the parton densities in the infinite momentum frame. In a second step lowest order QCD corrections are incorporated to these distributions. Crude, but reasonable, agreement with experiment is found for the F 2 , valence and q, anti q distributions for x> or approx.0.2. (orig.)

Quantum Brownian motion in a bath of parametric oscillators: A model for system-field interactions

International Nuclear Information System (INIS)

Hu, B.L.; Matacz, A.

1994-01-01

The quantum Brownian motion paradigm provides a unified framework where one can see the interconnection of some basic quantum statistical processes such as decoherence, dissipation, particle creation, noise, and fluctuation. The present paper continues the investigation begun in earlier papers on the quantum Brownian motion in a general environment via the influence functional formalism. Here, the Brownian particle is coupled linearly to a bath of the most general time-dependent quadratic oscillators. This bath of parametric oscillators minics a scalar field, while the motion of the Brownian particle modeled by a single oscillator could be used to depict the behavior of a particle detector, a quantum field mode, or the scale factor of the Universe. An important result of this paper is the derivation of the influence functional encompassing the noise and dissipation kernels in terms of the Bogolubov coefficients, thus setting the stage for the influence functional formalism treatment of problems in quantum field theory in curved spacetime. This method enables one to trace the source of statistical processes such as decoherence and dissipation to vacuum fluctuations and particle creation, and in turn impart a statistical mechanical interpretation of quantum field processes. With this result we discuss the statistical mechanical origin of quantum noise and thermal radiance from black holes and from uniformly accelerated observers in Minkowski space as well as from the de Sitter universe discovered by Hawking, Unruh, and Gibbons and Hawking. We also derive the exact evolution operator and master equation for the reduced density matrix of the system interacting with a parametric oscillator bath in an initial squeezed thermal state. These results are useful for decoherence and back reaction studies for systems and processes of interest in semiclassical cosmology and gravity. Our model and results are also expected to be useful for related problems in quantum optics

Quantum Statistical Entropy of Non-extreme and Nearly Extreme Black Holes in Higher-Dimensional Space-Time

Institute of Scientific and Technical Information of China (English)

XU Dian-Yan

2003-01-01

The free energy and entropy of Reissner-Nordstrom black holes in higher-dimensional space-time are calculated by the quantum statistic method with a brick wall model. The space-time of the black holes is divided into three regions: region 1, (r > r0); region 2, (r0 > r > n); and region 3, (T-J > r > 0), where r0 is the radius of the outer event horizon, and r, is the radius of the inner event horizon. Detailed calculation shows that the entropy contributed by region 2 is zero, the entropy contributed by region 1 is positive and proportional to the outer event horizon area, the entropy contributed by region 3 is negative and proportional to the inner event horizon area. The total entropy contributed by all the three regions is positive and proportional to the area difference between the outer and inner event horizons. As rt approaches r0 in the nearly extreme case, the total quantum statistical entropy approaches zero.

Structural characterization and condition for measurement statistics preservation of a unital quantum operation

International Nuclear Information System (INIS)

Lee, Kai-Yan; Fung, Chi-Hang Fred; Chau, H F

2013-01-01

We investigate the necessary and sufficient condition for a convex cone of positive semidefinite operators to be fixed by a unital quantum operation ϕ acting on finite-dimensional quantum states. By reducing this problem to the problem of simultaneous diagonalization of the Kraus operators associated with ϕ, we can completely characterize the kinds of quantum states that are fixed by ϕ. Our work has several applications. It gives a simple proof of the structural characterization of a unital quantum operation that acts on finite-dimensional quantum states—a result not explicitly mentioned in earlier studies. It also provides a necessary and sufficient condition for determining what kind of measurement statistics is preserved by a unital quantum operation. Finally, our result clarifies and extends the work of Størmer by giving a proof of a reduction theorem on the unassisted and entanglement-assisted classical capacities, coherent information, and minimal output Renyi entropy of a unital channel acting on a finite-dimensional quantum state. (paper)

Multiscale Monte Carlo algorithms in statistical mechanics and quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Lauwers, P G

1990-12-01

Conventional Monte Carlo simulation algorithms for models in statistical mechanics and quantum field theory are afflicted by problems caused by their locality. They become highly inefficient if investigations of critical or nearly-critical systems, i.e., systems with important large scale phenomena, are undertaken. We present two types of multiscale approaches that alleveate problems of this kind: Stochastic cluster algorithms and multigrid Monte Carlo simulation algorithms. Another formidable computational problem in simulations of phenomenologically relevant field theories with fermions is the need for frequently inverting the Dirac operator. This inversion can be accelerated considerably by means of deterministic multigrid methods, very similar to the ones used for the numerical solution of differential equations. (orig.).

Statistical analysis of time-resolved emission from ensembles of semiconductor quantum dots: Interpretation of exponential decay models

DEFF Research Database (Denmark)

Van Driel, A.F.; Nikolaev, I.S.; Vergeer, P.

2007-01-01

We present a statistical analysis of time-resolved spontaneous emission decay curves from ensembles of emitters, such as semiconductor quantum dots, with the aim of interpreting ubiquitous non-single-exponential decay. Contrary to what is widely assumed, the density of excited emitters...... and the intensity in an emission decay curve are not proportional, but the density is a time integral of the intensity. The integral relation is crucial to correctly interpret non-single-exponential decay. We derive the proper normalization for both a discrete and a continuous distribution of rates, where every...... decay component is multiplied by its radiative decay rate. A central result of our paper is the derivation of the emission decay curve when both radiative and nonradiative decays are independently distributed. In this case, the well-known emission quantum efficiency can no longer be expressed...

Maximum entropy principle and hydrodynamic models in statistical mechanics

International Nuclear Information System (INIS)

Trovato, M.; Reggiani, L.

2012-01-01

This review presents the state of the art of the maximum entropy principle (MEP) in its classical and quantum (QMEP) formulation. Within the classical MEP we overview a general theory able to provide, in a dynamical context, the macroscopic relevant variables for carrier transport in the presence of electric fields of arbitrary strength. For the macroscopic variables the linearized maximum entropy approach is developed including full-band effects within a total energy scheme. Under spatially homogeneous conditions, we construct a closed set of hydrodynamic equations for the small-signal (dynamic) response of the macroscopic variables. The coupling between the driving field and the energy dissipation is analyzed quantitatively by using an arbitrary number of moments of the distribution function. Analogously, the theoretical approach is applied to many one-dimensional n + nn + submicron Si structures by using different band structure models, different doping profiles, different applied biases and is validated by comparing numerical calculations with ensemble Monte Carlo simulations and with available experimental data. Within the quantum MEP we introduce a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is then asserted as fundamental principle of quantum statistical mechanics. Accordingly, we have developed a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theory is formulated both in thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of ħ 2 , being ħ the reduced Planck constant. In particular, by using an arbitrary number of moments, we prove that: i) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives both of the

Philosophical perspectives on quantum chaos: Models and interpretations

Science.gov (United States)

Bokulich, Alisa Nicole

2001-09-01

The problem of quantum chaos is a special case of the larger problem of understanding how the classical world emerges from quantum mechanics. While we have learned that chaos is pervasive in classical systems, it appears to be almost entirely absent in quantum systems. The aim of this dissertation is to determine what implications the interpretation of quantum mechanics has for attempts to explain the emergence of classical chaos. There are three interpretations of quantum mechanics that have set out programs for solving the problem of quantum chaos: the standard interpretation, the statistical interpretation, and the deBroglie-Bohm causal interpretation. One of the main conclusions of this dissertation is that an interpretation alone is insufficient for solving the problem of quantum chaos and that the phenomenon of decoherence must be taken into account. Although a completely satisfactory solution of the problem of quantum chaos is still outstanding, I argue that the deBroglie-Bohm interpretation with the help of decoherence outlines the most promising research program to pursue. In addition to making a contribution to the debate in the philosophy of physics concerning the interpretation of quantum mechanics, this dissertation reveals two important methodological lessons for the philosophy of science. First, issues of reductionism and intertheoretic relations cannot be divorced from questions concerning the interpretation of the theories involved. Not only is the exploration of intertheoretic relations a central part of the articulation and interpretation of an individual theory, but the very terms used to discuss intertheoretic relations, such as `state' and `classical limit', are themselves defined by particular interpretations of the theory. The second lesson that emerges is that, when it comes to characterizing the relationship between classical chaos and quantum mechanics, the traditional approaches to intertheoretic relations, namely reductionism and

Completeness of classical spin models and universal quantum computation

International Nuclear Information System (INIS)

De las Cuevas, Gemma; Dür, Wolfgang; Briegel, Hans J; Van den Nest, Maarten

2009-01-01

We study mappings between different classical spin systems that leave the partition function invariant. As recently shown in Van den Nest et al (2008 Phys. Rev. Lett. 100 110501), the partition function of the 2D square lattice Ising model in the presence of an inhomogeneous magnetic field can specialize to the partition function of any Ising system on an arbitrary graph. In this sense the 2D Ising model is said to be 'complete'. However, in order to obtain the above result, the coupling strengths on the 2D lattice must assume complex values, and thus do not allow for a physical interpretation. Here we show how a complete model with real—and, hence, 'physical'—couplings can be obtained if the 3D Ising model is considered. We furthermore show how to map general q-state systems with possibly many-body interactions to the 2D Ising model with complex parameters, and give completeness results for these models with real parameters. We also demonstrate that the computational overhead in these constructions is in all relevant cases polynomial. These results are proved by invoking a recently found cross-connection between statistical mechanics and quantum information theory, where partition functions are expressed as quantum mechanical amplitudes. Within this framework, there exists a natural correspondence between many-body quantum states that allow for universal quantum computation via local measurements only, and complete classical spin systems

Probing the exchange statistics of one-dimensional anyon models

Science.gov (United States)

Greschner, Sebastian; Cardarelli, Lorenzo; Santos, Luis

2018-05-01

We propose feasible scenarios for revealing the modified exchange statistics in one-dimensional anyon models in optical lattices based on an extension of the multicolor lattice-depth modulation scheme introduced in [Phys. Rev. A 94, 023615 (2016), 10.1103/PhysRevA.94.023615]. We show that the fast modulation of a two-component fermionic lattice gas in the presence a magnetic field gradient, in combination with additional resonant microwave fields, allows for the quantum simulation of hardcore anyon models with periodic boundary conditions. Such a semisynthetic ring setup allows for realizing an interferometric arrangement sensitive to the anyonic statistics. Moreover, we show as well that simple expansion experiments may reveal the formation of anomalously bound pairs resulting from the anyonic exchange.

Single-server blind quantum computation with quantum circuit model

Science.gov (United States)

Zhang, Xiaoqian; Weng, Jian; Li, Xiaochun; Luo, Weiqi; Tan, Xiaoqing; Song, Tingting

2018-06-01

Blind quantum computation (BQC) enables the client, who has few quantum technologies, to delegate her quantum computation to a server, who has strong quantum computabilities and learns nothing about the client's quantum inputs, outputs and algorithms. In this article, we propose a single-server BQC protocol with quantum circuit model by replacing any quantum gate with the combination of rotation operators. The trap quantum circuits are introduced, together with the combination of rotation operators, such that the server is unknown about quantum algorithms. The client only needs to perform operations X and Z, while the server honestly performs rotation operators.

Parameter optimization in biased decoy-state quantum key distribution with both source errors and statistical fluctuations

Science.gov (United States)

Zhu, Jian-Rong; Li, Jian; Zhang, Chun-Mei; Wang, Qin

2017-10-01

The decoy-state method has been widely used in commercial quantum key distribution (QKD) systems. In view of the practical decoy-state QKD with both source errors and statistical fluctuations, we propose a universal model of full parameter optimization in biased decoy-state QKD with phase-randomized sources. Besides, we adopt this model to carry out simulations of two widely used sources: weak coherent source (WCS) and heralded single-photon source (HSPS). Results show that full parameter optimization can significantly improve not only the secure transmission distance but also the final key generation rate. And when taking source errors and statistical fluctuations into account, the performance of decoy-state QKD using HSPS suffered less than that of decoy-state QKD using WCS.

Statistical analysis of AFM topographic images of self-assembled quantum dots

Energy Technology Data Exchange (ETDEWEB)

Sevriuk, V. A.; Brunkov, P. N., E-mail: brunkov@mail.ioffe.ru; Shalnev, I. V.; Gutkin, A. A.; Klimko, G. V.; Gronin, S. V.; Sorokin, S. V.; Konnikov, S. G. [Russian Academy of Sciences, Ioffe Physical-Technical Institute (Russian Federation)

2013-07-15

To obtain statistical data on quantum-dot sizes, AFM topographic images of the substrate on which the dots under study are grown are analyzed. Due to the nonideality of the substrate containing height differences on the order of the size of nanoparticles at distances of 1-10 {mu}m and the insufficient resolution of closely arranged dots due to the finite curvature radius of the AFM probe, automation of the statistical analysis of their large dot array requires special techniques for processing topographic images to eliminate the loss of a particle fraction during conventional processing. As such a technique, convolution of the initial matrix of the AFM image with a specially selected matrix is used. This makes it possible to determine the position of each nanoparticle and, using the initial matrix, to measure their geometrical parameters. The results of statistical analysis by this method of self-assembled InAs quantum dots formed on the surface of an AlGaAs epitaxial layer are presented. It is shown that their concentration, average size, and half-width of height distribution depend strongly on the In flow and total amount of deposited InAs which are varied within insignificant limits.

Quantum Statistics of the Toda Oscillator in the Wigner Function Formalism

Science.gov (United States)

Vojta, Günter; Vojta, Matthias

Classical and quantum mechanical Toda systems (Toda molecules, Toda lattices, Toda quantum fields) recently found growing interest as nonlinear systems showing solitons and chaos. In this paper the statistical thermodynamics of a system of quantum mechanical Toda oscillators characterized by a potential energy V(q) = Vo cos h q is treated within the Wigner function formalism (phase space formalism of quantum statistics). The partition function is given as a Wigner- Kirkwood series expansion in terms of powers of h2 (semiclassical expansion). The partition function and all thermodynamic functions are written, with considerable exactness, as simple closed expressions containing only the modified Hankel functions Ko and K1 of the purely imaginary argument i with = Vo/kT.Translated AbstractQuantenstatistik des Toda-Oszillators im Formalismus der Wigner-FunktionKlassische und quantenmechanische Toda-Systeme (Toda-Moleküle, Toda-Gitter, Toda-Quantenfelder) haben als nichtlineare Systeme mit Solitonen und Chaos in jüngster Zeit zunehmend an Interesse gewonnen. Wir untersuchen die statistische Thermodynamik eines Systems quantenmechanischer Toda-Oszillatoren, die durch eine potentielle Energie der Form V(q) = Vo cos h q charakterisiert sind, im Formalismus der Wigner-Funktion (Phasenraum-Formalismus der Quantenstatistik). Die Zustandssumme wird als Wigner-Kirkwood-Reihe nach Potenzen von h2 (semiklassische Entwicklung) dargestellt, und aus ihr werden die thermodynamischen Funktionen berechnet. Sämtliche Funktionen sind durch einfache geschlossene Formeln allein mit den modifizierten Hankel-Funktionen Ko und K1 des rein imaginären Arguments i mit = Vo/kT mit großer Genauigkeit darzustellen.

On the role of complex phases in the quantum statistics of weak measurements

International Nuclear Information System (INIS)

Hofmann, Holger F

2011-01-01

Weak measurements carried out between quantum state preparation and post-selection result in complex values for self-adjoint operators, corresponding to complex conditional probabilities for the projections on specific eigenstates. In this paper it is shown that the complex phases of these weak conditional probabilities describe the dynamic response of the system to unitary transformations. Quantum mechanics thus unifies the statistical overlap of different states with the dynamical structure of transformations between these states. Specifically, it is possible to identify the phase of weak conditional probabilities directly with the action of a unitary transform that maximizes the overlap of initial and final states. This action provides a quantitative measure of how much quantum correlations can diverge from the deterministic relations between physical properties expected from classical physics or hidden variable theories. In terms of quantum information, the phases of weak conditional probabilities thus represent the logical tension between sets of three quantum states that is at the heart of quantum paradoxes. (paper)

Statistics, synergy, and mechanism of multiple photogeneration of excitons in quantum dots: Fundamental and applied aspects

International Nuclear Information System (INIS)

Oksengendler, B. L.; Turaeva, N. N.; Uralov, I.; Marasulov, M. B.

2012-01-01

The effect of multiple exciton generation is analyzed based on statistical physics, quantum mechanics, and synergetics. Statistical problems of the effect of multiple exciton generation (MEG) are broadened and take into account not only exciton generation, but also background excitation. The study of the role of surface states of quantum dots is based on the synergy of self-catalyzed electronic reactions. An analysis of the MEG mechanism is based on the idea of electronic shaking using the sudden perturbation method in quantum mechanics. All of the above-mentioned results are applied to the problem of calculating the limiting efficiency to transform solar energy into electric energy. (authors)

Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions

NARCIS (Netherlands)

Marcolli, Matilde; Cornelissen, Gunther

2014-01-01

The zeta function of a number field can be interpreted as the partition function of an associated quantum statistical mechanical (QSM) system, built from abelian class field theory. We introduce a general notion of isomorphism of QSM-systems and prove that it preserves (extremal) KMS equilibrium

Quantum theory of multiscale coarse-graining.

Science.gov (United States)

Han, Yining; Jin, Jaehyeok; Wagner, Jacob W; Voth, Gregory A

2018-03-14

Coarse-grained (CG) models serve as a powerful tool to simulate molecular systems at much longer temporal and spatial scales. Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in quantum statistical mechanics, by generalizing the multiscale coarse-graining (MS-CG) method to quantum Boltzmann statistics. A rigorous derivation of the sufficient thermodynamic consistency condition is first presented via imaginary time Feynman path integrals. It identifies the optimal choice of CG action functional and effective quantum CG (qCG) force field to generate a quantum MS-CG (qMS-CG) description of the equilibrium system that is consistent with the quantum fine-grained model projected onto the CG variables. A variational principle then provides a class of algorithms for optimally approximating the qMS-CG force fields. Specifically, a variational method based on force matching, which was also adopted in the classical MS-CG theory, is generalized to quantum Boltzmann statistics. The qMS-CG numerical algorithms and practical issues in implementing this variational minimization procedure are also discussed. Then, two numerical examples are presented to demonstrate the method. Finally, as an alternative strategy, a quasi-classical approximation for the thermal density matrix expressed in the CG variables is derived. This approach provides an interesting physical picture for coarse-graining in quantum Boltzmann statistical mechanics in which the consistency with the quantum particle delocalization is obviously manifest, and it opens up an avenue for using path integral centroid-based effective classical force fields in a coarse-graining methodology.

Quantum theory of multiscale coarse-graining

Science.gov (United States)

Han, Yining; Jin, Jaehyeok; Wagner, Jacob W.; Voth, Gregory A.

2018-03-01

Coarse-grained (CG) models serve as a powerful tool to simulate molecular systems at much longer temporal and spatial scales. Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in quantum statistical mechanics, by generalizing the multiscale coarse-graining (MS-CG) method to quantum Boltzmann statistics. A rigorous derivation of the sufficient thermodynamic consistency condition is first presented via imaginary time Feynman path integrals. It identifies the optimal choice of CG action functional and effective quantum CG (qCG) force field to generate a quantum MS-CG (qMS-CG) description of the equilibrium system that is consistent with the quantum fine-grained model projected onto the CG variables. A variational principle then provides a class of algorithms for optimally approximating the qMS-CG force fields. Specifically, a variational method based on force matching, which was also adopted in the classical MS-CG theory, is generalized to quantum Boltzmann statistics. The qMS-CG numerical algorithms and practical issues in implementing this variational minimization procedure are also discussed. Then, two numerical examples are presented to demonstrate the method. Finally, as an alternative strategy, a quasi-classical approximation for the thermal density matrix expressed in the CG variables is derived. This approach provides an interesting physical picture for coarse-graining in quantum Boltzmann statistical mechanics in which the consistency with the quantum particle delocalization is obviously manifest, and it opens up an avenue for using path integral centroid-based effective classical force fields in a coarse-graining methodology.

Quantum mechanical analysis on faujasite-type molecular sieves by using fermi dirac statistics and quantum theory of dielectricity

International Nuclear Information System (INIS)

Jabeen, S.; Raza, S.M.; Ahmed, M.A.; Zai, M.Y.; Akbar, S.; Jafri, Y.Z.

2012-01-01

We studied Faujasite type molecular sieves by using Fermi Dirac statistics and the quantum theory of dielectricity. We developed an empirical relationship for quantum capacitance which follows an inverse Gaussian profile in the frequency range of 66 Hz - 3 MHz. We calculated quantum capacitance, sample crystal momentum, charge quantization and quantized energy of Faujasite type molecular sieves in the frequency range of 0.1 Hz - 10/sup 4/ MHz. Our calculations for diameter of sodalite and super-cages of Faujasite type molecular sieves are in agreement with experimental results reported in this manuscript. We also calculated quantum polarizability, quantized molecular field, orientational polarizability and deformation polarizability by using experimental results of Ligia Frunza etal. The phonons are over damped in the frequency range 0.1 Hz - 10 kHz and become a source for producing cages in the Faujasite type molecular sieves. Ion exchange recovery processes occur due to over damped phonon excitations in Faujasite type molecular sieves and with increasing temperatures. (author)

Quantum Simulation of the Quantum Rabi Model in a Trapped Ion

Science.gov (United States)

Lv, Dingshun; An, Shuoming; Liu, Zhenyu; Zhang, Jing-Ning; Pedernales, Julen S.; Lamata, Lucas; Solano, Enrique; Kim, Kihwan

2018-04-01

The quantum Rabi model, involving a two-level system and a bosonic field mode, is arguably the simplest and most fundamental model describing quantum light-matter interactions. Historically, due to the restricted parameter regimes of natural light-matter processes, the richness of this model has been elusive in the lab. Here, we experimentally realize a quantum simulation of the quantum Rabi model in a single trapped ion, where the coupling strength between the simulated light mode and atom can be tuned at will. The versatility of the demonstrated quantum simulator enables us to experimentally explore the quantum Rabi model in detail, including a wide range of otherwise unaccessible phenomena, as those happening in the ultrastrong and deep strong-coupling regimes. In this sense, we are able to adiabatically generate the ground state of the quantum Rabi model in the deep strong-coupling regime, where we are able to detect the nontrivial entanglement between the bosonic field mode and the two-level system. Moreover, we observe the breakdown of the rotating-wave approximation when the coupling strength is increased, and the generation of phonon wave packets that bounce back and forth when the coupling reaches the deep strong-coupling regime. Finally, we also measure the energy spectrum of the quantum Rabi model in the ultrastrong-coupling regime.

Quantum Simulation of the Quantum Rabi Model in a Trapped Ion

Directory of Open Access Journals (Sweden)

Dingshun Lv

2018-04-01

Full Text Available The quantum Rabi model, involving a two-level system and a bosonic field mode, is arguably the simplest and most fundamental model describing quantum light-matter interactions. Historically, due to the restricted parameter regimes of natural light-matter processes, the richness of this model has been elusive in the lab. Here, we experimentally realize a quantum simulation of the quantum Rabi model in a single trapped ion, where the coupling strength between the simulated light mode and atom can be tuned at will. The versatility of the demonstrated quantum simulator enables us to experimentally explore the quantum Rabi model in detail, including a wide range of otherwise unaccessible phenomena, as those happening in the ultrastrong and deep strong-coupling regimes. In this sense, we are able to adiabatically generate the ground state of the quantum Rabi model in the deep strong-coupling regime, where we are able to detect the nontrivial entanglement between the bosonic field mode and the two-level system. Moreover, we observe the breakdown of the rotating-wave approximation when the coupling strength is increased, and the generation of phonon wave packets that bounce back and forth when the coupling reaches the deep strong-coupling regime. Finally, we also measure the energy spectrum of the quantum Rabi model in the ultrastrong-coupling regime.

Theoretical physics vol. 2. Quantum mechanics, relativistic quantum mechanics, quantum field theory, elementar-particle theory, thermodynamics and statistics

International Nuclear Information System (INIS)

Rebhan, E.

2005-01-01

The present second volume treats quantum mechanics, relativistic quantum mechanics, the foundations of quantum-field and elementary-particle theory as well as thermodynamics and statistics. Both volumes comprehend all fields, which are usually offered in a course about theoretical physics. In all treated fields a very careful introduction to the basic natural laws forms the starting point, whereby it is thoroughly analysed, which of them is based on empirics, which is logically deducible, and which role play basic definitions. Extendingly the matter extend of the corresponding courses starting from the relativistic quantum theory an introduction to the elementary particles is developed. All problems are very thoroughly and such extensively studied, that each step is singularly reproducible. On motivation and good understandability is cared much about. The mixing of mathematical difficulties with problems of physical nature often obstructive in the learning is so circumvented, that important mathematical methods are presented in own chapters (for instance Hilbert spaces, Lie groups). By means of many examples and problems (for a large part with solutions) the matter worked out is deepened and exercised. Developments, which are indeed important, but seem for the first approach abandonable, are pursued in excurses. This book starts from courses, which the author has held at the Heinrich-Heine university in Duesseldorf, and was in many repetitions fitted to the requirements of the students. It is conceived in such a way, that it is also after the study suited as dictionary or for the regeneration

Quantum group and quantum symmetry

International Nuclear Information System (INIS)

Chang Zhe.

1994-05-01

This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum group is primarily introduced as a systematic method for solving the Yang-Baxter equation. Quantum group theory is presented within the framework of quantum double through quantizing Lie bi-algebra. Both the highest weight and the cyclic representations are investigated for the quantum group and emphasis is laid on the new features of representations for q being a root of unity. Quantum symmetries are explored in selected topics of modern physics. For a Hamiltonian system the quantum symmetry is an enlarged symmetry that maintains invariance of equations of motion and allows a deformation of the Hamiltonian and symplectic form. The configuration space of the integrable lattice model is analyzed in terms of the representation theory of quantum group. By means of constructing the Young operators of quantum group, the Schroedinger equation of the model is transformed to be a set of coupled linear equations that can be solved by the standard method. Quantum symmetry of the minimal model and the WZNW model in conformal field theory is a hidden symmetry expressed in terms of screened vertex operators, and has a deep interplay with the Virasoro algebra. In quantum group approach a complete description for vibrating and rotating diatomic molecules is given. The exact selection rules and wave functions are obtained. The Taylor expansion of the analytic formulas of the approach reproduces the famous Dunham expansion. (author). 133 refs, 20 figs

Theoretical modelling of quantum circuit systems

International Nuclear Information System (INIS)

Stiffell, Peter Barry

2002-01-01

The work in this thesis concentrates on the interactions between circuit systems operating in the quantum regime. The main thrust of this work involves the use of a new model for investigating the way in which different components in such systems behave when coupled together. This is achieved by utilising the matrix representation of quantum mechanics, in conjunction with a number of other theoretical techniques (such as Wigner functions and entanglement entropies). With these tools in place it then becomes possible to investigate and review different quantum circuit systems. These investigations cover systems ranging from simple electromagnetic (cm) field oscillators in isolation to coupled SQUID rings in more sophisticated multi-component arrangements. Primarily, we look at the way SQUID rings couple to em fields, and how the ring-field interaction can be mediated by the choice of external flux, Φ x , applied to the SQUID ring. A lot of interest is focused on the transfer of energy between the system modes. However, we also investigate the statistical properties of the system, including squeezing, entropy and entanglement. Among the phenomena uncovered in this research we note the ability to control coupling in SQUID rings via the external flux, the capacity for entanglement between quantum circuit modes, frequency conversions of photons, flux squeezing and the existence of Schroedinger Cat states. (author)

Extent of multiparticle quantum nonlocality

International Nuclear Information System (INIS)

Jones, Nick S.; Linden, Noah; Massar, Serge

2005-01-01

It is well known that entangled quantum states are nonlocal: the corrrelations between local measurements carried out on these states cannot be reproduced by local hidden variable models. Svetlichny, followed by others, showed that multipartite quantum states are more nonlocal than bipartite ones in the sense that even some nonlocal classical models with (super-luminal) communication between some of the parties cannot reproduce the quantum correlations. Here we study in detail the kinds of nonlocality present in quantum states. More precisely, we enquire what kinds of classical communication patterns cannot reproduce quantum correlations. By studying the extremal points of the space of all multiparty probability distributions, in which all parties can make one of a pair of measurements each with two possible outcomes, we find a necessary condition for classical nonlocal models to reproduce the statistics of all quantum states. This condition extends and generalizes work of Svetlichny and others in which it was showed that a particular class of classical nonlocal models, the 'separable' models, cannot reproduce the statistics of all multiparticle quantum states. Our condition shows that the nonlocality present in some entangled multiparticle quantum states is much stronger than previously thought. We also study the sufficiency of our condition

Renormalization of boundary conditions for distribution functions of quasiparticles obeying quantum statistics at interfaces between crystalline grains

International Nuclear Information System (INIS)

Grendel, M.

1981-01-01

Boundary conditions for distribution functions of quasiparticles scattered by an interface between two crystalline grains are presented. Contrary to former formulations where Maxwell-Boltzmann statistics was considered, the present boundary conditions take into account the quantum statistics (Fermi-Dirac or Bose-Einstein) of quasiparticles. Provided that small deviations only from thermodynamic equilibrium are present, the boundary conditions are linearized, and then their ''renormalization'' is investigated in case of elastic scattering. The final results of the renormalization, which are obtained for a simplified model of an interface, sugo.est that the portion of the Fermi (Bose)-quasiparticles reflected or transmitted specularly is decreased (increased) in comparison with the case of quasiparticles obeying Maxwell-Boltzmann statistics. (author)

Quantum statistics for a two-mode magnon system with microwave pumping: application to coupled ferromagnetic nanowires.

Science.gov (United States)

Haghshenasfard, Zahra; Cottam, M G

2017-05-17

A microscopic (Hamiltonian-based) method for the quantum statistics of bosonic excitations in a two-mode magnon system is developed. Both the exchange and the dipole-dipole interactions, as well as the Zeeman term for an external applied field, are included in the spin Hamiltonian, and the model also contains the nonlinear effects due to parallel pumping and four-magnon interactions. The quantization of spin operators is achieved through the Holstein-Primakoff formalism, and then a coherent magnon state representation is used to study the occupation magnon number and the quantum statistical behaviour of the system. Particular attention is given to the cross correlation between the two coupled magnon modes in a ferromagnetic nanowire geometry formed by two lines of spins. Manipulation of the collapse-and-revival phenomena for the temporal evolution of the magnon number as well as the control of the cross correlation between the two magnon modes is demonstrated by tuning the parallel pumping field amplitude. The role of the four-magnon interactions is particularly interesting and leads to anti-correlation in some cases with coherent states.

Quantum statistics for a two-mode magnon system with microwave pumping: application to coupled ferromagnetic nanowires

International Nuclear Information System (INIS)

Haghshenasfard, Zahra; Cottam, M G

2017-01-01

A microscopic (Hamiltonian-based) method for the quantum statistics of bosonic excitations in a two-mode magnon system is developed. Both the exchange and the dipole–dipole interactions, as well as the Zeeman term for an external applied field, are included in the spin Hamiltonian, and the model also contains the nonlinear effects due to parallel pumping and four-magnon interactions. The quantization of spin operators is achieved through the Holstein–Primakoff formalism, and then a coherent magnon state representation is used to study the occupation magnon number and the quantum statistical behaviour of the system. Particular attention is given to the cross correlation between the two coupled magnon modes in a ferromagnetic nanowire geometry formed by two lines of spins. Manipulation of the collapse-and-revival phenomena for the temporal evolution of the magnon number as well as the control of the cross correlation between the two magnon modes is demonstrated by tuning the parallel pumping field amplitude. The role of the four-magnon interactions is particularly interesting and leads to anti-correlation in some cases with coherent states. (paper)

Non-extensive statistical mechanics and black hole entropy from quantum geometry

Directory of Open Access Journals (Sweden)

Abhishek Majhi

2017-12-01

Full Text Available Using non-extensive statistical mechanics, the Bekenstein–Hawking area law is obtained from microstates of black holes in loop quantum gravity, for arbitrary real positive values of the Barbero–Immirzi parameter (γ. The arbitrariness of γ is encoded in the strength of the “bias” created in the horizon microstates through the coupling with the quantum geometric fields exterior to the horizon. An experimental determination of γ will fix this coupling, leaving out the macroscopic area of the black hole to be the only free quantity of the theory.

Quantum theory and statistical thermodynamics principles and worked examples

CERN Document Server

Hertel, Peter

2017-01-01

This textbook presents a concise yet detailed introduction to quantum physics. Concise, because it condenses the essentials to a few principles. Detailed, because these few principles –  necessarily rather abstract – are illustrated by several telling examples. A fairly complete overview of the conventional quantum mechanics curriculum is the primary focus, but the huge field of statistical thermodynamics is covered as well. The text explains why a few key discoveries shattered the prevailing broadly accepted classical view of physics. First, matter appears to consist of particles which, when propagating, resemble waves. Consequently, some observable properties cannot be measured simultaneously with arbitrary precision. Second, events with single particles are not determined, but are more or less probable. The essence of this is that the observable properties of a physical system are to be represented by non-commuting mathematical objects instead of real numbers.  Chapters on exceptionally simple, but h...

Statistical interpretation of transient current power-law decay in colloidal quantum dot arrays

Energy Technology Data Exchange (ETDEWEB)

Sibatov, R T, E-mail: ren_sib@bk.ru [Ulyanovsk State University, 432000, 42 Leo Tolstoy Street, Ulyanovsk (Russian Federation)

2011-08-01

A new statistical model of the charge transport in colloidal quantum dot arrays is proposed. It takes into account Coulomb blockade forbidding multiple occupancy of nanocrystals and the influence of energetic disorder of interdot space. The model explains power-law current transients and the presence of the memory effect. The fractional differential analogue of the Ohm law is found phenomenologically for nanocrystal arrays. The model combines ideas that were considered as conflicting by other authors: the Scher-Montroll idea about the power-law distribution of waiting times in localized states for disordered semiconductors is applied taking into account Coulomb blockade; Novikov's condition about the asymptotic power-law distribution of time intervals between successful current pulses in conduction channels is fulfilled; and the carrier injection blocking predicted by Ginger and Greenham (2000 J. Appl. Phys. 87 1361) takes place.

Statistical interpretation of transient current power-law decay in colloidal quantum dot arrays

International Nuclear Information System (INIS)

Sibatov, R T

2011-01-01

A new statistical model of the charge transport in colloidal quantum dot arrays is proposed. It takes into account Coulomb blockade forbidding multiple occupancy of nanocrystals and the influence of energetic disorder of interdot space. The model explains power-law current transients and the presence of the memory effect. The fractional differential analogue of the Ohm law is found phenomenologically for nanocrystal arrays. The model combines ideas that were considered as conflicting by other authors: the Scher-Montroll idea about the power-law distribution of waiting times in localized states for disordered semiconductors is applied taking into account Coulomb blockade; Novikov's condition about the asymptotic power-law distribution of time intervals between successful current pulses in conduction channels is fulfilled; and the carrier injection blocking predicted by Ginger and Greenham (2000 J. Appl. Phys. 87 1361) takes place.

An introduction to conformal invariance in quantum field theory and statistical mechanics

International Nuclear Information System (INIS)

Boyanovsky, D.; Naon, C.M.

1990-01-01

The subject of conformal invariance provides an extraordinarly successful and productive symbiosis between statistical mechanics and quantum field theory. The main goal of this paper, which is tailored to a wide audience, is to give an introduction to such vast subject (C.P.)

Quantum secure communication models comparison

Directory of Open Access Journals (Sweden)

Georgi Petrov Bebrov

2017-12-01

Full Text Available The paper concerns the quantum cryptography, more specifically, the quantum secure communication type of schemes. The main focus here is on making a comparison between the distinct secure quantum communication models – quantum secure direct communication and deterministic secure quantum communication, in terms of three parameters: resource efficiency, eavesdropping check efficiency, and security (degree of preserving the confidentiality.

A quantum-implementable neural network model

Science.gov (United States)

Chen, Jialin; Wang, Lingli; Charbon, Edoardo

2017-10-01

A quantum-implementable neural network, namely quantum probability neural network (QPNN) model, is proposed in this paper. QPNN can use quantum parallelism to trace all possible network states to improve the result. Due to its unique quantum nature, this model is robust to several quantum noises under certain conditions, which can be efficiently implemented by the qubus quantum computer. Another advantage is that QPNN can be used as memory to retrieve the most relevant data and even to generate new data. The MATLAB experimental results of Iris data classification and MNIST handwriting recognition show that much less neuron resources are required in QPNN to obtain a good result than the classical feedforward neural network. The proposed QPNN model indicates that quantum effects are useful for real-life classification tasks.

Exactly solvable models of 2D-quantum gravity on the lattice. Course 5

International Nuclear Information System (INIS)

Kazakov, V.A.

1990-01-01

It is shown that statistical mechanical models defined on randomly triangulated surfaces can be solved exactly and that thereby the results on 2-D quantum gravity can be confirmed. (author). 32 refs.; 4 figs.; 2 tabs

Decoy-state quantum key distribution with both source errors and statistical fluctuations

International Nuclear Information System (INIS)

Wang Xiangbin; Yang Lin; Peng Chengzhi; Pan Jianwei

2009-01-01

We show how to calculate the fraction of single-photon counts of the 3-intensity decoy-state quantum cryptography faithfully with both statistical fluctuations and source errors. Our results rely only on the bound values of a few parameters of the states of pulses.

Statistical representation of quantum states

Energy Technology Data Exchange (ETDEWEB)

Montina, A [Dipartimento di Fisica, Universita di Firenze, Via Sansone 1, 50019 Sesto Fiorentino (Italy)

2007-05-15

In the standard interpretation of quantum mechanics, the state is described by an abstract wave function in the representation space. Conversely, in a realistic interpretation, the quantum state is replaced by a probability distribution of physical quantities. Bohm mechanics is a consistent example of realistic theory, where the wave function and the particle positions are classically defined quantities. Recently, we proved that the probability distribution in a realistic theory cannot be a quadratic function of the quantum state, in contrast to the apparently obvious suggestion given by the Born rule for transition probabilities. Here, we provide a simplified version of this proof.

Trajectory phases of a quantum dot model

International Nuclear Information System (INIS)

Genway, Sam; Hickey, James M; Garrahan, Juan P; Armour, Andrew D

2014-01-01

We present a thermodynamic formalism to study the trajectories of charge transport through a quantum dot coupled to two leads in the resonant-level model. We show that a close analogue of equilibrium phase transitions exists for the statistics of transferred charge; by tuning an appropriate ‘counting field’, crossovers to different trajectory phases are possible. Our description reveals a mapping between the statistics of a given device and current measurements over a range of devices with different dot–lead coupling strengths. Furthermore insight into features of the trajectory phases are found by studying the occupation of the dot conditioned on the transported charge between the leads; this is calculated from first principles using a trajectory biased two-point projective measurement scheme. (paper)

Spin-Wave Wave Function for Quantum Spin Models : Condensed Matter and Statistical Physics

OpenAIRE

Franjo, FRANJIC; Sandro, SORELLA; Istituto Nazionale di Fisica della Materia International School for Advance Studies; Istituto Nazionale di Fisica della Materia International School for Advance Studies

1997-01-01

We present a new approach to determine an accurate variational wave function for general quantum spin models, completely defined by a consistency requirement with the simple and well-known linear spin-wave expansion. With this wave function, it is also possible to obtain the correct behavior of the long distance correlation functions for the 1D S=1/2 antiferromagnet. In 2D the proposed spin-wave wave function represents an excellent approximation to the exact ground state of the S=1.2 XY mode...

The Gtr-Model a Universal Framework for Quantum-Like Measurements

Science.gov (United States)

Aerts, Diederik; Bianchi, Massimiliano Sassoli De

We present a very general geometrico-dynamical description of physical or more abstract entities, called the general tension-reduction (GTR) model, where not only states, but also measurement-interactions can be represented, and the associated outcome probabilities calculated. Underlying the model is the hypothesis that indeterminism manifests as a consequence of unavoidable uctuations in the experimental context, in accordance with the hidden-measurements interpretation of quantum mechanics. When the structure of the state space is Hilbertian, and measurements are of the universal kind, i.e., are the result of an average over all possible ways of selecting an outcome, the GTR-model provides the same predictions of the Born rule, and therefore provides a natural completed version of quantum mechanics. However, when the structure of the state space is non-Hilbertian and/or not all possible ways of selecting an outcome are available to be actualized, the predictions of the model generally differ from the quantum ones, especially when sequential measurements are considered. Some paradigmatic examples will be discussed, taken from physics and human cognition. Particular attention will be given to some known psychological effects, like question order effects and response replicability, which we show are able to generate non-Hilbertian statistics. We also suggest a realistic interpretation of the GTR-model, when applied to human cognition and decision, which we think could become the generally adopted interpretative framework in quantum cognition research.

Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics

OpenAIRE

Salathé, Y.; Mondal, M.; Oppliger, M.; Heinsoo, J.; Kurpiers, P.; Potočnik, A.; Mezzacapo, Antonio; Las Heras García, Urtzi; Lamata Manuel, Lucas; Solano Villanueva, Enrique Leónidas; Filipp, S.; Wallraff, A.

2015-01-01

Systems of interacting quantum spins show a rich spectrum of quantum phases and display interesting many-body dynamics. Computing characteristics of even small systems on conventional computers poses significant challenges. A quantum simulator has the potential to outperform standard computers in calculating the evolution of complex quantum systems. Here, we perform a digital quantum simulation of the paradigmatic Heisenberg and Ising interacting spin models using a two transmon-qubit circuit...

Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics

Directory of Open Access Journals (Sweden)

Y. Salathé

2015-06-01

Full Text Available Systems of interacting quantum spins show a rich spectrum of quantum phases and display interesting many-body dynamics. Computing characteristics of even small systems on conventional computers poses significant challenges. A quantum simulator has the potential to outperform standard computers in calculating the evolution of complex quantum systems. Here, we perform a digital quantum simulation of the paradigmatic Heisenberg and Ising interacting spin models using a two transmon-qubit circuit quantum electrodynamics setup. We make use of the exchange interaction naturally present in the simulator to construct a digital decomposition of the model-specific evolution and extract its full dynamics. This approach is universal and efficient, employing only resources that are polynomial in the number of spins, and indicates a path towards the controlled simulation of general spin dynamics in superconducting qubit platforms.

Reason of method of density functional in classical and quantum statistical mechanisms

International Nuclear Information System (INIS)

Dinariev, O.Yu.

2000-01-01

Interaction between phenomenological description of a multi-component mixture on the basis of entropy functional with members, square in terms of component density gradients and temperature, on the one hand, and description in the framework of classical and quantum statistical mechanics, on the other hand, was investigated. Explicit expressions for the entropy functional in the classical and quantum theory were derived. Then a square approximation for the case of minor disturbances of uniform state was calculated. In the approximation the addends square in reference to the gradient were singlet out. It permits calculation of the relevant phenomenological coefficients from the leading principles [ru

Conjugate pair of non-extensive statistics in quantum scattering

International Nuclear Information System (INIS)

Ion, D.B.; Ion, M.L.D.

1999-01-01

In this paper, by defining the Fourier transform of the scattering amplitudes as a bounded linear mapping from the space L 2p to the space L 2q when 1/(2p)+1/(2q)=1, we introduced a new concept in quantum physics in terms of Tsallis-like entropies S J (p) and S θ (q), namely, that of conjugate pair of non-extensive statistics. This new concept is experimentally illustrated by using 88 + 49 sets of pion-nucleon and pion-nucleus phase shifts. From the experimental determination of the (p,q) - non-extensivity indices by choosing the pairs for which the [χ L 2 (p) + χ θ 2 (q min )] - optimal - test function is minimum we get the conjugate pair of [(p min ,J),(q min , θ)]- non-extensive statistics with 0.50 ≤ p min ≤ 0.60. This new non-extensive statistical effect is experimentally evidenced with high degree of accuracy (CL≥ 99%). Moreover, it is worth to mention that the modification of the statistics has been more efficient than the modification of the PMD-SQS-optimum principle in obtaining the best overall fitting to the experimental data. (authors)

On quantum models of the human mind.

Science.gov (United States)

Wang, Hongbin; Sun, Yanlong

2014-01-01

Recent years have witnessed rapidly increasing interests in developing quantum theoretical models of human cognition. Quantum mechanisms have been taken seriously to describe how the mind reasons and decides. Papers in this special issue report the newest results in the field. Here we discuss why the two levels of commitment, treating the human brain as a quantum computer and merely adopting abstract quantum probability principles to model human cognition, should be integrated. We speculate that quantum cognition models gain greater modeling power due to a richer representation scheme. Copyright © 2013 Cognitive Science Society, Inc.

Statistical inference with quantum measurements: methodologies for nitrogen vacancy centers in diamond

Science.gov (United States)

Hincks, Ian; Granade, Christopher; Cory, David G.

2018-01-01

The analysis of photon count data from the standard nitrogen vacancy (NV) measurement process is treated as a statistical inference problem. This has applications toward gaining better and more rigorous error bars for tasks such as parameter estimation (e.g. magnetometry), tomography, and randomized benchmarking. We start by providing a summary of the standard phenomenological model of the NV optical process in terms of Lindblad jump operators. This model is used to derive random variables describing emitted photons during measurement, to which finite visibility, dark counts, and imperfect state preparation are added. NV spin-state measurement is then stated as an abstract statistical inference problem consisting of an underlying biased coin obstructed by three Poisson rates. Relevant frequentist and Bayesian estimators are provided, discussed, and quantitatively compared. We show numerically that the risk of the maximum likelihood estimator is well approximated by the Cramér-Rao bound, for which we provide a simple formula. Of the estimators, we in particular promote the Bayes estimator, owing to its slightly better risk performance, and straightforward error propagation into more complex experiments. This is illustrated on experimental data, where quantum Hamiltonian learning is performed and cross-validated in a fully Bayesian setting, and compared to a more traditional weighted least squares fit.

Models of optical quantum computing

Directory of Open Access Journals (Sweden)

Krovi Hari

2017-03-01

Full Text Available I review some work on models of quantum computing, optical implementations of these models, as well as the associated computational power. In particular, we discuss the circuit model and cluster state implementations using quantum optics with various encodings such as dual rail encoding, Gottesman-Kitaev-Preskill encoding, and coherent state encoding. Then we discuss intermediate models of optical computing such as boson sampling and its variants. Finally, we review some recent work in optical implementations of adiabatic quantum computing and analog optical computing. We also provide a brief description of the relevant aspects from complexity theory needed to understand the results surveyed.

Quantum decoration transformation for spin models

Energy Technology Data Exchange (ETDEWEB)

Braz, F.F.; Rodrigues, F.C.; Souza, S.M. de; Rojas, Onofre, E-mail: ors@dfi.ufla.br

2016-09-15

It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the “classical” limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising–Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.

Quantum decoration transformation for spin models

International Nuclear Information System (INIS)

Braz, F.F.; Rodrigues, F.C.; Souza, S.M. de; Rojas, Onofre

2016-01-01

It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the “classical” limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising–Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.

Representation of the contextual statistical model by hyperbolic amplitudes

International Nuclear Information System (INIS)

Khrennikov, Andrei

2005-01-01

We continue the development of a so-called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric cos-interference, there exist contexts producing the hyperbolic cos-interference. Starting with the corresponding interference formula of total probability we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of the Hilbert space. There is obtained a hyperbolic Born's rule. Incompatible observables are represented by noncommutative operators. This paper can be considered as the first step towards hyperbolic quantum probability. We also discuss possibilities of experimental verification of hyperbolic quantum mechanics: in physics of elementary particles, string theory as well as in experiments with nonphysical systems, e.g., in psychology, cognitive sciences, and economy

Quantum integrable models of field theory

International Nuclear Information System (INIS)

Faddeev, L.D.

1979-01-01

Fundamental features of the classical method of the inverse problem have been formulated in the form which is convenient for its quantum reformulation. Typical examples are studied which may help to formulate the quantum method of the inverse problem. Examples are considered for interaction with both attraction and repulsion at a final density. The sine-Gordon model and the XYZ model from the quantum theory of magnetics are examined in short. It is noted that all the achievements of the one-dimensional mathematical physics as applied to exactly solvable quantum models may be put to an extent within the framework of the quantum method of the inverse problem. Unsolved questions are enumerated and perspectives of applying the inverse problem method are shown

Fermions from classical statistics

International Nuclear Information System (INIS)

Wetterich, C.

2010-01-01

We describe fermions in terms of a classical statistical ensemble. The states τ of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability distribution can be associated to a quantum state for fermions. If the time evolution of the classical probabilities p τ amounts to a rotation of the wave function q τ (t)=±√(p τ (t)), we infer the unitary time evolution of a quantum system of fermions according to a Schroedinger equation. We establish how such classical statistical ensembles can be mapped to Grassmann functional integrals. Quantum field theories for fermions arise for a suitable time evolution of classical probabilities for generalized Ising models.

Quantum mechanics as a natural generalization of classical statistical mechanics

International Nuclear Information System (INIS)

Xu Laizi; Qian Shangwu

1994-01-01

By comparison between equations of motion of geometrical optics (GO) and that of classical statistical mechanics (CSM), it is found that there should be an analogy between GO and CSM instead of GO and classical mechanics (CM). Furthermore, by comparison between the classical limit (CL) of quantum mechanics (QM) and CSM, the authors find that CL of QM is CSM not CM, hence they demonstrated that QM is a natural generalization of CSM instead of CM

Modeling techniques for quantum cascade lasers

Energy Technology Data Exchange (ETDEWEB)

Jirauschek, Christian [Institute for Nanoelectronics, Technische Universität München, D-80333 Munich (Germany); Kubis, Tillmann [Network for Computational Nanotechnology, Purdue University, 207 S Martin Jischke Drive, West Lafayette, Indiana 47907 (United States)

2014-03-15

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation of quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.

Modeling techniques for quantum cascade lasers

Science.gov (United States)

Jirauschek, Christian; Kubis, Tillmann

2014-03-01

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation of quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.

From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems

Science.gov (United States)

Lozada Aguilar, Miguel Ángel; Khrennikov, Andrei; Oleschko, Klaudia

2018-04-01

As was recently shown by the authors, quantum probability theory can be used for the modelling of the process of decision-making (e.g. probabilistic risk analysis) for macroscopic geophysical structures such as hydrocarbon reservoirs. This approach can be considered as a geophysical realization of Hilbert's programme on axiomatization of statistical models in physics (the famous sixth Hilbert problem). In this conceptual paper, we continue development of this approach to decision-making under uncertainty which is generated by complexity, variability, heterogeneity, anisotropy, as well as the restrictions to accessibility of subsurface structures. The belief state of a geological expert about the potential of exploring a hydrocarbon reservoir is continuously updated by outputs of measurements, and selection of mathematical models and scales of numerical simulation. These outputs can be treated as signals from the information environment E. The dynamics of the belief state can be modelled with the aid of the theory of open quantum systems: a quantum state (representing uncertainty in beliefs) is dynamically modified through coupling with E; stabilization to a steady state determines a decision strategy. In this paper, the process of decision-making about hydrocarbon reservoirs (e.g. `explore or not?'; `open new well or not?'; `contaminated by water or not?'; `double or triple porosity medium?') is modelled by using the Gorini-Kossakowski-Sudarshan-Lindblad equation. In our model, this equation describes the evolution of experts' predictions about a geophysical structure. We proceed with the information approach to quantum theory and the subjective interpretation of quantum probabilities (due to quantum Bayesianism). This article is part of the theme issue `Hilbert's sixth problem'.

From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems.

Science.gov (United States)

Lozada Aguilar, Miguel Ángel; Khrennikov, Andrei; Oleschko, Klaudia

2018-04-28

As was recently shown by the authors, quantum probability theory can be used for the modelling of the process of decision-making (e.g. probabilistic risk analysis) for macroscopic geophysical structures such as hydrocarbon reservoirs. This approach can be considered as a geophysical realization of Hilbert's programme on axiomatization of statistical models in physics (the famous sixth Hilbert problem). In this conceptual paper , we continue development of this approach to decision-making under uncertainty which is generated by complexity, variability, heterogeneity, anisotropy, as well as the restrictions to accessibility of subsurface structures. The belief state of a geological expert about the potential of exploring a hydrocarbon reservoir is continuously updated by outputs of measurements, and selection of mathematical models and scales of numerical simulation. These outputs can be treated as signals from the information environment E The dynamics of the belief state can be modelled with the aid of the theory of open quantum systems: a quantum state (representing uncertainty in beliefs) is dynamically modified through coupling with E ; stabilization to a steady state determines a decision strategy. In this paper, the process of decision-making about hydrocarbon reservoirs (e.g. 'explore or not?'; 'open new well or not?'; 'contaminated by water or not?'; 'double or triple porosity medium?') is modelled by using the Gorini-Kossakowski-Sudarshan-Lindblad equation. In our model, this equation describes the evolution of experts' predictions about a geophysical structure. We proceed with the information approach to quantum theory and the subjective interpretation of quantum probabilities (due to quantum Bayesianism).This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Collision models in quantum optics

Science.gov (United States)

Ciccarello, Francesco

2017-12-01

Quantum collision models (CMs) provide advantageous case studies for investigating major issues in open quantum systems theory, and especially quantum non-Markovianity. After reviewing their general definition and distinctive features, we illustrate the emergence of a CM in a familiar quantum optics scenario. This task is carried out by highlighting the close connection between the well-known input-output formalism and CMs. Within this quantum optics framework, usual assumptions in the CMs' literature - such as considering a bath of noninteracting yet initially correlated ancillas - have a clear physical origin.

Integrable quantum impurity models

International Nuclear Information System (INIS)

Eckle, H.P.

1998-01-01

By modifying some of the local L operators of the algebraic form of the Bethe Ansatz inhomogeneous one dimensional quantum lattice models can be constructed. This fact has recently attracted new attention, the inhomogeneities being interpreted as local impurities. The Hamiltonians of the so constructed one-dimensional quantum models have a nearest neighbour structure except in the vicinity of the local impurities which involve three-site interactions. The pertinent feature of these models is the absence of backscattering at the impurities: the impurities are transparent. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)

Integrable models in 1+1 dimensional quantum field theory

International Nuclear Information System (INIS)

Faddeev, Ludvig.

1982-09-01

The goal of this lecture is to present a unifying view on the exactly soluble models. There exist several reasons arguing in favor of the 1+1 dimensional models: every exact solution of a field-theoretical model can teach about the ability of quantum field theory to describe spectrum and scattering; some 1+1 d models have physical applications in the solid state theory. There are several ways to become acquainted with the methods of exactly soluble models: via classical statistical mechanics, via Bethe Ansatz, via inverse scattering method. Fundamental Poisson bracket relation FPR and/or fundamental commutation relations FCR play fundamental role. General classification of FPR is given with promizing generalizations to FCR

Thermo-dynamical contours of electronic-vibrational spectra simulated using the statistical quantum-mechanical methods

DEFF Research Database (Denmark)

Pomogaev, Vladimir; Pomogaeva, Anna; Avramov, Pavel

2011-01-01

Three polycyclic organic molecules in various solvents focused on thermo-dynamical aspects were theoretically investigated using the recently developed statistical quantum mechanical/classical molecular dynamics method for simulating electronic-vibrational spectra. The absorption bands of estradiol...

Classical and Quantum Models in Non-Equilibrium Statistical Mechanics: Moment Methods and Long-Time Approximations

Directory of Open Access Journals (Sweden)

Ramon F. Alvarez-Estrada

2012-02-01

Full Text Available We consider non-equilibrium open statistical systems, subject to potentials and to external “heat baths” (hb at thermal equilibrium at temperature T (either with ab initio dissipation or without it. Boltzmann’s classical equilibrium distributions generate, as Gaussian weight functions in momenta, orthogonal polynomials in momenta (the position-independent Hermite polynomialsHn’s. The moments of non-equilibrium classical distributions, implied by the Hn’s, fulfill a hierarchy: for long times, the lowest moment dominates the evolution towards thermal equilibrium, either with dissipation or without it (but under certain approximation. We revisit that hierarchy, whose solution depends on operator continued fractions. We review our generalization of that moment method to classical closed many-particle interacting systems with neither a hb nor ab initio dissipation: with initial states describing thermal equilibrium at T at large distances but non-equilibrium at finite distances, the moment method yields, approximately, irreversible thermalization of the whole system at T, for long times. Generalizations to non-equilibrium quantum interacting systems meet additional difficulties. Three of them are: (i equilibrium distributions (represented through Wigner functions are neither Gaussian in momenta nor known in closed form; (ii they may depend on dissipation; and (iii the orthogonal polynomials in momenta generated by them depend also on positions. We generalize the moment method, dealing with (i, (ii and (iii, to some non-equilibrium one-particle quantum interacting systems. Open problems are discussed briefly.

Lifetime statistics of quantum chaos studied by a multiscale analysis

KAUST Repository

Di Falco, A.

2012-04-30

In a series of pump and probe experiments, we study the lifetime statistics of a quantum chaotic resonator when the number of open channels is greater than one. Our design embeds a stadium billiard into a two dimensional photonic crystal realized on a silicon-on-insulator substrate. We calculate resonances through a multiscale procedure that combines energy landscape analysis and wavelet transforms. Experimental data is found to follow the universal predictions arising from random matrix theory with an excellent level of agreement.

Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model

International Nuclear Information System (INIS)

Langmann, Edwin

2006-01-01

We present remarkable functional identities related to the elliptic Calogero-Sutherland (eCS) system. We derive them from a second quantization of the eCS model within a quantum field theory model of anyons on a circle and at finite temperature. The identities involve two eCS Hamiltonians with arbitrary and, in general, different particle numbers N and M, and a particular function of N+M variables arising as anyon correlation function of N particles and M antiparticles. In addition to identities obtained from anyons with the same statistics parameter λ, we also obtain 'dual' relations involving 'mixed' correlation functions of anyons with two different statistics parameters λ and 1/λ. We also give alternative, elementary proofs of these identities by direct computations

Quantum kinematics of spacetime. II. A model quantum cosmology with real clocks

International Nuclear Information System (INIS)

Hartle, J.B.

1988-01-01

Nonrelativistic model quantum cosmologies are studied in which the basic time variable is the position of a clock indicator and the time parameter of the Schroedinger equation is an unobservable label. Familiar Schroedinger-Heisenberg quantum mechanics emerges if the clock is ideal: arbitrarily accurate for arbitrarily long times. More realistically, however, the usual formulation emerges only as an approximation appropriate to states of this model universe in which part of the system functions approximately as an ideal clock. It is suggested that the quantum kinematics of spacetime theories such as general relativity may be analogous to those of this model. In particular it is suggested that our familiar notion of time in quantum mechanics is not an inevitable property of a general quantum framework but an approximate feature of specific initial conditions

Quantum lattice model solver HΦ

Science.gov (United States)

Kawamura, Mitsuaki; Yoshimi, Kazuyoshi; Misawa, Takahiro; Yamaji, Youhei; Todo, Synge; Kawashima, Naoki

2017-08-01

HΦ [aitch-phi ] is a program package based on the Lanczos-type eigenvalue solution applicable to a broad range of quantum lattice models, i.e., arbitrary quantum lattice models with two-body interactions, including the Heisenberg model, the Kitaev model, the Hubbard model and the Kondo-lattice model. While it works well on PCs and PC-clusters, HΦ also runs efficiently on massively parallel computers, which considerably extends the tractable range of the system size. In addition, unlike most existing packages, HΦ supports finite-temperature calculations through the method of thermal pure quantum (TPQ) states. In this paper, we explain theoretical background and user-interface of HΦ. We also show the benchmark results of HΦ on supercomputers such as the K computer at RIKEN Advanced Institute for Computational Science (AICS) and SGI ICE XA (Sekirei) at the Institute for the Solid State Physics (ISSP).

Vortices in superconducting films: Statistics and fractional quantum Hall effect

International Nuclear Information System (INIS)

Dziarmaga, J.

1996-01-01

We present a derivation of the Berry phase picked up during exchange of parallel vortices. This derivation is based on the Bogolubov endash de Gennes formalism. The origin of the Magnus force is also critically reanalyzed. The Magnus force can be interpreted as an interaction with the effective magnetic field. The effective magnetic field may be even of the order 10 6 T/A. We discuss a possibility of the fractional quantum Hall effect (FQHE) in vortex systems. As the real magnetic field is varied to drive changes in vortex density, the vortex density will prefer to stay at some quantized values. The mere existence of the FQHE does not depend on vortex quantum statistics, although the pattern of the plateaux does. We also discuss how the density of anyonic vortices can lower the effective strengh of the Magnus force, what might be observable in measurements of Hall resistivity. copyright 1996 The American Physical Society

Index of subfactors and statistics of quantum fields. Pt. 2

International Nuclear Information System (INIS)

Longo, R.

1990-01-01

The endomorphism semigroup End(M) of an infinite factor M is endowed with a natural conjugation (modulo inner automorphisms) anti ρ=ρ -1. γ, where γ is the canonical endomorphism of ρ(M) into M. In Quantum Field Theory conjugate endomorphisms are shown to correspond to conjugate superselection sectors in the description of Doplicher, Haag and Roberts. On the other hand one easily sees that conjugate endormorphisms correspond to conjugate correspondences in the setting of A. Connes. In particular we identify the canonical tower associated with the inclusion ρ(A(O)is contained inA(O) relative to a sector ρ. As a corollary, making use of our previously established index-statistics correspondence, we conpletely describe, in low dimensional theories, the statistics of a selfconjugate superselection sector ρ with 3 or less channels, in particular with statistical dimension d(ρ)<2, by obtaining the braid group representations of V. Jones and Birman, Wenzyl and Murakami. The statistics is thus described in these cases by the polynomial invariants for knots and links of Jones and Kauffman. Selfconjugate sectors are subdivided in real and pseudoreal ones and the effect of this distinction on the statistics is analyzed. The FYHLMO polynomial describes arbitrary 2-channels sectors. (orig.)

Super-quantum curves from super-eigenvalue models

Energy Technology Data Exchange (ETDEWEB)

Ciosmak, Paweł [Faculty of Mathematics, Informatics and Mechanics, University of Warsaw,ul. Banacha 2, 02-097 Warsaw (Poland); Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagiellonian University,ul. Łojasiewicza 11, 30-348 Kraków (Poland); Manabe, Masahide [Faculty of Physics, University of Warsaw,ul. Pasteura 5, 02-093 Warsaw (Poland); Sułkowski, Piotr [Faculty of Physics, University of Warsaw,ul. Pasteura 5, 02-093 Warsaw (Poland); Walter Burke Institute for Theoretical Physics, California Institute of Technology,1200 E. California Blvd, Pasadena, CA 91125 (United States)

2016-10-10

In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

Super-quantum curves from super-eigenvalue models

International Nuclear Information System (INIS)

Ciosmak, Paweł; Hadasz, Leszek; Manabe, Masahide; Sułkowski, Piotr

2016-01-01

In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

Super-quantum curves from super-eigenvalue models

Science.gov (United States)

Ciosmak, Paweł; Hadasz, Leszek; Manabe, Masahide; Sułkowski, Piotr

2016-10-01

In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/ β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

Effective-field-theory model for the fractional quantum Hall effect

International Nuclear Information System (INIS)

Zhang, S.C.; Hansson, T.H.; Kivelson, S.

1989-01-01

Starting directly from the microscopic Hamiltonian, we derive a field-theory model for the fractional quantum hall effect. By considering an approximate coarse-grained version of the same model, we construct a Landau-Ginzburg theory similar to that of Girvin. The partition function of the model exhibits cusps as a function of density and the Hall conductance is quantized at filling factors ν = (2k-1)/sup -1/ with k an arbitrary integer. At these fractions the ground state is incompressible, and the quasiparticles and quasiholes have fractional charge and obey fractional statistics. Finally, we show that the collective density fluctuations are massive

Quantum-Like Model for Decision Making Process in Two Players Game. A Non-Kolmogorovian Model

Science.gov (United States)

Asano, Masanari; Ohya, Masanori; Khrennikov, Andrei

2011-03-01

In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4-17, 2005; Biosystems 84:225-241, 2006; Found. Phys. 35(10):1655-1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105-117, 2009), it was pointed out that statistics collected in such the experiments have "quantum-like" properties, which can not be explained in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33-59, 1999).

Ubiquitous Quantum Structure From Psychology to Finance

CERN Document Server

Khrennikov, Andrei Y

2010-01-01

Quantum-like structure is present practically everywhere. Quantum-like (QL) models, i.e. models based on the mathematical formalism of quantum mechanics and its generalizations can be successfully applied to cognitive science, psychology, genetics, economics, finances, and game theory. This book is not about quantum mechanics as a physical theory. The short review of quantum postulates is therefore mainly of historical value: quantum mechanics is just the first example of the successful application of non-Kolmogorov probabilities, the first step towards a contextual probabilistic description of natural, biological, psychological, social, economical or financial phenomena. A general contextual probabilistic model (Växjö model) is presented. It can be used for describing probabilities in both quantum and classical (statistical) mechanics as well as in the above mentioned phenomena. This model can be represented in a quantum-like way, namely, in complex and more general Hilbert spaces. In this way quantum prob...

Quantum protocols within Spekkens' toy model

Science.gov (United States)

Disilvestro, Leonardo; Markham, Damian

2017-05-01

Quantum mechanics is known to provide significant improvements in information processing tasks when compared to classical models. These advantages range from computational speedups to security improvements. A key question is where these advantages come from. The toy model developed by Spekkens [R. W. Spekkens, Phys. Rev. A 75, 032110 (2007), 10.1103/PhysRevA.75.032110] mimics many of the features of quantum mechanics, such as entanglement and no cloning, regarded as being important in this regard, despite being a local hidden variable theory. In this work, we study several protocols within Spekkens' toy model where we see it can also mimic the advantages and limitations shown in the quantum case. We first provide explicit proofs for the impossibility of toy bit commitment and the existence of a toy error correction protocol and consequent k -threshold secret sharing. Then, defining a toy computational model based on the quantum one-way computer, we prove the existence of blind and verified protocols. Importantly, these two last quantum protocols are known to achieve a better-than-classical security. Our results suggest that such quantum improvements need not arise from any Bell-type nonlocality or contextuality, but rather as a consequence of steering correlations.

Quantum Statistics: Is there an effective fermion repulsion or boson attraction?

OpenAIRE

Mullin, W. J.; Blaylock, G.

2003-01-01

Physicists often claim that there is an effective repulsion between fermions, implied by the Pauli principle, and a corresponding effective attraction between bosons. We examine the origins of such exchange force ideas, the validity for them, and the areas where they are highly misleading. We propose that future explanations of quantum statistics should avoid the idea of a effective force completely and replace it with more appropriate physical insights, some of which are suggested here.

Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors.

Science.gov (United States)

Pandey, Akhilesh; Kumar, Avanish; Puri, Sanjay

2017-11-01

Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte Carlo simulations. These models yield new universality classes, and provide a theoretical framework for the study of banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α, the appropriate FRCG model has the effective range d=b^{2}/N=α^{2}/N, for large N matrix dimensionality. As d increases, there is a transition from Poisson to classical random matrix statistics.

Quantum vertex model for reversible classical computing.

Science.gov (United States)

Chamon, C; Mucciolo, E R; Ruckenstein, A E; Yang, Z-C

2017-05-12

Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching solution even for easy problems known to be solvable in polynomial time. Here we map universal reversible classical computations onto a planar vertex model that exhibits no bulk classical thermodynamic phase transition, independent of the computational circuit. Within our approach the solution of the computation is encoded in the ground state of the vertex model and its complexity is reflected in the dynamics of the relaxation of the system to its ground state. We use thermal annealing with and without 'learning' to explore typical computational problems. We also construct a mapping of the vertex model into the Chimera architecture of the D-Wave machine, initiating an approach to reversible classical computation based on state-of-the-art implementations of quantum annealing.

Are quantum-mechanical-like models possible, or necessary, outside quantum physics?

International Nuclear Information System (INIS)

Plotnitsky, Arkady

2014-01-01

This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well. (paper)

Multiscale representation of generating and correlation functions for some models of statistical mechanics and quantum field theory

International Nuclear Information System (INIS)

O'Carroll, M.

1993-01-01

The author considers models of statistical mechanics and quantum field theory (in the Euclidean formulation) which are treated using renormalization group methods and where the action is a small perturbation of a quadratic action. The author obtains multiscale formulas for the generating and correlation functions after n renormalization group transformations which bring out the relation with the nth effective action. The author derives and compares the formulas for different RGs. The formulas for correlation functions involve (1) two propagators which are determined by a sequence of approximate wave function renormalization constants and renormalization group operators associated with the decomposition into scales of the quadratic form and (2) field derivatives of the nth effective action. For the case of the block field open-quotes δ-functionclose quotes RG the formulas are especially simple and for asymptotic free theories only the derivatives at zero field are needed; the formulas have been previously used directly to obtain bounds on correlation functions using information obtained from the analysis of effective actions. The simplicity can be traced to an open-quotes orthogonality-of-scalesclose quotes property which follows from an implicit wavelet structure. Other commonly used RGs do not have the open-quotes orthogonality of scalesclose quotes property. 19 refs

Quantum kinetic Ising models

International Nuclear Information System (INIS)

Augusiak, R; Cucchietti, F M; Lewenstein, M; Haake, F

2010-01-01

In this paper, we introduce a quantum generalization of classical kinetic Ising models (KIM), described by a certain class of quantum many-body master equations. Similarly to KIMs with detailed balance that are equivalent to certain Hamiltonian systems, our models reduce to a set of Hamiltonian systems determining the dynamics of the elements of the many-body density matrix. The ground states of these Hamiltonians are well described by the matrix product, or pair entangled projected states. We discuss critical properties of such Hamiltonians, as well as entanglement properties of their low-energy states.

Quantum mechanics with non-negative quantum distribution function

International Nuclear Information System (INIS)

Zorin, A.V.; Sevastianov, L.A.

2010-01-01

Full text: (author)Among numerous approaches to probabilistic interpretation of the conventional quantum mechanics the most close to the N. Bohr idea of the correspondence principle is the D.I. Blokhintzev - Ya.P. Terletsky approach using the quantum distribution function on the coordinate- momentum space. The detailed investigation of this approach has lead to the correspondence rule of V.V. Kuryshkin. Quantum mechanics of Kuryshkin (QMK) embody the program proposed by Yu.M. Shirokov for unifying classical and quantum mechanics in similar mathematical models. QMK develops and enhances Wigner's proposal concerning the calculation of quantum corrections to classical thermodynamic parameters using a phase distribution function. The main result of QMK is the possibility of description by mean of a positively-valued distribution function. This represents an important step towards a completely statistical model of quantum phenomena, compared with the quasi-probabilistic nature of Wigner distribution. Wigner's model does not permit to perform correctly the classical limit in quantum mechanics as well. On the other hand, QMK has a much more complex structure of operators of observables. One of the unsolved problems of QMK is the absence of a priori rules for establishing of auxiliary functions. Nevertheless, while it is impossible to overcome the complex form of operators, we find it quite possible to derive some methods of filing sets of auxiliary functions

Quantum probabilistic logic programming

Science.gov (United States)

Balu, Radhakrishnan

2015-05-01

We describe a quantum mechanics based logic programming language that supports Horn clauses, random variables, and covariance matrices to express and solve problems in probabilistic logic. The Horn clauses of the language wrap random variables, including infinite valued, to express probability distributions and statistical correlations, a powerful feature to capture relationship between distributions that are not independent. The expressive power of the language is based on a mechanism to implement statistical ensembles and to solve the underlying SAT instances using quantum mechanical machinery. We exploit the fact that classical random variables have quantum decompositions to build the Horn clauses. We establish the semantics of the language in a rigorous fashion by considering an existing probabilistic logic language called PRISM with classical probability measures defined on the Herbrand base and extending it to the quantum context. In the classical case H-interpretations form the sample space and probability measures defined on them lead to consistent definition of probabilities for well formed formulae. In the quantum counterpart, we define probability amplitudes on Hinterpretations facilitating the model generations and verifications via quantum mechanical superpositions and entanglements. We cast the well formed formulae of the language as quantum mechanical observables thus providing an elegant interpretation for their probabilities. We discuss several examples to combine statistical ensembles and predicates of first order logic to reason with situations involving uncertainty.

Quantum social science

CERN Document Server

Haven, Emmanuel

2013-01-01

Written by world experts in the foundations of quantum mechanics and its applications to social science, this book shows how elementary quantum mechanical principles can be applied to decision-making paradoxes in psychology and used in modelling information in finance and economics. The book starts with a thorough overview of some of the salient differences between classical, statistical and quantum mechanics. It presents arguments on why quantum mechanics can be applied outside of physics and defines quantum social science. The issue of the existence of quantum probabilistic effects in psychology, economics and finance is addressed and basic questions and answers are provided. Aimed at researchers in economics and psychology, as well as physics, basic mathematical preliminaries and elementary concepts from quantum mechanics are defined in a self-contained way.

Fractionalizing Majorana Fermions: Non-Abelian Statistics on the Edges of Abelian Quantum Hall States

Directory of Open Access Journals (Sweden)

Netanel H. Lindner

2012-10-01

Full Text Available We study the non-Abelian statistics characterizing systems where counterpropagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity coupling to superconductors and ferromagnets. The most transparent example is that of a fractional quantum spin Hall state, in which electrons of one spin direction occupy a fractional quantum Hall state of ν=1/m, while electrons of the opposite spin occupy a similar state with ν=-1/m. However, we also propose other examples of such systems, which are easier to realize experimentally. We find that each interface between a region on the edge coupled to a superconductor and a region coupled to a ferromagnet corresponds to a non-Abelian anyon of quantum dimension sqrt[2m]. We calculate the unitary transformations that are associated with the braiding of these anyons, and we show that they are able to realize a richer set of non-Abelian representations of the braid group than the set realized by non-Abelian anyons based on Majorana fermions. We carry out this calculation both explicitly and by applying general considerations. Finally, we show that topological manipulations with these anyons cannot realize universal quantum computation.

Modeling Quantum Well Lasers

Directory of Open Access Journals (Sweden)

Dan Alexandru Anghel

2012-01-01

Full Text Available In semiconductor laser modeling, a good mathematical model gives near-reality results. Three methods of modeling solutions from the rate equations are presented and analyzed. A method based on the rate equations modeled in Simulink to describe quantum well lasers was presented. For different signal types like step function, saw tooth and sinus used as input, a good response of the used equations is obtained. Circuit model resulting from one of the rate equations models is presented and simulated in SPICE. Results show a good modeling behavior. Numerical simulation in MathCad gives satisfactory results for the study of the transitory and dynamic operation at small level of the injection current. The obtained numerical results show the specific limits of each model, according to theoretical analysis. Based on these results, software can be built that integrates circuit simulation and other modeling methods for quantum well lasers to have a tool that model and analysis these devices from all points of view.

Existence and uniqueness of Gibbs states for a statistical mechanical polyacetylene model

International Nuclear Information System (INIS)

Park, Y.M.

1987-01-01

One-dimensional polyacetylene is studied as a model of statistical mechanics. In a semiclassical approximation the system is equivalent to a quantum XY model interacting with unbounded classical spins in one-dimensional lattice space Z. By establishing uniform estimates, an infinite-volume-limit Hilbert space, a strongly continuous time evolution group of unitary operators, and an invariant vector are constructed. Moreover, it is proven that any infinite-limit state satisfies Gibbs conditions. Finally, a modification of Araki's relative entropy method is used to establish the uniqueness of Gibbs states

Decoding β-decay systematics: A global statistical model for β- half-lives

International Nuclear Information System (INIS)

Costiris, N. J.; Mavrommatis, E.; Gernoth, K. A.; Clark, J. W.

2009-01-01

Statistical modeling of nuclear data provides a novel approach to nuclear systematics complementary to established theoretical and phenomenological approaches based on quantum theory. Continuing previous studies in which global statistical modeling is pursued within the general framework of machine learning theory, we implement advances in training algorithms designed to improve generalization, in application to the problem of reproducing and predicting the half-lives of nuclear ground states that decay 100% by the β - mode. More specifically, fully connected, multilayer feed-forward artificial neural network models are developed using the Levenberg-Marquardt optimization algorithm together with Bayesian regularization and cross-validation. The predictive performance of models emerging from extensive computer experiments is compared with that of traditional microscopic and phenomenological models as well as with the performance of other learning systems, including earlier neural network models as well as the support vector machines recently applied to the same problem. In discussing the results, emphasis is placed on predictions for nuclei that are far from the stability line, and especially those involved in r-process nucleosynthesis. It is found that the new statistical models can match or even surpass the predictive performance of conventional models for β-decay systematics and accordingly should provide a valuable additional tool for exploring the expanding nuclear landscape.

Engineering quantum mechanics

CERN Document Server

Ahn, Doyeol

2011-01-01

A clear introduction to quantum mechanics concepts Quantum mechanics has become an essential tool for modern engineering, particularly due to the recent developments in quantum computing as well as the rapid progress in optoelectronic devices. Engineering Quantum Mechanics explains the fundamentals of this exciting field, providing broad coverage of both traditional areas such as semiconductor and laser physics as well as relatively new yet fast-growing areas such as quantum computation and quantum information technology. The book begins with basic quantum mechanics, reviewing measurements and probability, Dirac formulation, the uncertainty principle, harmonic oscillator, angular momentum eigenstates, and perturbation theory. Then, quantum statistical mechanics is explored, from second quantization and density operators to coherent and squeezed states, coherent interactions between atoms and fields, and the Jaynes-Cummings model. From there, the book moves into elementary and modern applications, discussing s...

Field theory of anyons and the fractional quantum Hall effect

International Nuclear Information System (INIS)

Viefers, S.F.

1997-11-01

The thesis is devoted to a theoretical study of anyons, i.e. particles with fractional statistics moving in two space dimensions, and the quantum Hall effect. The latter constitutes the only known experimental realization of anyons in that the quasiparticle excitations in the fractional quantum Hall system are believed to obey fractional statistics. First, the properties of ideal quantum gases in two dimensions and in particular the equation of state of the free anyons gas are discussed. Then, a field theory formulation of anyons in a strong magnetic field is presented and later extended to a system with several species of anyons. The relation of this model to fractional exclusion statistics, i.e. intermediate statistics introduced by a generalization of the Pauli principle, and to the low-energy excitations at the edge of the quantum Hall system is discussed. Finally, the Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect is studied, mainly focusing on edge effects; both the ground state and the low-energy edge excitations are examined in the simple one-component model and in an extended model which includes spin effects

The determinants of bond angle variability in protein/peptide backbones: A comprehensive statistical/quantum mechanics analysis.

Science.gov (United States)

Improta, Roberto; Vitagliano, Luigi; Esposito, Luciana

2015-11-01

The elucidation of the mutual influence between peptide bond geometry and local conformation has important implications for protein structure refinement, validation, and prediction. To gain insights into the structural determinants and the energetic contributions associated with protein/peptide backbone plasticity, we here report an extensive analysis of the variability of the peptide bond angles by combining statistical analyses of protein structures and quantum mechanics calculations on small model peptide systems. Our analyses demonstrate that all the backbone bond angles strongly depend on the peptide conformation and unveil the existence of regular trends as function of ψ and/or φ. The excellent agreement of the quantum mechanics calculations with the statistical surveys of protein structures validates the computational scheme here employed and demonstrates that the valence geometry of protein/peptide backbone is primarily dictated by local interactions. Notably, for the first time we show that the position of the H(α) hydrogen atom, which is an important parameter in NMR structural studies, is also dependent on the local conformation. Most of the trends observed may be satisfactorily explained by invoking steric repulsive interactions; in some specific cases the valence bond variability is also influenced by hydrogen-bond like interactions. Moreover, we can provide a reliable estimate of the energies involved in the interplay between geometry and conformations. © 2015 Wiley Periodicals, Inc.

Some properties of the statistical models of the spherical Friedman world

International Nuclear Information System (INIS)

Rumyantseva, E.N.

1981-01-01

Considered are some properties of the statistical model of the spherical Friedman world filled with quantum gas of massless particles the spin of which can be equal to 0, 1/2, 1. Obtained are approximate expressions for a number of particles of Fermi- and Bose-gas and for the radius of the world taking into account mainly the dependence on the spin. The dependence of the number of particles on the radius of the world and temperature of the gas is illustrated [ru

Quantum metrology

International Nuclear Information System (INIS)

Xiang Guo-Yong; Guo Guang-Can

2013-01-01

The statistical error is ineluctable in any measurement. Quantum techniques, especially with the development of quantum information, can help us squeeze the statistical error and enhance the precision of measurement. In a quantum system, there are some quantum parameters, such as the quantum state, quantum operator, and quantum dimension, which have no classical counterparts. So quantum metrology deals with not only the traditional parameters, but also the quantum parameters. Quantum metrology includes two important parts: measuring the physical parameters with a precision beating the classical physics limit and measuring the quantum parameters precisely. In this review, we will introduce how quantum characters (e.g., squeezed state and quantum entanglement) yield a higher precision, what the research areas are scientists most interesting in, and what the development status of quantum metrology and its perspectives are. (topical review - quantum information)

Quantum statistics and squeezing for a microwave-driven interacting magnon system.

Science.gov (United States)

Haghshenasfard, Zahra; Cottam, Michael G

2017-02-01

Theoretical studies are reported for the statistical properties of a microwave-driven interacting magnon system. Both the magnetic dipole-dipole and the exchange interactions are included and the theory is developed for the case of parallel pumping allowing for the inclusion of the nonlinear processes due to the four-magnon interactions. The method of second quantization is used to transform the total Hamiltonian from spin operators to boson creation and annihilation operators. By using the coherent magnon state representation we have studied the magnon occupation number and the statistical behavior of the system. In particular, it is shown that the nonlinearities introduced by the parallel pumping field and the four-magnon interactions lead to non-classical quantum statistical properties of the system, such as magnon squeezing. Also control of the collapse-and-revival phenomena for the time evolution of the average magnon number is demonstrated by varying the parallel pumping amplitude and the four-magnon coupling.

Characterization of Strong Light-Matter Coupling in Semiconductor Quantum-Dot Microcavities via Photon-Statistics Spectroscopy

Science.gov (United States)

Schneebeli, L.; Kira, M.; Koch, S. W.

2008-08-01

It is shown that spectrally resolved photon-statistics measurements of the resonance fluorescence from realistic semiconductor quantum-dot systems allow for high contrast identification of the two-photon strong-coupling states. Using a microscopic theory, the second-rung resonance of Jaynes-Cummings ladder is analyzed and optimum excitation conditions are determined. The computed photon-statistics spectrum displays gigantic, experimentally robust resonances at the energetic positions of the second-rung emission.

Formulation of uncertainty relation of error and disturbance in quantum measurement by using quantum estimation theory

International Nuclear Information System (INIS)

Yu Watanabe; Masahito Ueda

2012-01-01

quantum measurement [2]. We prove that the product of the errors of two observables and the product of the error and disturbance are both bounded by the commutation relation of the observables. However, the bounds cannot be attained in general. Therefore, it is expected that there exist tighter bounds. We obtain the attainable bounds of the product of the errors of two observables and the product of the error and disturbance. The bounds are both determined by quantum fluctuations and correlation function of the observables. The quantum fluctuation and correlation function characterize the non-classical fluctuations and correlation of the observables. Third, we introduce an information geometrical aspect of the uncertainty relations. Quantum measurement induces an classical statistical model of measurement outcomes from quantum statistical model of initial quantum states. The difference between the Fisher metrics on those statistical models gives the error incurred in the measurement process. Quantum measurement causes unavoidable state change, therefore, the Fisher metric on the statistical model of the post-measurement states decreases from the original one. (author), References: [1] Y. Watanabe, T. Sagawa, and M. Ueda, Phys. Rev. A 84, 042121 (2011). [2] Y. Watanabe, M. Ueda, arXiv:1106.2526 (2011).

Statistical physics

CERN Document Server

Sadovskii, Michael V

2012-01-01

This volume provides a compact presentation of modern statistical physics at an advanced level. Beginning with questions on the foundations of statistical mechanics all important aspects of statistical physics are included, such as applications to ideal gases, the theory of quantum liquids and superconductivity and the modern theory of critical phenomena. Beyond that attention is given to new approaches, such as quantum field theory methods and non-equilibrium problems.

Model of a programmable quantum processing unit based on a quantum transistor effect

Science.gov (United States)

Ablayev, Farid; Andrianov, Sergey; Fetisov, Danila; Moiseev, Sergey; Terentyev, Alexandr; Urmanchev, Andrey; Vasiliev, Alexander

2018-02-01

In this paper we propose a model of a programmable quantum processing device realizable with existing nano-photonic technologies. It can be viewed as a basis for new high performance hardware architectures. Protocols for physical implementation of device on the controlled photon transfer and atomic transitions are presented. These protocols are designed for executing basic single-qubit and multi-qubit gates forming a universal set. We analyze the possible operation of this quantum computer scheme. Then we formalize the physical architecture by a mathematical model of a Quantum Processing Unit (QPU), which we use as a basis for the Quantum Programming Framework. This framework makes it possible to perform universal quantum computations in a multitasking environment.

Opinion dynamics model based on quantum formalism

Energy Technology Data Exchange (ETDEWEB)

Artawan, I. Nengah, E-mail: nengahartawan@gmail.com [Theoretical Physics Division, Department of Physics, Udayana University (Indonesia); Trisnawati, N. L. P., E-mail: nlptrisnawati@gmail.com [Biophysics, Department of Physics, Udayana University (Indonesia)

2016-03-11

Opinion dynamics model based on quantum formalism is proposed. The core of the quantum formalism is on the half spin dynamics system. In this research the implicit time evolution operators are derived. The analogy between the model with Deffuant dan Sznajd models is discussed.

Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution.

Science.gov (United States)

Yang, Jaw-Yen; Yan, Chih-Yuan; Diaz, Manuel; Huang, Juan-Chen; Li, Zhihui; Zhang, Hanxin

2014-01-08

The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al . 2012 Proc. R. Soc. A 468 , 1799-1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi-Dirac or Bose-Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas.

Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution

Science.gov (United States)

Yang, Jaw-Yen; Yan, Chih-Yuan; Diaz, Manuel; Huang, Juan-Chen; Li, Zhihui; Zhang, Hanxin

2014-01-01

The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al. 2012 Proc. R. Soc. A 468, 1799–1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi–Dirac or Bose–Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas. PMID:24399919

Scaling properties of localized quantum chaos

International Nuclear Information System (INIS)

Izrailev, F.M.

1991-01-01

Statistical properties of spectra and eigenfunctions are studied for the model of quantum chaos in the presence of dynamical localization. The main attention is paid to the scaling properties of localization length and level spacing distribution in the intermediate region between Poissonian and Wigner-Dyson statistics. It is shown that main features of such localized quantum chaos are well described by the introduced ensemble of band random matrices. 28 refs.; 7 figs

Quantum statistics of stimulated Raman and hyper-Raman scattering by master equation approach

International Nuclear Information System (INIS)

Gupta, P.S.; Dash, J.

1991-01-01

A quantum theoretical density matrix formalism of stimulated Raman and hyper-Raman scattering using master equation approach is presented. The atomic system is described by two energy levels. The effects of upper level population and the cavity loss are incorporated. The photon statistics, coherence characteristics and the building up of the Stokes field are investigated. (author). 8 figs., 5 refs

Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation

Science.gov (United States)

Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui

2014-01-01

Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904

Modelling of multidimensional quantum systems by the numerical functional integration

International Nuclear Information System (INIS)

Lobanov, Yu.Yu.; Zhidkov, E.P.

1990-01-01

The employment of the numerical functional integration for the description of multidimensional systems in quantum and statistical physics is considered. For the multiple functional integrals with respect to Gaussian measures in the full separable metric spaces the new approximation formulas exact on a class of polynomial functionals of a given summary degree are constructed. The use of the formulas is demonstrated on example of computation of the Green function and the ground state energy in multidimensional Calogero model. 15 refs.; 2 tabs

Probing the statistical properties of Anderson localization with quantum emitters

International Nuclear Information System (INIS)

Smolka, Stephan; Thyrrestrup, Henri; Sapienza, Luca; Lehmann, Tau B; Rix, Kristian R; GarcIa, Pedro D; Lodahl, Peter; Froufe-Perez, Luis S

2011-01-01

Wave propagation in disordered media can be strongly modified by multiple scattering and wave interference. Ultimately, the so-called Anderson-localized regime is reached when the waves become strongly confined in space. So far, Anderson localization of light has been probed in transmission experiments by measuring the intensity of an external light source after propagation through a disordered medium. However, discriminating between Anderson localization and losses in these experiments remains a major challenge. In this paper, we present an alternative approach where we use quantum emitters embedded in disordered photonic crystal waveguides as light sources. Anderson-localized modes are efficiently excited and the analysis of the photoluminescence spectra allows us to explore their statistical properties, for example the localization length and average loss length. With increasing the amount of disorder induced in the photonic crystal, we observe a pronounced increase in the localization length that is attributed to changes in the local density of states, a behavior that is in stark contrast to entirely random systems. The analysis may pave the way for accurate models and the control of Anderson localization in disordered photonic crystals.

Sub-Poissonian statistics in order-to-chaos transition

International Nuclear Information System (INIS)

Kryuchkyan, Gagik Yu.; Manvelyan, Suren B.

2003-01-01

We study the phenomena at the overlap of quantum chaos and nonclassical statistics for the time-dependent model of nonlinear oscillator. It is shown in the framework of Mandel Q parameter and Wigner function that the statistics of oscillatory excitation numbers is drastically changed in the order-to-chaos transition. The essential improvement of sub-Poissonian statistics in comparison with an analogous one for the standard model of driven anharmonic oscillator is observed for the regular operational regime. It is shown that in the chaotic regime, the system exhibits the range of sub-Poissonian and super-Poissonian statistics which alternate one to other depending on time intervals. Unusual dependence of the variance of oscillatory number on the external noise level for the chaotic dynamics is observed. The scaling invariance of the quantum statistics is demonstrated and its relation to dissipation and decoherence is studied

Wave Mechanics or Wave Statistical Mechanics

International Nuclear Information System (INIS)

Qian Shangwu; Xu Laizi

2007-01-01

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.

Quantum cosmological models

International Nuclear Information System (INIS)

Coule, D H

2005-01-01

We contrast the initial condition requirements of various contemporary cosmological models including inflationary and bouncing cosmologies. Canonical quantization of general relativity is used, as a first approximation to full quantum gravity, to determine whether suitable initial conditions are present. Various proposals such as Hartle-Hawking's 'no boundary' or tunnelling boundary conditions are assessed on grounds of naturalness and fine tuning. Alternatively, a quiescent initial state or an initial closed timelike curve 'time machine' is considered. Possible extensions to brane models are also addressed. Further ideas about universe creation from a meta-universe are outlined. Semiclassical and time asymmetry requirements of cosmology are briefly discussed and contrasted with the black-hole final-state proposal. We compare the recent loop quantum cosmology of Bojowald and co-workers with these earlier schemes. A number of possible difficulties and limitations are outlined. (topical review)

Integrable models in classical and quantum mechanics

International Nuclear Information System (INIS)

Jurco, B.

1991-01-01

Integrable systems are investigated, especially the rational and trigonometric Gaudin models. The Gaudin models are diagonalized for the case of classical Lie algebras. Their relation to the other integrable models and to the quantum inverse scattering method is investigated. Applications in quantum optics and plasma physics are discussed. (author). 94 refs

Ubiquitous quantum structure. From psychology to finance

International Nuclear Information System (INIS)

Khrennikov, Andrei

2010-01-01

Quantum-like structure is present practically everywhere. Quantum-like (QL) models, i.e. models based on the mathematical formalism of quantum mechanics and its generalizations can be successfully applied to cognitive science, psychology, genetics, economics, finances, and game theory. This book is not about quantum mechanics as a physical theory. The short review of quantum postulates is therefore mainly of historical value: quantum mechanics is just the first example of the successful application of non-Kolmogorov probabilities, the first step towards a contextual probabilistic description of natural, biological, psychological, social, economical or financial phenomena. A general contextual probabilistic model (Vaexjoemodel) is presented. It can be used for describing probabilities in both quantum and classical (statistical) mechanics as well as in the above mentioned phenomena. This model can be represented in a quantum-like way, namely, in complex and more general Hilbert spaces. In this way quantum probability is totally demystified: Born's representation of quantum probabilities by complex probability amplitudes, wave functions, is simply a special representation of this type. (orig.)

Ubiquitous quantum structure. From psychology to finance

Energy Technology Data Exchange (ETDEWEB)

Khrennikov, Andrei [University of Vaexjoe (Sweden). International Center for Mathematical Modeling in Physics and Cognitive Science

2010-07-01

Quantum-like structure is present practically everywhere. Quantum-like (QL) models, i.e. models based on the mathematical formalism of quantum mechanics and its generalizations can be successfully applied to cognitive science, psychology, genetics, economics, finances, and game theory. This book is not about quantum mechanics as a physical theory. The short review of quantum postulates is therefore mainly of historical value: quantum mechanics is just the first example of the successful application of non-Kolmogorov probabilities, the first step towards a contextual probabilistic description of natural, biological, psychological, social, economical or financial phenomena. A general contextual probabilistic model (Vaexjoemodel) is presented. It can be used for describing probabilities in both quantum and classical (statistical) mechanics as well as in the above mentioned phenomena. This model can be represented in a quantum-like way, namely, in complex and more general Hilbert spaces. In this way quantum probability is totally demystified: Born's representation of quantum probabilities by complex probability amplitudes, wave functions, is simply a special representation of this type. (orig.)

Transformation & uncertainty : some thoughts on quantum probability theory, quantum statistics, and natural bundles

NARCIS (Netherlands)

Janssens, B.

2010-01-01

This PHD thesis is concerned partly with uncertainty relations in quantum probability theory, partly with state estimation in quantum stochastics, and partly with natural bundles in differential geometry. The laws of quantum mechanics impose severe restrictions on the performance of measurement.

A quantum-like model of homeopathy clinical trials: importance of in situ randomization and unblinding.

Science.gov (United States)

Beauvais, Francis

2013-04-01

The randomized controlled trial (RCT) is the 'gold standard' of modern clinical pharmacology. However, for many practitioners of homeopathy, blind RCTs are an inadequate research tool for testing complex therapies such as homeopathy. Classical probabilities used in biological sciences and in medicine are only a special case of the generalized theory of probability used in quantum physics. I describe homeopathy trials using a quantum-like statistical model, a model inspired by quantum physics and taking into consideration superposition of states, non-commuting observables, probability interferences, contextuality, etc. The negative effect of blinding on success of homeopathy trials and the 'smearing effect' ('specific' effects of homeopathy medicine occurring in the placebo group) are described by quantum-like probabilities without supplementary ad hoc hypotheses. The difference of positive outcome rates between placebo and homeopathy groups frequently vanish in centralized blind trials. The model proposed here suggests a way to circumvent such problems in masked homeopathy trials by incorporating in situ randomization/unblinding. In this quantum-like model of homeopathy clinical trials, success in open-label setting and failure with centralized blind RCTs emerge logically from the formalism. This model suggests that significant differences between placebo and homeopathy in blind RCTs would be found more frequently if in situ randomization/unblinding was used. Copyright © 2013. Published by Elsevier Ltd.

Universe before Planck time: A quantum gravity model

International Nuclear Information System (INIS)

Padmanabhan, T.

1983-01-01

A model for quantum gravity can be constructed by treating the conformal degree of freedom of spacetime as a quantum variable. An isotropic, homogeneous cosmological solution in this quantum gravity model is presented. The spacetime is nonsingular for all the three possible values of three-space curvature, and agrees with the classical solution for time scales larger than the Planck time scale. A possibility of quantum fluctuations creating the matter in the universe is suggested

Modeling stock return distributions with a quantum harmonic oscillator

Science.gov (United States)

Ahn, K.; Choi, M. Y.; Dai, B.; Sohn, S.; Yang, B.

2017-11-01

We propose a quantum harmonic oscillator as a model for the market force which draws a stock return from short-run fluctuations to the long-run equilibrium. The stochastic equation governing our model is transformed into a Schrödinger equation, the solution of which features “quantized” eigenfunctions. Consequently, stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., the geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness-of-fit statistics. In addition, making use of analogy, we provide an economic rationale of the physics concepts such as the eigenstate, eigenenergy, and angular frequency, which sheds light on the relationship between finance and econophysics literature.

Toy Models of a Nonassociative Quantum Mechanics

International Nuclear Information System (INIS)

Dzhunushaliev, V.

2007-01-01

Toy models of a nonassociative quantum mechanics are presented. The Heisenberg equation of motion is modified using a nonassociative commutator. Possible physical applications of a nonassociative quantum mechanics are considered. The idea is discussed that a nonassociative algebra could be the operator language for the nonperturbative quantum theory. In such approach the nonperturbative quantum theory has observables and un observables quantities.

Quantum billiards in multidimensional models with branes

Energy Technology Data Exchange (ETDEWEB)

Ivashchuk, V.D.; Melnikov, V.N. [VNIIMS, Center for Gravitation and Fundamental Metrology, Moscow (Russian Federation); Peoples' Friendship University of Russia, Institute of Gravitation and Cosmology, Moscow (Russian Federation)

2014-03-15

gravitational D-dimensional model with l scalar fields and several forms is considered. When a cosmological-type diagonal metric is chosen, an electromagnetic composite brane ansatz is adopted and certain restrictions on the branes are imposed; the conformally covariant Wheeler-DeWitt (WDW) equation for the model is studied. Under certain restrictions asymptotic solutions to WDW equation are found in the limit of the formation of the billiard walls which reduce the problem to the so-called quantum billiard on the (D+l-2)-dimensional Lobachevsky space. Two examples of quantum billiards are considered. The first one deals with 9-dimensional quantum billiard for D = 11 model with 330 four-forms which mimic space-like M2- and M5-branes of D = 11 supergravity. The second one deals with the 9-dimensional quantum billiard for D = 10 gravitational model with one scalar field, 210 four-forms and 120 three-forms which mimic space-like D2-, D4-, FS1- and NS5-branes in D = 10 IIA supergravity. It is shown that in both examples wave functions vanish in the limit of the formation of the billiard walls (i.e. we get a quantum resolution of the singularity for 11D model) but magnetic branes could not be neglected in calculations of quantum asymptotic solutions while they are irrelevant for classical oscillating behavior when all 120 electric branes are present. (orig.)

Quantum simulation of transverse Ising models with Rydberg atoms

Science.gov (United States)

Schauss, Peter

2018-04-01

Quantum Ising models are canonical models for the study of quantum phase transitions (Sachdev 1999 Quantum Phase Transitions (Cambridge: Cambridge University Press)) and are the underlying concept for many analogue quantum computing and quantum annealing ideas (Tanaka et al Quantum Spin Glasses, Annealing and Computation (Cambridge: Cambridge University Press)). Here we focus on the implementation of finite-range interacting Ising spin models, which are barely tractable numerically. Recent experiments with cold atoms have reached the interaction-dominated regime in quantum Ising magnets via optical coupling of trapped neutral atoms to Rydberg states. This approach allows for the tunability of all relevant terms in an Ising spin Hamiltonian with 1/{r}6 interactions in transverse and longitudinal fields. This review summarizes the recent progress of these implementations in Rydberg lattices with site-resolved detection. Strong correlations in quantum Ising models have been observed in several experiments, starting from a single excitation in the superatom regime up to the point of crystallization. The rapid progress in this field makes spin systems based on Rydberg atoms a promising platform for quantum simulation because of the unmatched flexibility and strength of interactions combined with high control and good isolation from the environment.

One-Way Deficit and Quantum Phase Transitions in XX Model

Science.gov (United States)

Wang, Yao-Kun; Zhang, Yu-Ran

2018-02-01

Quantum correlations including entanglement and quantum discord have drawn much attention in characterizing quantum phase transitions. Quantum deficit originates in questions regarding work extraction from quantum systems coupled to a heat bath (Oppenheim et al. Phys. Rev. Lett. 89, 180402, 2002). It links quantum thermodynamics with quantum correlations and provides a new standpoint for understanding quantum non-locality. In this paper, we evaluate the one-way deficit of two adjacent spins in the bulk for the XX model. In the thermodynamic limit, the XX model undergoes a first order transition from fully polarized to a critical phase with quasi-long-range order with decrease of quantum parameter. We find that the one-way deficit becomes nonzero after the critical point. Therefore, the one-way deficit characterizes the quantum phase transition in the XX model.

Mapping of parent hamiltonians from abelian and non-abelian quantum hall states to exact models of critical spin chains

CERN Document Server

Greiter, Martin

2011-01-01

This monograph introduces an exact model for a critical spin chain with arbitrary spin S, which includes the Haldane--Shastry model as the special case S=1/2.  While spinons in the Haldane-Shastry model obey abelian half-fermi statistics, the spinons in the general model introduced here obey non-abelian statistics.  This manifests itself through topological choices for the fractional momentum spacings.  The general model is derived by mapping exact models of quantized Hall states onto spin chains.  The book begins with pedagogical review of all the relevant models including the non-abelian statistics in the Pfaffian Hall state, and is understandable to every student with a graduate course in quantum mechanics.

Dynamics of quantum-classical differences for chaotic systems

International Nuclear Information System (INIS)

Ballentine, L.E.

2002-01-01

The differences between quantum and classical dynamics can be studied through the moments and correlations of the position and momentum variables in corresponding quantum and classical statistical states. In chaotic states the quantum-classical differences grow exponentially with an exponent that exceeds the classical Lyapunov exponent. It is shown analytically that the quantum-classical differences scale as (ℎ/2π) 2 , and that the exponent for the growth of these differences is independent of (ℎ/2π). The quantum-classical difference exponent is studied for two quartic potential models, and the results are compared with previous work on the Henon-Heiles model

Introduction to the basic concepts of modern physics special relativity, quantum and statistical physics

CERN Document Server

Becchi, Carlo Maria

2016-01-01

This is the third edition of a well-received textbook on modern physics theory. This book provides an elementary but rigorous and self-contained presentation of the simplest theoretical framework that will meet the needs of undergraduate students. In addition, a number of examples of relevant applications and an appropriate list of solved problems are provided.Apart from a substantial extension of the proposed problems, the new edition provides more detailed discussion on Lorentz transformations and their group properties, a deeper treatment of quantum mechanics in a central potential, and a closer comparison of statistical mechanics in classical and in quantum physics. The first part of the book is devoted to special relativity, with a particular focus on space-time relativity and relativistic kinematics. The second part deals with Schrödinger's formulation of quantum mechanics. The presentation concerns mainly one-dimensional problems, but some three-dimensional examples are discussed in detail. The third...

Rabi model as a quantum coherent heat engine: From quantum biology to superconducting circuits

Science.gov (United States)

Altintas, Ferdi; Hardal, Ali Ü. C.; Müstecaplıoǧlu, Özgür E.

2015-02-01

We propose a multilevel quantum heat engine with a working medium described by a generalized Rabi model which consists of a two-level system coupled to a single-mode bosonic field. The model is constructed to be a continuum limit of a quantum biological description of light-harvesting complexes so that it can amplify quantum coherence by a mechanism which is a quantum analog of classical Huygens clocks. The engine operates in a quantum Otto cycle where the working medium is coupled to classical heat baths in the isochoric processes of the four-stroke cycle, while either the coupling strength or the resonance frequency is changed in the adiabatic stages. We found that such an engine can produce work with an efficiency close to the Carnot bound when it operates at low temperatures and in the ultrastrong-coupling regime. The interplay of the effects of quantum coherence and quantum correlations on the engine performance is discussed in terms of second-order coherence, quantum mutual information, and the logarithmic negativity of entanglement. We point out that the proposed quantum Otto engine can be implemented experimentally with modern circuit quantum electrodynamic systems where flux qubits can be coupled ultrastrongly to superconducting transmission-line resonators.

Modeling a space-based quantum link that includes an adaptive optics system

Science.gov (United States)

Duchane, Alexander W.; Hodson, Douglas D.; Mailloux, Logan O.

2017-10-01

Quantum Key Distribution uses optical pulses to generate shared random bit strings between two locations. If a high percentage of the optical pulses are comprised of single photons, then the statistical nature of light and information theory can be used to generate secure shared random bit strings which can then be converted to keys for encryption systems. When these keys are incorporated along with symmetric encryption techniques such as a one-time pad, then this method of key generation and encryption is resistant to future advances in quantum computing which will significantly degrade the effectiveness of current asymmetric key sharing techniques. This research first reviews the transition of Quantum Key Distribution free-space experiments from the laboratory environment to field experiments, and finally, ongoing space experiments. Next, a propagation model for an optical pulse from low-earth orbit to ground and the effects of turbulence on the transmitted optical pulse is described. An Adaptive Optics system is modeled to correct for the aberrations caused by the atmosphere. The long-term point spread function of the completed low-earth orbit to ground optical system is explored in the results section. Finally, the impact of this optical system and its point spread function on an overall quantum key distribution system as well as the future work necessary to show this impact is described.

Quantum Biometrics with Retinal Photon Counting

Science.gov (United States)

Loulakis, M.; Blatsios, G.; Vrettou, C. S.; Kominis, I. K.

2017-10-01

It is known that the eye's scotopic photodetectors, rhodopsin molecules, and their associated phototransduction mechanism leading to light perception, are efficient single-photon counters. We here use the photon-counting principles of human rod vision to propose a secure quantum biometric identification based on the quantum-statistical properties of retinal photon detection. The photon path along the human eye until its detection by rod cells is modeled as a filter having a specific transmission coefficient. Precisely determining its value from the photodetection statistics registered by the conscious observer is a quantum parameter estimation problem that leads to a quantum secure identification method. The probabilities for false-positive and false-negative identification of this biometric technique can readily approach 10-10 and 10-4, respectively. The security of the biometric method can be further quantified by the physics of quantum measurements. An impostor must be able to perform quantum thermometry and quantum magnetometry with energy resolution better than 10-9ℏ , in order to foil the device by noninvasively monitoring the biometric activity of a user.

Quantum mechanics model on a Kaehler conifold

International Nuclear Information System (INIS)

Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen

2004-01-01

We propose an exactly solvable model of the quantum oscillator on the class of Kaehler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum number, when the space has nonconstant curvature. We reduce the model to a three-dimensional system interacting with the Dirac monopole. Owing to noncommutativity of the reduction and quantization procedures, the Hamiltonian of the reduced system gets nontrivial quantum corrections. We transform the reduced system into a MIC-Kepler-like one and find that quantum corrections arise only in its energy and coupling constant. We present the exact spectrum of the generalized MIC-Kepler system. The one-(complex) dimensional analog of the suggested model is formulated on the Riemann surface over the complex projective plane and could be interpreted as a system with fractional spin

Thermodynamics and statistical physics. 2. rev. ed.

International Nuclear Information System (INIS)

Schnakenberg, J.

2002-01-01

This textbook covers tthe following topics: Thermodynamic systems and equilibrium, irreversible thermodynamics, thermodynamic potentials, stability, thermodynamic processes, ideal systems, real gases and phase transformations, magnetic systems and Landau model, low temperature thermodynamics, canonical ensembles, statistical theory, quantum statistics, fermions and bosons, kinetic theory, Bose-Einstein condensation, photon gas

From localized to extended states in a time-dependent quantum model

International Nuclear Information System (INIS)

Jose, J.V.

1986-01-01

The problem of a particle inside a rigid box with one of the walls oscillating periodically in time is studied quantum mechanically. In the classical limit, this model was introduced by Fermi in the context of cosmic ray physics. The classical solutions can go from being quasiperiodic to chaotic, as a function of the amplitude of the wall oscillation. In the quantum case, the authors calculate the spectral properties of the corresponding evolution operator, i.e.: the quasi-energy eigenvalues and eigenvectors. The specific form of the wall oscillation, e.g. iota(t) = √ 1 + 2δabsolute value of t, with absolute value of t ≤ 1/2, and iota(t + 1) = iota(t), is essential to the solutions presented here. It is found that as h increases with δ fixed, the nearest neighbor separation between quasi-energy eigenvalues changes from showing no energy level repulsion to energy level repulsion. This transition, from Poisson-like statistics to Gaussian-Orthogonal-Ensemble-like statistics is tested by looking at the distribution of quasi-energy level nearest neighbor separations and the Δ/sub e/(L) statistics. these results are also correlated to a transition between localized to extended states in energy space. The possible relevance of the results presented here to experiments in quasi-one-dimensional atoms is also discussed

Quantum Graphical Models and Belief Propagation

International Nuclear Information System (INIS)

Leifer, M.S.; Poulin, D.

2008-01-01

Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markov Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersley-Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described

Critical, statistical, and thermodynamical properties of lattice models

Energy Technology Data Exchange (ETDEWEB)

Varma, Vipin Kerala

2013-10-15

In this thesis we investigate zero temperature and low temperature properties - critical, statistical and thermodynamical - of lattice models in the contexts of bosonic cold atom systems, magnetic materials, and non-interacting particles on various lattice geometries. We study quantum phase transitions in the Bose-Hubbard model with higher body interactions, as relevant for optical lattice experiments of strongly interacting bosons, in one and two dimensions; the universality of the Mott insulator to superfluid transition is found to remain unchanged for even large three body interaction strengths. A systematic renormalization procedure is formulated to fully re-sum these higher (three and four) body interactions into the two body terms. In the strongly repulsive limit, we analyse the zero and low temperature physics of interacting hard-core bosons on the kagome lattice at various fillings. Evidence for a disordered phase in the Ising limit of the model is presented; in the strong coupling limit, the transition between the valence bond solid and the superfluid is argued to be first order at the tip of the solid lobe.

Critical, statistical, and thermodynamical properties of lattice models

International Nuclear Information System (INIS)

Varma, Vipin Kerala

2013-10-01

In this thesis we investigate zero temperature and low temperature properties - critical, statistical and thermodynamical - of lattice models in the contexts of bosonic cold atom systems, magnetic materials, and non-interacting particles on various lattice geometries. We study quantum phase transitions in the Bose-Hubbard model with higher body interactions, as relevant for optical lattice experiments of strongly interacting bosons, in one and two dimensions; the universality of the Mott insulator to superfluid transition is found to remain unchanged for even large three body interaction strengths. A systematic renormalization procedure is formulated to fully re-sum these higher (three and four) body interactions into the two body terms. In the strongly repulsive limit, we analyse the zero and low temperature physics of interacting hard-core bosons on the kagome lattice at various fillings. Evidence for a disordered phase in the Ising limit of the model is presented; in the strong coupling limit, the transition between the valence bond solid and the superfluid is argued to be first order at the tip of the solid lobe.

Repeated interactions in open quantum systems

Energy Technology Data Exchange (ETDEWEB)

Bruneau, Laurent, E-mail: laurent.bruneau@u-cergy.fr [Laboratoire AGM, Université de Cergy-Pontoise, Site Saint-Martin, BP 222, 95302 Cergy-Pontoise (France); Joye, Alain, E-mail: Alain.Joye@ujf-grenoble.fr [Institut Fourier, UMR 5582, CNRS-Université Grenoble I, BP 74, 38402 Saint-Martin d’Hères (France); Merkli, Marco, E-mail: merkli@mun.ca [Department of Mathematics and Statistics Memorial University of Newfoundland, St. John' s, NL Canada A1C 5S7 (Canada)

2014-07-15

Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the dynamics of quantum coherences (decoherence) and quantum correlations (entanglement), or the emergence of heat and particle fluxes in non-equilibrium situations. From the mathematical physics perspective, one of the main challenges is to derive the irreversible dynamics of the open system, starting from a unitary dynamics of the system and its environment. The repeated interactions systems considered in these notes are models of non-equilibrium quantum statistical mechanics. They are relevant in quantum optics, and more generally, serve as a relatively well treatable approximation of a more difficult quantum dynamics. In particular, the repeated interaction models allow to determine the large time (stationary) asymptotics of quantum systems out of equilibrium.

Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models

Science.gov (United States)

Benedetti, Marcello; Realpe-Gómez, John; Biswas, Rupak; Perdomo-Ortiz, Alejandro

2017-10-01

Mainstream machine-learning techniques such as deep learning and probabilistic programming rely heavily on sampling from generally intractable probability distributions. There is increasing interest in the potential advantages of using quantum computing technologies as sampling engines to speed up these tasks or to make them more effective. However, some pressing challenges in state-of-the-art quantum annealers have to be overcome before we can assess their actual performance. The sparse connectivity, resulting from the local interaction between quantum bits in physical hardware implementations, is considered the most severe limitation to the quality of constructing powerful generative unsupervised machine-learning models. Here, we use embedding techniques to add redundancy to data sets, allowing us to increase the modeling capacity of quantum annealers. We illustrate our findings by training hardware-embedded graphical models on a binarized data set of handwritten digits and two synthetic data sets in experiments with up to 940 quantum bits. Our model can be trained in quantum hardware without full knowledge of the effective parameters specifying the corresponding quantum Gibbs-like distribution; therefore, this approach avoids the need to infer the effective temperature at each iteration, speeding up learning; it also mitigates the effect of noise in the control parameters, making it robust to deviations from the reference Gibbs distribution. Our approach demonstrates the feasibility of using quantum annealers for implementing generative models, and it provides a suitable framework for benchmarking these quantum technologies on machine-learning-related tasks.

Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models

Directory of Open Access Journals (Sweden)

Marcello Benedetti

2017-11-01

Full Text Available Mainstream machine-learning techniques such as deep learning and probabilistic programming rely heavily on sampling from generally intractable probability distributions. There is increasing interest in the potential advantages of using quantum computing technologies as sampling engines to speed up these tasks or to make them more effective. However, some pressing challenges in state-of-the-art quantum annealers have to be overcome before we can assess their actual performance. The sparse connectivity, resulting from the local interaction between quantum bits in physical hardware implementations, is considered the most severe limitation to the quality of constructing powerful generative unsupervised machine-learning models. Here, we use embedding techniques to add redundancy to data sets, allowing us to increase the modeling capacity of quantum annealers. We illustrate our findings by training hardware-embedded graphical models on a binarized data set of handwritten digits and two synthetic data sets in experiments with up to 940 quantum bits. Our model can be trained in quantum hardware without full knowledge of the effective parameters specifying the corresponding quantum Gibbs-like distribution; therefore, this approach avoids the need to infer the effective temperature at each iteration, speeding up learning; it also mitigates the effect of noise in the control parameters, making it robust to deviations from the reference Gibbs distribution. Our approach demonstrates the feasibility of using quantum annealers for implementing generative models, and it provides a suitable framework for benchmarking these quantum technologies on machine-learning-related tasks.

Methods of statistical physics

CERN Document Server

Akhiezer, Aleksandr I

1981-01-01

Methods of Statistical Physics is an exposition of the tools of statistical mechanics, which evaluates the kinetic equations of classical and quantized systems. The book also analyzes the equations of macroscopic physics, such as the equations of hydrodynamics for normal and superfluid liquids and macroscopic electrodynamics. The text gives particular attention to the study of quantum systems. This study begins with a discussion of problems of quantum statistics with a detailed description of the basics of quantum mechanics along with the theory of measurement. An analysis of the asymptotic be

Sampling, Probability Models and Statistical Reasoning Statistical

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 5. Sampling, Probability Models and Statistical Reasoning Statistical Inference. Mohan Delampady V R Padmawar. General Article Volume 1 Issue 5 May 1996 pp 49-58 ...

Quantum leptogenesis I

International Nuclear Information System (INIS)

Anisimov, A.; Drewes, M.; Mendizabal, S.

2010-12-01

Thermal leptogenesis explains the observed matter-antimatter asymmetry of the universe in terms of neutrino masses, consistent with neutrino oscillation experiments. We present a full quantum mechanical calculation of the generated lepton asymmetry based on Kadanoff-Baym equations. Origin of the asymmetry is the departure from equilibrium of the statistical propagator of the heavy Majorana neutrino, together with CP violating couplings. The lepton asymmetry is calculated directly in terms of Green's functions without referring to ''number densities''. Compared to Boltzmann and quantum Boltzmann equations, the crucial difference are memory effects, rapid oscillations much faster than the heavy neutrino equilibration time. These oscillations strongly suppress the generated lepton asymmetry, unless the standard model gauge interactions, which cause thermal damping, are properly taken into account. We find that these damping effects essentially compensate the enhancement due to quantum statistical factors, so that finally the conventional Boltzmann equations again provide rather accurate predictions for the lepton asymmetry. (orig.)

Optimal evolution models for quantum tomography

International Nuclear Information System (INIS)

Czerwiński, Artur

2016-01-01

The research presented in this article concerns the stroboscopic approach to quantum tomography, which is an area of science where quantum physics and linear algebra overlap. In this article we introduce the algebraic structure of the parametric-dependent quantum channels for 2-level and 3-level systems such that the generator of evolution corresponding with the Kraus operators has no degenerate eigenvalues. In such cases the index of cyclicity of the generator is equal to 1, which physically means that there exists one observable the measurement of which performed a sufficient number of times at distinct instants provides enough data to reconstruct the initial density matrix and, consequently, the trajectory of the state. The necessary conditions for the parameters and relations between them are introduced. The results presented in this paper seem to have considerable potential applications in experiments due to the fact that one can perform quantum tomography by conducting only one kind of measurement. Therefore, the analyzed evolution models can be considered optimal in the context of quantum tomography. Finally, we introduce some remarks concerning optimal evolution models in the case of n-dimensional Hilbert space. (paper)

On the structure of the quantum-mechanical probability models

International Nuclear Information System (INIS)

Cufaro-Petroni, N.

1992-01-01

In this paper the role of the mathematical probability models in the classical and quantum physics in shortly analyzed. In particular the formal structure of the quantum probability spaces (QPS) is contrasted with the usual Kolmogorovian models of probability by putting in evidence the connections between this structure and the fundamental principles of the quantum mechanics. The fact that there is no unique Kolmogorovian model reproducing a QPS is recognized as one of the main reasons of the paradoxical behaviors pointed out in the quantum theory from its early days. 8 refs

On Mathematical Modeling Of Quantum Systems

International Nuclear Information System (INIS)

Achuthan, P.; Narayanankutty, Karuppath

2009-01-01

The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.

Nucleic acid reactivity : challenges for next-generation semiempirical quantum models

OpenAIRE

Huang, Ming; Giese, Timothy J.; York, Darrin M.

2015-01-01

Semiempirical quantum models are routinely used to study mechanisms of RNA catalysis and phosphoryl transfer reactions using combined quantum mechanical/molecular mechanical methods. Herein, we provide a broad assessment of the performance of existing semiempirical quantum models to describe nucleic acid structure and reactivity in order to quantify their limitations and guide the development of next-generation quantum models with improved accuracy. Neglect of diatomic diffierential overlap (...

Quantum Brownian motion model for the stock market

Science.gov (United States)

Meng, Xiangyi; Zhang, Jian-Wei; Guo, Hong

2016-06-01

It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysical framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system-a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics.

Introduction to the basic concepts of modern physics special relativity, quantum and statistical physics

CERN Document Server

Becchi, Carlo Maria

2007-01-01

These notes are designed as a text book for a course on the Modern Physics Theory for undergraduate students. The purpose is providing a rigorous and self-contained presentation of the simplest theoretical framework using elementary mathematical tools. A number of examples of relevant applications and an appropriate list of exercises and answered questions are also given. The first part is devoted to Special Relativity concerning in particular space-time relativity and relativistic kinematics. The second part deals with Schroedinger's formulation of quantum mechanics. The presentation concerns mainly one dimensional problems, in particular tunnel effect, discrete energy levels and band spectra. The third part concerns the application of Gibbs statistical methods to quantum systems and in particular to Bose and Fermi gasses.

Toward quantum-like modeling of financial processes

International Nuclear Information System (INIS)

Choustova, Olga

2007-01-01

We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Trajectories of prices are determined by two financial potentials: classical-like V(q) ('hard' market conditions, e.g., natural resources) and quantum-like U(q) (behavioral market conditions). On the one hand, our Bohmian model is a quantum-like model for the financial market, cf. with works of W. Segal, I. E. Segal, E. Haven, E. W. Piotrowski, J. Sladkowski. On the other hand (since Bohmian mechanics provides the possibility to describe individual price trajectories) it belongs to the domain of extended research on deterministic dynamics for financial assets (C.W.J. Granger, W.A. Barnett, A. J. Benhabib, W.A. Brock, C. Sayers, J. Y. Campbell, A. W. Lo, A. C. MacKinlay, A. Serletis, S. Kuchta, M. Frank, R. Gencay, T. Stengos, M. J. Hinich, D. Patterson, D. A. Hsieh, D. T. Caplan, J.A. Scheinkman, B. LeBaron and many others)

Fractional statistics and quantum scaling properties of the integrable Penson-Kolb-Hubbard chain

Science.gov (United States)

Vitoriano, Carlindo; Coutinho-Filho, M. D.

2010-09-01

We investigate the ground-state and low-temperature properties of the integrable version of the Penson-Kolb-Hubbard chain. The model obeys fractional statistical properties, which give rise to fractional elementary excitations and manifest differently in the four regions of the phase diagram U/t versus n , where U is the Coulomb coupling, t is the correlated hopping amplitude, and n is the particle density. In fact, we can find local pair formation, fractionalization of the average occupation number per orbital k , or U - and n -dependent average electric charge per orbital k . We also study the scaling behavior near the U -driven quantum phase transitions and characterize their universality classes. Finally, it is shown that in the regime of parameters where local pair formation is energetically more favorable, the ground state exhibits power-law superconductivity; we also stress that above half filling the pair-hopping term stabilizes local Cooper pairs in the repulsive- U regime for U

New Spin Foam Models of Quantum Gravity

Science.gov (United States)

Miković, A.

We give a brief and a critical review of the Barret-Crane spin foam models of quantum gravity. Then we describe two new spin foam models which are obtained by direct quantization of General Relativity and do not have some of the drawbacks of the Barret-Crane models. These are the model of spin foam invariants for the embedded spin networks in loop quantum gravity and the spin foam model based on the integration of the tetrads in the path integral for the Palatini action.

Elementary quantum field theory

International Nuclear Information System (INIS)

Thirring, W.; Henley, E.M.

1975-01-01

The first section of the book deals with the mathematical and physical description of a quantum field with the Bose-Einstein statistics and discusses observables, invariants of the field, and inner symmetries. The second section develops further methods for solvable interactions of a quantum field with static source. Section 3 explains with the aid of the Chew-Low model especially pion-nucleon scattering, static properties of nucleons, electromagnetic phenomena, and nuclear forces. (BJ/LN) [de

Quantum entanglement and quantum phase transitions in frustrated Majumdar-Ghosh model

International Nuclear Information System (INIS)

Liu Guanghua; Wang Chunhai; Deng Xiaoyan

2011-01-01

By using the density matrix renormalization group technique, the quantum phase transitions in the frustrated Majumdar-Ghosh model are investigated. The behaviors of the conventional order parameter and the quantum entanglement entropy are analyzed in detail. The order parameter is found to peak at J 2 ∼0.58, but not at the Majumdar-Ghosh point (J 2 =0.5). Although, the quantum entanglements calculated with different subsystems display dissimilarly, the extremes of their first derivatives approach to the same critical point. By finite size scaling, this quantum critical point J C 2 converges to around 0.301 in the thermodynamic limit, which is consistent with those predicted previously by some authors (Tonegawa and Harada, 1987 ; Kuboki and Fukuyama, 1987 ; Chitra et al., 1995 ). Across the J C 2 , the system undergoes a quantum phase transition from a gapless spin-fluid phase to a gapped dimerized phase.

Rank-based model selection for multiple ions quantum tomography

International Nuclear Information System (INIS)

Guţă, Mădălin; Kypraios, Theodore; Dryden, Ian

2012-01-01

The statistical analysis of measurement data has become a key component of many quantum engineering experiments. As standard full state tomography becomes unfeasible for large dimensional quantum systems, one needs to exploit prior information and the ‘sparsity’ properties of the experimental state in order to reduce the dimensionality of the estimation problem. In this paper we propose model selection as a general principle for finding the simplest, or most parsimonious explanation of the data, by fitting different models and choosing the estimator with the best trade-off between likelihood fit and model complexity. We apply two well established model selection methods—the Akaike information criterion (AIC) and the Bayesian information criterion (BIC)—two models consisting of states of fixed rank and datasets such as are currently produced in multiple ions experiments. We test the performance of AIC and BIC on randomly chosen low rank states of four ions, and study the dependence of the selected rank with the number of measurement repetitions for one ion states. We then apply the methods to real data from a four ions experiment aimed at creating a Smolin state of rank 4. By applying the two methods together with the Pearson χ 2 test we conclude that the data can be suitably described with a model whose rank is between 7 and 9. Additionally we find that the mean square error of the maximum likelihood estimator for pure states is close to that of the optimal over all possible measurements. (paper)

Statistical physics as an approximate method of many-body quantum mechanics in the representation of occupation numbers

International Nuclear Information System (INIS)

Kushnirenko, A.N.

1989-01-01

An attempt was made to substantiate statistical physics from the viewpoint of many-body quantum mechanics in the representation of occupation numbers. This approach enabled to develop the variation method for solution of stationary and nonstationary nonequilibrium problems

Canonical transformations in problems of quantum statistical mechanics

International Nuclear Information System (INIS)

Sankovich, D.P.

1985-01-01

The problem of general canonical transformations in quantum systems possessing a classical analog is considered. The main role plays the Weyl representation of dynamic variables of the quantum system considered. One managed to build a general diagram of canonical transformations in a quantum case and to develop a method for reducing one or another operator to the simplest canonical form. In this case the procedure, being analogous to the Poincare-Birkhof normalization based on the Lie series theory, occurs

Quantum ratchet effect in a time non-uniform double-kicked model

Science.gov (United States)

Chen, Lei; Wang, Zhen-Yu; Hui, Wu; Chu, Cheng-Yu; Chai, Ji-Min; Xiao, Jin; Zhao, Yu; Ma, Jin-Xiang

2017-07-01

The quantum ratchet effect means that the directed transport emerges in a quantum system without a net force. The delta-kicked model is a quantum Hamiltonian model for the quantum ratchet effect. This paper investigates the quantum ratchet effect based on a time non-uniform double-kicked model, in which two flashing potentials alternately act on a particle with a homogeneous initial state of zero momentum, while the intervals between adjacent actions are not equal. The evolution equation of the state of the particle is derived from its Schrödinger equation, and the numerical method to solve the evolution equation is pointed out. The results show that quantum resonances can induce the ratchet effect in this time non-uniform double-kicked model under certain conditions; some quantum resonances, which cannot induce the ratchet effect in previous models, can induce the ratchet effect in this model, and the strengths of the ratchet effect in this model are stronger than those in previous models under certain conditions. These results enrich people’s understanding of the delta-kicked model, and provides a new optional scheme to control the quantum transport of cold atoms in experiment.

Role of quantum statistics in multi-particle decay dynamics

Science.gov (United States)

Marchewka, Avi; Granot, Er'el

2015-04-01

The role of quantum statistics in the decay dynamics of a multi-particle state, which is suddenly released from a confining potential, is investigated. For an initially confined double particle state, the exact dynamics is presented for both bosons and fermions. The time-evolution of the probability to measure two-particle is evaluated and some counterintuitive features are discussed. For instance, it is shown that although there is a higher chance of finding the two bosons (as oppose to fermions, and even distinguishable particles) at the initial trap region, there is a higher chance (higher than fermions) of finding them on two opposite sides of the trap as if the repulsion between bosons is higher than the repulsion between fermions. The results are demonstrated by numerical simulations and are calculated analytically in the short-time approximation. Furthermore, experimental validation is suggested.

Role of quantum statistics in multi-particle decay dynamics

International Nuclear Information System (INIS)

Marchewka, Avi; Granot, Er’el

2015-01-01

The role of quantum statistics in the decay dynamics of a multi-particle state, which is suddenly released from a confining potential, is investigated. For an initially confined double particle state, the exact dynamics is presented for both bosons and fermions. The time-evolution of the probability to measure two-particle is evaluated and some counterintuitive features are discussed. For instance, it is shown that although there is a higher chance of finding the two bosons (as oppose to fermions, and even distinguishable particles) at the initial trap region, there is a higher chance (higher than fermions) of finding them on two opposite sides of the trap as if the repulsion between bosons is higher than the repulsion between fermions. The results are demonstrated by numerical simulations and are calculated analytically in the short-time approximation. Furthermore, experimental validation is suggested

Role of quantum statistics in multi-particle decay dynamics

Energy Technology Data Exchange (ETDEWEB)

Marchewka, Avi, E-mail: avi.marchewka@gmail.com [Galei Tchelet St 8 Herzliya (Israel); Granot, Er’el [Department of Electrical and Electronics Engineering, Ariel University, Ariel (Israel)

2015-04-15

The role of quantum statistics in the decay dynamics of a multi-particle state, which is suddenly released from a confining potential, is investigated. For an initially confined double particle state, the exact dynamics is presented for both bosons and fermions. The time-evolution of the probability to measure two-particle is evaluated and some counterintuitive features are discussed. For instance, it is shown that although there is a higher chance of finding the two bosons (as oppose to fermions, and even distinguishable particles) at the initial trap region, there is a higher chance (higher than fermions) of finding them on two opposite sides of the trap as if the repulsion between bosons is higher than the repulsion between fermions. The results are demonstrated by numerical simulations and are calculated analytically in the short-time approximation. Furthermore, experimental validation is suggested.

Statistical Model of Extreme Shear

DEFF Research Database (Denmark)

Larsen, Gunner Chr.; Hansen, Kurt Schaldemose

2004-01-01

In order to continue cost-optimisation of modern large wind turbines, it is important to continously increase the knowledge on wind field parameters relevant to design loads. This paper presents a general statistical model that offers site-specific prediction of the probability density function...... by a model that, on a statistically consistent basis, describe the most likely spatial shape of an extreme wind shear event. Predictions from the model have been compared with results from an extreme value data analysis, based on a large number of high-sampled full-scale time series measurements...... are consistent, given the inevitabel uncertainties associated with model as well as with the extreme value data analysis. Keywords: Statistical model, extreme wind conditions, statistical analysis, turbulence, wind loading, statistical analysis, turbulence, wind loading, wind shear, wind turbines....

Statistical Physics An Introduction

CERN Document Server

Yoshioka, Daijiro

2007-01-01

This book provides a comprehensive presentation of the basics of statistical physics. The first part explains the essence of statistical physics and how it provides a bridge between microscopic and macroscopic phenomena, allowing one to derive quantities such as entropy. Here the author avoids going into details such as Liouville’s theorem or the ergodic theorem, which are difficult for beginners and unnecessary for the actual application of the statistical mechanics. In the second part, statistical mechanics is applied to various systems which, although they look different, share the same mathematical structure. In this way readers can deepen their understanding of statistical physics. The book also features applications to quantum dynamics, thermodynamics, the Ising model and the statistical dynamics of free spins.

Full counting statistics of level renormalization in electron transport through double quantum dots

International Nuclear Information System (INIS)

Luo Junyan; Shen Yu; Cen Gang; He Xiaoling; Wang Changrong; Jiao Hujun

2011-01-01

We examine the full counting statistics of electron transport through double quantum dots coupled in series, with particular attention being paid to the unique features originating from level renormalization. It is clearly illustrated that the energy renormalization gives rise to a dynamic charge blockade mechanism, which eventually results in super-Poissonian noise. Coupling of the double dots to an external heat bath leads to dephasing and relaxation mechanisms, which are demonstrated to suppress the noise in a unique way.

Circuit models and SPICE macro-models for quantum Hall effect devices

International Nuclear Information System (INIS)

Ortolano, Massimo; Callegaro, Luca

2015-01-01

Precise electrical measurement technology based on the quantum Hall effect is one of the pillars of modern quantum electrical metrology. Electrical networks including one or more QHE elements can be used as quantum resistance and impedance standards. The analysis of these networks allows metrologists to evaluate the effect of the inevitable parasitic parameters on their performance as standards. This paper presents a concise review of the various circuit models for QHE elements proposed in the literature, and the development of a new model. This last model is particularly suited to be employed with the analogue electronic circuit simulator SPICE. The SPICE macro-model and examples of SPICE simulations, validated by comparison with the corresponding analytical solution and/or experimental data, are provided. (paper)

A reciprocal of Coleman's theorem and the quantum statistics of systems with spontaneous symmetry breaking

International Nuclear Information System (INIS)

Chaichian, M.; Montonen, C.; Perez Rojas, H.

1991-01-01

The completely different conservation properties of charges associated to unbroken and broken symmetries are discussed. The impossibility of establishing a conservation law for nondegenerate Hilbert space representations in the broken case leads to a reciprocal of Coleman's theorem. The quantum statistical implication is that these charges cannot be introduced as conserved operators in the density matrix. (orig.)

A quantum mechanical model of "dark matter"

OpenAIRE

Belokurov, V. V.; Shavgulidze, E. T.

2014-01-01

The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.

Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes

International Nuclear Information System (INIS)

Yoshida, Beni

2011-01-01

Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and the lack of a general framework for classifications. While frustration-free Hamiltonians, which appear as fixed point Hamiltonians of renormalization group transformations, may serve as representatives of quantum phases, it is still difficult to analyze and classify quantum phases of arbitrary frustration-free Hamiltonians exhaustively. Here, we address these problems by sharpening our considerations to a certain subclass of frustration-free Hamiltonians, called stabilizer Hamiltonians, which have been actively studied in quantum information science. We propose a model of frustration-free Hamiltonians which covers a large class of physically realistic stabilizer Hamiltonians, constrained to only three physical conditions; the locality of interaction terms, translation symmetries and scale symmetries, meaning that the number of ground states does not grow with the system size. We show that quantum phases arising in two-dimensional models can be classified exactly through certain quantum coding theoretical operators, called logical operators, by proving that two models with topologically distinct shapes of logical operators are always separated by quantum phase transitions.

Modeling of the quantum dot filling and the dark current of quantum dot infrared photodetectors

International Nuclear Information System (INIS)

Ameen, Tarek A.; El-Batawy, Yasser M.; Abouelsaood, A. A.

2014-01-01

A generalized drift-diffusion model for the calculation of both the quantum dot filling profile and the dark current of quantum dot infrared photodetectors is proposed. The confined electrons inside the quantum dots produce a space-charge potential barrier between the two contacts, which controls the quantum dot filling and limits the dark current in the device. The results of the model reasonably agree with a published experimental work. It is found that increasing either the doping level or the temperature results in an exponential increase of the dark current. The quantum dot filling turns out to be nonuniform, with a dot near the contacts containing more electrons than one in the middle of the device where the dot occupation approximately equals the number of doping atoms per dot, which means that quantum dots away from contacts will be nearly unoccupied if the active region is undoped

Scrambling in the quantum Lifshitz model

Science.gov (United States)

Plamadeala, Eugeniu; Fradkin, Eduardo

2018-06-01

We study signatures of chaos in the quantum Lifshitz model through out-of-time ordered correlators (OTOC) of current operators. This model is a free scalar field theory with dynamical critical exponent z  =  2. It describes the quantum phase transition in 2D systems, such as quantum dimer models, between a phase with a uniform ground state to another one with spontaneously broken translation invariance. At the lowest temperatures the chaotic dynamics are dominated by a marginally irrelevant operator which induces a temperature dependent stiffness term. The numerical computations of OTOC exhibit a non-zero Lyapunov exponent (LE) in a wide range of temperatures and interaction strengths. The LE (in units of temperature) is a weakly temperature-dependent function; it vanishes at weak interaction and saturates for strong interaction. The Butterfly velocity increases monotonically with interaction strength in the studied region while remaining smaller than the interaction-induced velocity/stiffness.

Hunting Solomonoff's Swans: Exploring the Boundary Between Physics and Statistics in Hydrological Modeling

Science.gov (United States)

Nearing, G. S.

2014-12-01

Statistical models consistently out-perform conceptual models in the short term, however to account for a nonstationary future (or an unobserved past) scientists prefer to base predictions on unchanging and commutable properties of the universe - i.e., physics. The problem with physically-based hydrology models is, of course, that they aren't really based on physics - they are based on statistical approximations of physical interactions, and we almost uniformly lack an understanding of the entropy associated with these approximations. Thermodynamics is successful precisely because entropy statistics are computable for homogeneous (well-mixed) systems, and ergodic arguments explain the success of Newton's laws to describe systems that are fundamentally quantum in nature. Unfortunately, similar arguments do not hold for systems like watersheds that are heterogeneous at a wide range of scales. Ray Solomonoff formalized the situation in 1968 by showing that given infinite evidence, simultaneously minimizing model complexity and entropy in predictions always leads to the best possible model. The open question in hydrology is about what happens when we don't have infinite evidence - for example, when the future will not look like the past, or when one watershed does not behave like another. How do we isolate stationary and commutable components of watershed behavior? I propose that one possible answer to this dilemma lies in a formal combination of physics and statistics. In this talk I outline my recent analogue (Solomonoff's theorem was digital) of Solomonoff's idea that allows us to quantify the complexity/entropy tradeoff in a way that is intuitive to physical scientists. I show how to formally combine "physical" and statistical methods for model development in a way that allows us to derive the theoretically best possible model given any given physics approximation(s) and available observations. Finally, I apply an analogue of Solomonoff's theorem to evaluate the

Information Graph Flow: A Geometric Approximation of Quantum and Statistical Systems

Science.gov (United States)

Vanchurin, Vitaly

2018-05-01

Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distributions) we describe how it can be approximated with a very low-dimensional field theory with geometric degrees of freedom. The geometric approximation procedure consists of three steps. The first step is to construct weighted graphs (we call information graphs) with vertices representing subsystems (e.g., qubits or random variables) and edges representing mutual information (or the flow of information) between subsystems. The second step is to deform the adjacency matrices of the information graphs to that of a (locally) low-dimensional lattice using the graph flow equations introduced in the paper. (Note that the graph flow produces very sparse adjacency matrices and thus might also be used, for example, in machine learning or network science where the task of graph sparsification is of a central importance.) The third step is to define an emergent metric and to derive an effective description of the metric and possibly other degrees of freedom. To illustrate the procedure we analyze (numerically and analytically) two information graph flows with geometric attractors (towards locally one- and two-dimensional lattices) and metric perturbations obeying a geometric flow equation. Our analysis also suggests a possible approach to (a non-perturbative) quantum gravity in which the geometry (a secondary object) emerges directly from a quantum state (a primary object) due to the flow of the information graphs.

Dynamic structure factor for liquid He4 and quantum lattice model

International Nuclear Information System (INIS)

Lee, M.H.

1975-01-01

It has been realized for some time now that the quantum lattice model (or the anisotropic Heisenberg antiferromagnetic model) is a useful model for studying the properties of quantum liquids especially near the lambda transition. The static critical values calculated from the quantum lattice model are in good agreement with the observed values. Furthermore, it was shown recently that there are collective modes in the quantum lattice model which are equivalent to the plasmons. Hence, it would seem to be interesting to study the dynamic structure factor for the quantum lattice model and to make a comparison with experiment. Work on the dynamic structure factor is reported here. (Auth.)

Toward quantum-like modeling of financial processes

Energy Technology Data Exchange (ETDEWEB)

Choustova, Olga [International Center for Mathematical Modeling in Physics and Cognitive Sciences, University of Vaexjoe, S-35195 (Sweden)

2007-05-15

We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Trajectories of prices are determined by two financial potentials: classical-like V(q) ('hard' market conditions, e.g., natural resources) and quantum-like U(q) (behavioral market conditions). On the one hand, our Bohmian model is a quantum-like model for the financial market, cf. with works of W. Segal, I. E. Segal, E. Haven, E. W. Piotrowski, J. Sladkowski. On the other hand (since Bohmian mechanics provides the possibility to describe individual price trajectories) it belongs to the domain of extended research on deterministic dynamics for financial assets (C.W.J. Granger, W.A. Barnett, A. J. Benhabib, W.A. Brock, C. Sayers, J. Y. Campbell, A. W. Lo, A. C. MacKinlay, A. Serletis, S. Kuchta, M. Frank, R. Gencay, T. Stengos, M. J. Hinich, D. Patterson, D. A. Hsieh, D. T. Caplan, J.A. Scheinkman, B. LeBaron and many others)

Why quantum mechanics?

International Nuclear Information System (INIS)

Landsberg, P.T.

1988-01-01

It is suggested that an oversight occurred in classical mechanics when time-derivatives of observables were treated on the same footing as the undifferentiated observables. Removal of this oversight points in the direction of quantum mechanics. Additional light is thrown on uncertainty relations and on quantum mechanics, as a possible form of a subtle statistical mechanics, by the formulation of a classical uncertainty relation for a very simple model. The existence of universal motion, i.e., of zero-point energy, is lastly made plausible in terms of a gravitational constant which is time-dependent. By these three considerations an attempt is made to link classical and quantum mechanics together more firmly, thus giving a better understanding of the latter

Matrix product state calculations for one-dimensional quantum chains and quantum impurity models

Energy Technology Data Exchange (ETDEWEB)

Muender, Wolfgang

2011-09-28

This thesis contributes to the field of strongly correlated electron systems with studies in two distinct fields thereof: the specific nature of correlations between electrons in one dimension and quantum quenches in quantum impurity problems. In general, strongly correlated systems are characterized in that their physical behaviour needs to be described in terms of a many-body description, i.e. interactions correlate all particles in a complex way. The challenge is that the Hilbert space in a many-body theory is exponentially large in the number of particles. Thus, when no analytic solution is available - which is typically the case - it is necessary to find a way to somehow circumvent the problem of such huge Hilbert spaces. Therefore, the connection between the two studies comes from our numerical treatment: they are tackled by the density matrix renormalization group (DMRG) and the numerical renormalization group (NRG), respectively, both based on matrix product states. The first project presented in this thesis addresses the problem of numerically finding the dominant correlations in quantum lattice models in an unbiased way, i.e. without using prior knowledge of the model at hand. A useful concept for this task is the correlation density matrix (CDM) which contains all correlations between two clusters of lattice sites. We show how to extract from the CDM, a survey of the relative strengths of the system's correlations in different symmetry sectors as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. We demonstrate this by a DMRG study of a one-dimensional spinless extended Hubbard model, while emphasizing that the proposed analysis of the CDM is not restricted to one dimension. The second project presented in this thesis is motivated by two phenomena under ongoing experimental and theoretical investigation in the context of quantum impurity models: optical absorption

Matrix product state calculations for one-dimensional quantum chains and quantum impurity models

International Nuclear Information System (INIS)

Muender, Wolfgang

2011-01-01

This thesis contributes to the field of strongly correlated electron systems with studies in two distinct fields thereof: the specific nature of correlations between electrons in one dimension and quantum quenches in quantum impurity problems. In general, strongly correlated systems are characterized in that their physical behaviour needs to be described in terms of a many-body description, i.e. interactions correlate all particles in a complex way. The challenge is that the Hilbert space in a many-body theory is exponentially large in the number of particles. Thus, when no analytic solution is available - which is typically the case - it is necessary to find a way to somehow circumvent the problem of such huge Hilbert spaces. Therefore, the connection between the two studies comes from our numerical treatment: they are tackled by the density matrix renormalization group (DMRG) and the numerical renormalization group (NRG), respectively, both based on matrix product states. The first project presented in this thesis addresses the problem of numerically finding the dominant correlations in quantum lattice models in an unbiased way, i.e. without using prior knowledge of the model at hand. A useful concept for this task is the correlation density matrix (CDM) which contains all correlations between two clusters of lattice sites. We show how to extract from the CDM, a survey of the relative strengths of the system's correlations in different symmetry sectors as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. We demonstrate this by a DMRG study of a one-dimensional spinless extended Hubbard model, while emphasizing that the proposed analysis of the CDM is not restricted to one dimension. The second project presented in this thesis is motivated by two phenomena under ongoing experimental and theoretical investigation in the context of quantum impurity models: optical absorption

Quantum-critical scaling of fidelity in 2D pairing models

Energy Technology Data Exchange (ETDEWEB)

Adamski, Mariusz, E-mail: mariusz.adamski@ift.uni.wroc.pl [Institute of Theoretical Physics, University of Wrocław, pl. Maksa Borna 9, 50–204, Wrocław (Poland); Jȩdrzejewski, Janusz [Institute of Theoretical Physics, University of Wrocław, pl. Maksa Borna 9, 50–204, Wrocław (Poland); Krokhmalskii, Taras [Institute for Condensed Matter Physics, 1 Svientsitski Street, 79011, Lviv (Ukraine)

2017-01-15

The laws of quantum-critical scaling theory of quantum fidelity, dependent on the underlying system dimensionality D, have so far been verified in exactly solvable 1D models, belonging to or equivalent to interacting, quadratic (quasifree), spinless or spinfull, lattice-fermion models. The obtained results are so appealing that in quest for correlation lengths and associated universal critical indices ν, which characterize the divergence of correlation lengths on approaching critical points, one might be inclined to substitute the hard task of determining an asymptotic behavior at large distances of a two-point correlation function by an easier one, of determining the quantum-critical scaling of the quantum fidelity. However, the role of system's dimensionality has been left as an open problem. Our aim in this paper is to fill up this gap, at least partially, by verifying the laws of quantum-critical scaling theory of quantum fidelity in a 2D case. To this end, we study correlation functions and quantum fidelity of 2D exactly solvable models, which are interacting, quasifree, spinfull, lattice-fermion models. The considered 2D models exhibit new, as compared with 1D ones, features: at a given quantum-critical point there exists a multitude of correlation lengths and multiple universal critical indices ν, since these quantities depend on spatial directions, moreover, the indices ν may assume larger values. These facts follow from the obtained by us analytical asymptotic formulae for two-point correlation functions. In such new circumstances we discuss the behavior of quantum fidelity from the perspective of quantum-critical scaling theory. In particular, we are interested in finding out to what extent the quantum fidelity approach may be an alternative to the correlation-function approach in studies of quantum-critical points beyond 1D.

Short-Term Load Forecasting Model Based on Quantum Elman Neural Networks

Directory of Open Access Journals (Sweden)

Zhisheng Zhang

2016-01-01

Full Text Available Short-term load forecasting model based on quantum Elman neural networks was constructed in this paper. The quantum computation and Elman feedback mechanism were integrated into quantum Elman neural networks. Quantum computation can effectively improve the approximation capability and the information processing ability of the neural networks. Quantum Elman neural networks have not only the feedforward connection but also the feedback connection. The feedback connection between the hidden nodes and the context nodes belongs to the state feedback in the internal system, which has formed specific dynamic memory performance. Phase space reconstruction theory is the theoretical basis of constructing the forecasting model. The training samples are formed by means of K-nearest neighbor approach. Through the example simulation, the testing results show that the model based on quantum Elman neural networks is better than the model based on the quantum feedforward neural network, the model based on the conventional Elman neural network, and the model based on the conventional feedforward neural network. So the proposed model can effectively improve the prediction accuracy. The research in the paper makes a theoretical foundation for the practical engineering application of the short-term load forecasting model based on quantum Elman neural networks.

Statistical analysis of error rate of large-scale single flux quantum logic circuit by considering fluctuation of timing parameters

International Nuclear Information System (INIS)

Yamanashi, Yuki; Masubuchi, Kota; Yoshikawa, Nobuyuki

2016-01-01

The relationship between the timing margin and the error rate of the large-scale single flux quantum logic circuits is quantitatively investigated to establish a timing design guideline. We observed that the fluctuation in the set-up/hold time of single flux quantum logic gates caused by thermal noises is the most probable origin of the logical error of the large-scale single flux quantum circuit. The appropriate timing margin for stable operation of the large-scale logic circuit is discussed by taking the fluctuation of setup/hold time and the timing jitter in the single flux quantum circuits. As a case study, the dependence of the error rate of the 1-million-bit single flux quantum shift register on the timing margin is statistically analyzed. The result indicates that adjustment of timing margin and the bias voltage is important for stable operation of a large-scale SFQ logic circuit.

Statistical analysis of error rate of large-scale single flux quantum logic circuit by considering fluctuation of timing parameters

Energy Technology Data Exchange (ETDEWEB)

Yamanashi, Yuki, E-mail: yamanasi@ynu.ac.jp [Department of Electrical and Computer Engineering, Yokohama National University, Tokiwadai 79-5, Hodogaya-ku, Yokohama 240-8501 (Japan); Masubuchi, Kota; Yoshikawa, Nobuyuki [Department of Electrical and Computer Engineering, Yokohama National University, Tokiwadai 79-5, Hodogaya-ku, Yokohama 240-8501 (Japan)

2016-11-15

The relationship between the timing margin and the error rate of the large-scale single flux quantum logic circuits is quantitatively investigated to establish a timing design guideline. We observed that the fluctuation in the set-up/hold time of single flux quantum logic gates caused by thermal noises is the most probable origin of the logical error of the large-scale single flux quantum circuit. The appropriate timing margin for stable operation of the large-scale logic circuit is discussed by taking the fluctuation of setup/hold time and the timing jitter in the single flux quantum circuits. As a case study, the dependence of the error rate of the 1-million-bit single flux quantum shift register on the timing margin is statistically analyzed. The result indicates that adjustment of timing margin and the bias voltage is important for stable operation of a large-scale SFQ logic circuit.

Generalized Tavis-Cummings models and quantum networks

Science.gov (United States)

Gorokhov, A. V.

2018-04-01

The properties of quantum networks based on generalized Tavis-Cummings models are theoretically investigated. We have calculated the information transfer success rate from one node to another in a simple model of a quantum network realized with two-level atoms placed in the cavities and interacting with an external laser field and cavity photons. The method of dynamical group of the Hamiltonian and technique of corresponding coherent states were used for investigation of the temporal dynamics of the two nodes model.

Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution

Directory of Open Access Journals (Sweden)

Ivan B. Djordjevic

2015-08-01

Full Text Available Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i Markovian classical model, (ii Markovian-like quantum model, and (iii hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage Markov chain-like models of aging, which

Remarks on the choice of trial hamiltonians for the quantum statistical treatment of anharmonic systems

International Nuclear Information System (INIS)

Tsallis, C.; Valle, J.W.F.

1979-01-01

The use of the Variational Method to discuss Quantum Statistical Mechanics of anharmonic systems requires, in order to be able to obtain the correct classical limit, the allowance for renormalization of every operator whose definition depends on the harmonic coefficients. The point is exhibited for a single anharmonic oscillator. In this particular case there is no need for mass renormalization. (Author) [pt

Probability and logical structure of statistical theories

International Nuclear Information System (INIS)

Hall, M.J.W.

1988-01-01

A characterization of statistical theories is given which incorporates both classical and quantum mechanics. It is shown that each statistical theory induces an associated logic and joint probability structure, and simple conditions are given for the structure to be of a classical or quantum type. This provides an alternative for the quantum logic approach to axiomatic quantum mechanics. The Bell inequalities may be derived for those statistical theories that have a classical structure and satisfy a locality condition weaker than factorizability. The relation of these inequalities to the issue of hidden variable theories for quantum mechanics is discussed and clarified

Quantum Annealing and Quantum Fluctuation Effect in Frustrated Ising Systems

OpenAIRE

Tanaka, Shu; Tamura, Ryo

2012-01-01

Quantum annealing method has been widely attracted attention in statistical physics and information science since it is expected to be a powerful method to obtain the best solution of optimization problem as well as simulated annealing. The quantum annealing method was incubated in quantum statistical physics. This is an alternative method of the simulated annealing which is well-adopted for many optimization problems. In the simulated annealing, we obtain a solution of optimization problem b...

Radiation from quantum weakly dynamical horizons in loop quantum gravity.

Science.gov (United States)

Pranzetti, Daniele

2012-07-06

We provide a statistical mechanical analysis of quantum horizons near equilibrium in the grand canonical ensemble. By matching the description of the nonequilibrium phase in terms of weakly dynamical horizons with a local statistical framework, we implement loop quantum gravity dynamics near the boundary. The resulting radiation process provides a quantum gravity description of the horizon evaporation. For large black holes, the spectrum we derive presents a discrete structure which could be potentially observable.

Quantum trajectories: Memory and continuous observation

Science.gov (United States)

Barchielli, Alberto; Pellegrini, Clément; Petruccione, Francesco

2012-12-01

Starting from a generalization of the quantum trajectory theory [based on the stochastic Schrödinger equation (SSE)], non-Markovian models of quantum dynamics are derived. In order to describe non-Markovian effects, the approach used in this article is based on the introduction of random coefficients in the usual linear SSE. A major interest is that this allows a consistent theory of quantum measurement in continuous time to be developed for these non-Markovian quantum trajectory models. In this context, the notions of “instrument,” “a priori,” and “a posteriori” states can be introduced. The key point is that by starting from a stochastic equation on the Hilbert space of the system, we are able to respect the complete positivity of the mean dynamics for the statistical operator and the requirements of the axioms of quantum measurement theory. The flexibility of the theory is next illustrated by a concrete physical model of a noisy oscillator where non-Markovian effects come from the random environment, colored noises, randomness in the stimulating light, and delay effects. The statistics of the emitted photons and the heterodyne and homodyne spectra are studied, and we show how these quantities are sensitive to the non-Markovian features of the system dynamics, so that, in principle, the observation and analysis of the fluorescent light could reveal the presence of non-Markovian effects and allow for a measure of the spectra of the noises affecting the system dynamics.

Composite quantum collision models

Science.gov (United States)

Lorenzo, Salvatore; Ciccarello, Francesco; Palma, G. Massimo

2017-09-01

A collision model (CM) is a framework to describe open quantum dynamics. In its memoryless version, it models the reservoir R as consisting of a large collection of elementary ancillas: the dynamics of the open system S results from successive collisions of S with the ancillas of R . Here, we present a general formulation of memoryless composite CMs, where S is partitioned into the very open system under study S coupled to one or more auxiliary systems {Si} . Their composite dynamics occurs through internal S -{Si} collisions interspersed with external ones involving {Si} and the reservoir R . We show that important known instances of quantum non-Markovian dynamics of S —such as the emission of an atom into a reservoir featuring a Lorentzian, or multi-Lorentzian, spectral density or a qubit subject to random telegraph noise—can be mapped on to such memoryless composite CMs.

Quantum phase transition of the transverse-field quantum Ising model on scale-free networks.

Science.gov (United States)

Yi, Hangmo

2015-01-01

I investigate the quantum phase transition of the transverse-field quantum Ising model in which nearest neighbors are defined according to the connectivity of scale-free networks. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quantum critical point and study its scaling characteristics. For the degree exponent λ=6, I obtain results that are consistent with the mean-field theory. For λ=4.5 and 4, however, the results suggest that the quantum critical point belongs to a non-mean-field universality class. Further simulations indicate that the quantum critical point remains mean-field-like if λ>5, but it continuously deviates from the mean-field theory as λ becomes smaller.

Thermodynamics of quantum strings

CERN Document Server

Morgan, M J

1994-01-01

A statistical mechanical analysis of an ideal gas of non-relativistic quantum strings is presented, in which the thermodynamic properties of the string gas are calculated from a canonical partition function. This toy model enables students to gain insight into the thermodynamics of a simple 'quantum field' theory, and provides a useful pedagogical introduction to the more complicated relativistic string theories. A review is also given of the thermodynamics of the open bosonic string gas and the type I (open) superstring gas. (author)

Exclusion statistics and integrable models

International Nuclear Information System (INIS)

Mashkevich, S.

1998-01-01

The definition of exclusion statistics that was given by Haldane admits a 'statistical interaction' between distinguishable particles (multispecies statistics). For such statistics, thermodynamic quantities can be evaluated exactly; explicit expressions are presented here for cluster coefficients. Furthermore, single-species exclusion statistics is realized in one-dimensional integrable models of the Calogero-Sutherland type. The interesting questions of generalizing this correspondence to the higher-dimensional and the multispecies cases remain essentially open; however, our results provide some hints as to searches for the models in question

Software-defined Quantum Networking Ecosystem

Energy Technology Data Exchange (ETDEWEB)

2017-01-01

The software enables a user to perform modeling and simulation of software-defined quantum networks. The software addresses the problem of how to synchronize transmission of quantum and classical signals through multi-node networks and to demonstrate quantum information protocols such as quantum teleportation. The software approaches this problem by generating a graphical model of the underlying network and attributing properties to each node and link in the graph. The graphical model is then simulated using a combination of discrete-event simulators to calculate the expected state of each node and link in the graph at a future time. A user interacts with the software by providing an initial network model and instantiating methods for the nodes to transmit information with each other. This includes writing application scripts in python that make use of the software library interfaces. A user then initiates the application scripts, which invokes the software simulation. The user then uses the built-in diagnostic tools to query the state of the simulation and to collect statistics on synchronization.

Cryptography In The Bounded Quantum-Storage Model

DEFF Research Database (Denmark)

Damgård, Ivan Bjerre; Salvail, Louis; Schaffner, Christian

2005-01-01

We initiate the study of two-party cryptographic primitives with unconditional security, assuming that the adversary's quantum memory is of bounded size. We show that oblivious transfer and bit commitment can be implemented in this model using protocols where honest parties need no quantum memory...

Cryptography in the Bounded Quantum-Storage Model

DEFF Research Database (Denmark)

Damgård, Ivan Bjerre; Serge, Fehr; Schaffner, Christian

2008-01-01

We initiate the study of two-party cryptographic primitives with unconditional security, assuming that the adversary's quantum memory is of bounded size. We show that oblivious transfer and bit commitment can be implemented in this model using protocols where honest parties need no quantum memory...

Projected Dipole Model for Quantum Plasmonics

DEFF Research Database (Denmark)

Yan, Wei; Wubs, Martijn; Mortensen, N. Asger

2015-01-01

of classical electrodynamics, while quantum properties are described accurately through an infinitely thin layer of dipoles oriented normally to the metal surface. The nonlocal polarizability of the dipole layer-the only introduced parameter-is mapped from the free-electron distribution near the metal surface...... as obtained with 1D quantum calculations, such as time-dependent density-functional theory (TDDFT), and is determined once and for all. The model can be applied in two and three dimensions to any system size that is tractable within classical electrodynamics, while capturing quantum plasmonic aspects......Quantum effects of plasmonic phenomena have been explored through ab initio studies, but only for exceedingly small metallic nanostructures, leaving most experimentally relevant structures too large to handle. We propose instead an effective description with the computationally appealing features...

Quantum Dynamics in the HMF Model

Science.gov (United States)

Plestid, Ryan; O'Dell, Duncan

2017-04-01

The Hamiltonian Mean Field (HMF) model represents a paradigm in the study of long-range interactions but has never been realized in a lab. Recently Shutz and Morigi (PRL 113) have come close but ultimately fallen short. Their proposal relied on cavity-induced interactions between atoms. If a design using cold atoms is to be successful, an understanding of quantum effects is essential. I will outline the natural quantum generalization of the HMF assuming a BEC by using a generalized Gross-Pitaevskii equation (gGPE). I will show how quantum effects modify features which are well understood in the classical model. More specifically, by working in the semi-classical regime (strong interparticle interactions) we can identify the universal features predicted by catastrophe theory dressed with quantum interference effects. The stationary states of gGPE can be solved exactly and are found to be described by self-consistent Mathieu functions. Finally, I will discuss the connection between the classical description of the dynamics in terms of the Vlassov equation, and the gGPE. We would like to thank the Government of Ontario's OGS program, NSERC, and the Perimeter Institute of Theoretical Physics.

Quantum-statistical mechanics of an atom-dimer mixture: Lee-Yang cluster expansion approach

International Nuclear Information System (INIS)

Ohkuma, Takahiro; Ueda, Masahito

2006-01-01

We use the Lee-Yang cluster expansion method to study quantum-statistical properties of a mixture of interconvertible atoms and dimers, where the dimers form in a two-body bound state of the atoms. We point out an infinite series of cluster diagrams whose summation leads to the Bose-Einstein condensation of the dimers below a critical temperature. Our theory captures some important features of a cold atom-dimer mixture such as interconversion of atoms and dimers and properties of the mixture at the unitarity limit

Studies on quantum field theory and statistical mechanics

International Nuclear Information System (INIS)

Zhang, S.

1987-01-01

This dissertation is a summary of research in various areas of theoretical physics and is divided into three parts. In the first part, quantum fluctuations of the recently proposed superconducting cosmic strings are studied. It is found that vortices on the string world sheet represent an important class of fluctuation modes which tend to disorder the system. Both heuristic arguments and detailed renormalization group analysis reveal that these vortices do not appear in bound pairs but rather from a gas of free vortices. Based on this observation we argue that this fluctuation mode violates the topological conservation law on which superconductivity is based. Anomalies and topological aspects of supersymmetric quantum field theories are studied in the second part of this dissertation. Using the superspace formulation of the N = 1 spinning string, we obtain a path integral measure which is free from the world-sheet general coordinate as well as the supersymmetry anomalies and therefore determine the conformal anomaly and critical dimension of the spinning string. We also apply Fujikawa's formalism to computer the chiral anomaly in conformal as well as ordinary supergravity. Finally, we given a Noether-method construction of the supersymmetrized Chern-Simons term in five dimensional supergravity. In the last part of this dissertation, the soliton excitations in the quarter-filled Peierls-Hubbard model are investigated in both the large and the small U limit. For a strictly one dimensional system at zero temperature, we find that solitons in both limits are in one-to-one correspondence, while in the presence of weak three dimensional couplings or at finite temperature, the large U systems differ qualitatively from the small U systems in that the spin associated with the solitons ceases to be a sharp quantum observable

Quantum cosmological relational model of shape and scale in 1D

International Nuclear Information System (INIS)

Anderson, Edward

2011-01-01

Relational particle models are useful toy models for quantum cosmology and the problem of time in quantum general relativity. This paper shows how to extend existing work on concrete examples of relational particle models in 1D to include a notion of scale. This is useful as regards forming a tight analogy with quantum cosmology and the emergent semiclassical time and hidden time approaches to the problem of time. This paper shows furthermore that the correspondence between relational particle models and classical and quantum cosmology can be strengthened using judicious choices of the mechanical potential. This gives relational particle mechanics models with analogues of spatial curvature, cosmological constant, dust and radiation terms. A number of these models are then tractable at the quantum level. These models can be used to study important issues (1) in canonical quantum gravity: the problem of time, the semiclassical approach to it and timeless approaches to it (such as the naive Schroedinger interpretation and records theory) and (2) in quantum cosmology, such as in the investigation of uniform states, robustness and the qualitative understanding of the origin of structure formation.

Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy*

Directory of Open Access Journals (Sweden)

Kostyantyn Kechedzhi

2016-05-01

Full Text Available Real-life quantum computers are inevitably affected by intrinsic noise resulting in dissipative nonunitary dynamics realized by these devices. We consider an open-system quantum annealing algorithm optimized for such a realistic analog quantum device which takes advantage of noise-induced thermalization and relies on incoherent quantum tunneling at finite temperature. We theoretically analyze the performance of this algorithm considering a p-spin model that allows for a mean-field quasiclassical solution and, at the same time, demonstrates the first-order phase transition and exponential degeneracy of states, typical characteristics of spin glasses. We demonstrate that finite-temperature effects introduced by the noise are particularly important for the dynamics in the presence of the exponential degeneracy of metastable states. We determine the optimal regime of the open-system quantum annealing algorithm for this model and find that it can outperform simulated annealing in a range of parameters. Large-scale multiqubit quantum tunneling is instrumental for the quantum speedup in this model, which is possible because of the unusual nonmonotonous temperature dependence of the quantum-tunneling action in this model, where the most efficient transition rate corresponds to zero temperature. This model calculation is the first analytically tractable example where open-system quantum annealing algorithm outperforms simulated annealing, which can, in principle, be realized using an analog quantum computer.

Hidden Statistics of Schroedinger Equation

Science.gov (United States)

Zak, Michail

2011-01-01

Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.

Quantum gravity and Standard-Model-like fermions

International Nuclear Information System (INIS)

Eichhorn, Astrid; Lippoldt, Stefan

2017-01-01

We discover that chiral symmetry does not act as an infrared attractor of the renormalization group flow under the impact of quantum gravity fluctuations. Thus, observationally viable quantum gravity models must respect chiral symmetry. In our truncation, asymptotically safe gravity does, as a chiral fixed point exists. A second non-chiral fixed point with massive fermions provides a template for models with dark matter. This fixed point disappears for more than 10 fermions, suggesting that an asymptotically safe ultraviolet completion for the standard model plus gravity enforces chiral symmetry.

Quantum model for electro-optical amplitude modulation.

Science.gov (United States)

Capmany, José; Fernández-Pousa, Carlos R

2010-11-22

We present a quantum model for electro-optic amplitude modulation, which is built upon quantum models of the main photonic components that constitute the modulator, that is, the guided-wave beamsplitter and the electro-optic phase modulator and accounts for all the different available modulator structures. General models are developed both for single and dual drive configurations and specific results are obtained for the most common configurations currently employed. Finally, the operation with two-photon input for the control of phase-modulated photons and the important topic of multicarrier modulation are also addressed.

The statistics of multi-step direct reactions

International Nuclear Information System (INIS)

Koning, A.J.; Akkermans, J.M.

1991-01-01

We propose a quantum-statistical framework that provides an integrated perspective on the differences and similarities between the many current models for multi-step direct reactions in the continuum. It is argued that to obtain a statistical theory two physically different approaches are conceivable to postulate randomness, respectively called leading-particle statistics and residual-system statistics. We present a new leading-particle statistics theory for multi-step direct reactions. It is shown that the model of Feshbach et al. can be derived as a simplification of this theory and thus can be founded solely upon leading-particle statistics. The models developed by Tamura et al. and Nishioka et al. are based upon residual-system statistics and hence fall into a physically different class of multi-step direct theories, although the resulting cross-section formulae for the important first step are shown to be the same. The widely used semi-classical models such as the generalized exciton model can be interpreted as further phenomenological simplifications of the leading-particle statistics theory. A more comprehensive exposition will appear before long. (author). 32 refs, 4 figs

Behavior of the maximum likelihood in quantum state tomography

Science.gov (United States)

Scholten, Travis L.; Blume-Kohout, Robin

2018-02-01

Quantum state tomography on a d-dimensional system demands resources that grow rapidly with d. They may be reduced by using model selection to tailor the number of parameters in the model (i.e., the size of the density matrix). Most model selection methods typically rely on a test statistic and a null theory that describes its behavior when two models are equally good. Here, we consider the loglikelihood ratio. Because of the positivity constraint ρ ≥ 0, quantum state space does not generally satisfy local asymptotic normality (LAN), meaning the classical null theory for the loglikelihood ratio (the Wilks theorem) should not be used. Thus, understanding and quantifying how positivity affects the null behavior of this test statistic is necessary for its use in model selection for state tomography. We define a new generalization of LAN, metric-projected LAN, show that quantum state space satisfies it, and derive a replacement for the Wilks theorem. In addition to enabling reliable model selection, our results shed more light on the qualitative effects of the positivity constraint on state tomography.

Behavior of the maximum likelihood in quantum state tomography

Energy Technology Data Exchange (ETDEWEB)

Blume-Kohout, Robin J [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States); Scholten, Travis L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States)

2018-02-22

Quantum state tomography on a d-dimensional system demands resources that grow rapidly with d. They may be reduced by using model selection to tailor the number of parameters in the model (i.e., the size of the density matrix). Most model selection methods typically rely on a test statistic and a null theory that describes its behavior when two models are equally good. Here, we consider the loglikelihood ratio. Because of the positivity constraint ρ ≥ 0, quantum state space does not generally satisfy local asymptotic normality (LAN), meaning the classical null theory for the loglikelihood ratio (the Wilks theorem) should not be used. Thus, understanding and quantifying how positivity affects the null behavior of this test statistic is necessary for its use in model selection for state tomography. We define a new generalization of LAN, metric-projected LAN, show that quantum state space satisfies it, and derive a replacement for the Wilks theorem. In addition to enabling reliable model selection, our results shed more light on the qualitative effects of the positivity constraint on state tomography.

Toward a Parastatistics in Quantum Nonextensive Statistical Mechanics

Science.gov (United States)

Zaripov, R. G.

2018-05-01

On the basis of Bose quantum states in parastatistics the equations for the equilibrium distribution of quantum additive and nonextensive systems are determined. The fluctuations and variances of physical quantities for the equilibrium system are found. The Abelian group of microscopic entropies is determined for the composition law with a quadratic nonlinearity.

From Entropic Dynamics to Quantum Theory

International Nuclear Information System (INIS)

Caticha, Ariel

2009-01-01

Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the configuration space is a statistical manifold. The dynamics then follows from a principle of inference, the method of Maximum Entropy. The concept of time is introduced as a convenient way to keep track of change. The resulting theory resembles both Nelson's stochastic mechanics and general relativity. The statistical manifold is a dynamical entity: its geometry determines the evolution of the probability distribution which, in its turn, reacts back and determines the evolution of the geometry. There is a new quantum version of the equivalence principle: 'osmotic' mass equals inertial mass. Mass and the phase of the wave function are explained as features of purely statistical origin.

Statistical mechanics of superconductivity

CERN Document Server

Kita, Takafumi

2015-01-01

This book provides a theoretical, step-by-step comprehensive explanation of superconductivity for undergraduate and graduate students who have completed elementary courses on thermodynamics and quantum mechanics. To this end, it adopts the unique approach of starting with the statistical mechanics of quantum ideal gases and successively adding and clarifying elements and techniques indispensible for understanding it. They include the spin-statistics theorem, second quantization, density matrices, the Bloch–De Dominicis theorem, the variational principle in statistical mechanics, attractive interaction, and bound states. Ample examples of their usage are also provided in terms of topics from advanced statistical mechanics such as two-particle correlations of quantum ideal gases, derivation of the Hartree–Fock equations, and Landau’s Fermi-liquid theory, among others. With these preliminaries, the fundamental mean-field equations of superconductivity are derived with maximum mathematical clarity based on ...

Quantum phase transitions in effective spin-ladder models for graphene zigzag nanoribbons

Science.gov (United States)

Koop, Cornelie; Wessel, Stefan

2017-10-01

We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte Carlo simulations to access the large-distance properties, accounting for quantum fluctuations beyond mean-field-theory approaches to edge magnetism. For certain chiral nanoribbons, antiferromagnetic interedge couplings were previously found to induce a gapped quantum disordered ground state of the effective spin model. We find that the extended nature of the intraedge couplings in the effective spin model for zigzag nanoribbons leads to a quantum phase transition at a large, finite value of the interedge coupling. This quantum critical point separates the quantum disordered region from a gapless phase of stable edge magnetism at weak intraedge coupling, which includes the ground states of spin-ladder models for wide zigzag nanoribbons. To study the quantum critical behavior, the effective spin model can be related to a model of two antiferromagnetically coupled Haldane-Shastry spin-half chains with long-ranged ferromagnetic intrachain couplings. The results for the critical exponents are compared also to several recent renormalization-group calculations for related long-ranged interacting quantum systems.

Statistical modelling with quantile functions

CERN Document Server

Gilchrist, Warren

2000-01-01

Galton used quantiles more than a hundred years ago in describing data. Tukey and Parzen used them in the 60s and 70s in describing populations. Since then, the authors of many papers, both theoretical and practical, have used various aspects of quantiles in their work. Until now, however, no one put all the ideas together to form what turns out to be a general approach to statistics.Statistical Modelling with Quantile Functions does just that. It systematically examines the entire process of statistical modelling, starting with using the quantile function to define continuous distributions. The author shows that by using this approach, it becomes possible to develop complex distributional models from simple components. A modelling kit can be developed that applies to the whole model - deterministic and stochastic components - and this kit operates by adding, multiplying, and transforming distributions rather than data.Statistical Modelling with Quantile Functions adds a new dimension to the practice of stati...

Spin chain model for correlated quantum channels

Energy Technology Data Exchange (ETDEWEB)

Rossini, Davide [International School for Advanced Studies SISSA/ISAS, via Beirut 2-4, I-34014 Trieste (Italy); Giovannetti, Vittorio; Montangero, Simone [NEST-CNR-INFM and Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa (Italy)], E-mail: monta@sns.it

2008-11-15

We analyze the quality of the quantum information transmission along a correlated quantum channel by studying the average fidelity between input and output states and the average output purity, giving bounds for the entropy of the channel. Noise correlations in the channel are modeled by the coupling of each channel use with an element of a one-dimensional interacting quantum spin chain. Criticality of the environment chain is seen to emerge in the changes of the fidelity and of the purity.

A Statistical Programme Assignment Model

DEFF Research Database (Denmark)

Rosholm, Michael; Staghøj, Jonas; Svarer, Michael

When treatment effects of active labour market programmes are heterogeneous in an observable way  across the population, the allocation of the unemployed into different programmes becomes a particularly  important issue. In this paper, we present a statistical model designed to improve the present...... duration of unemployment spells may result if a statistical programme assignment model is introduced. We discuss several issues regarding the  plementation of such a system, especially the interplay between the statistical model and  case workers....

Correlation between the number of quantum-statistical modes of the exciting field and the number of lines in the resonance fluorescence spectrum

International Nuclear Information System (INIS)

Kryzhanovskii, Boris V; Sokolov, G B

2000-01-01

The quasi-energy wave functions of a two-level atom in an electromagnetic field, the state of which represents a superposition of coherent states, were found. The fluorescence spectrum of an atom excited by such a field was investigated. It was shown that a spectral fluorescence mode corresponds to each mode of the quantum-statistical distribution of the field incident on the atom. This means that the number of statistical modes of the incident field may be recorded as the number of data bits of the information carried by the light pulse. (laser applications and other topics in quantum electronics)

Fock representations of the superalgebra sl(n+1 vertical bar m), its quantum analogue Uq[sl(n+1 vertical bar m)] and related quantum statistics

International Nuclear Information System (INIS)

Palev, T.D.; Stoilova, N.I.; Jeugt, J. van der

1999-12-01

Fock space representations of the Lie superalgebra sl(n + 1 vertical bar m) and of its quantum analogue U q [sl(n + 1 vertical bar m)] are written down. The results are based on a description of these superalgebras via creation and annihilation operators. The properties of the underlying statistics are briefly discussed. (author)

Quantum statistical metastability for a finite spin

Science.gov (United States)

Garanin, D. A.; Chudnovsky, E. M.

2001-01-01

We study quantum-classical escape-rate transitions for uniaxial and biaxial models with finite spins S=10 (such as Mn12Ac and Fe8) and S=100 by a direct numerical approach. At second-order transitions the level making a dominant contribution into thermally assisted tunneling changes gradually with temperature whereas at first-order transitions a group of levels is skipped. For finite spins, the quasiclassical boundaries between first- and second-order transitions are shifted, favoring a second-order transition: For Fe8 in zero field the transition should be first order according to a theory with S-->∞, but we show that there are no skipped levels at the transition. Applying a field along the hard axis in Fe8 makes transition the strongest first order. For the same model with S=100 we confirmed the existence of a region where a second-order transition is followed by a first-order transition [X. Martínes Hidalgo and E. M. Chudnovsky, J. Phys.: Condensed Matter 12, 4243 (2000)].

Zwitters: Particles between quantum and classical

International Nuclear Information System (INIS)

Wetterich, C.

2012-01-01

We describe both quantum particles and classical particles in terms of a classical statistical ensemble, with a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same quantum formalism. Quantum particles are characterized by a specific choice of observables and time evolution of the probability density. Then interference and tunneling are found within classical statistics. Zwitters are (effective) one-particle states for which the time evolution interpolates between quantum and classical particles. Experimental bounds on a small parameter can test quantum mechanics. -- Highlights: ► Quantum particles can be described within classical statistics. ► Classical particles are formulated in quantum formalism. ► Zwitters interpolate between classical and quantum particles. ► Zwitters allow for quantitative tests of quantum mechanics. ► Zwitters could be effective one-particle descriptions of droplets.

Model for calorimetric measurements in an open quantum system

Science.gov (United States)

Donvil, Brecht; Muratore-Ginanneschi, Paolo; Pekola, Jukka P.; Schwieger, Kay

2018-05-01

We investigate the experimental setup proposed in New J. Phys. 15, 115006 (2013), 10.1088/1367-2630/15/11/115006 for calorimetric measurements of thermodynamic indicators in an open quantum system. As a theoretical model we consider a periodically driven qubit coupled with a large yet finite electron reservoir, the calorimeter. The calorimeter is initially at equilibrium with an infinite phonon bath. As time elapses, the temperature of the calorimeter varies in consequence of energy exchanges with the qubit and the phonon bath. We show how under weak-coupling assumptions, the evolution of the qubit-calorimeter system can be described by a generalized quantum jump process including as dynamical variable the temperature of the calorimeter. We study the jump process by numeric and analytic methods. Asymptotically with the duration of the drive, the qubit-calorimeter attains a steady state. In this same limit, we use multiscale perturbation theory to derive a Fokker-Planck equation governing the calorimeter temperature distribution. We inquire the properties of the temperature probability distribution close and at the steady state. In particular, we predict the behavior of measurable statistical indicators versus the qubit-calorimeter coupling constant.

Quantum Kolmogorov complexity and the quantum Turing machine

Energy Technology Data Exchange (ETDEWEB)

Mueller, M.

2007-08-31

The purpose of this thesis is to give a formal definition of quantum Kolmogorov complexity and rigorous mathematical proofs of its basic properties. Classical Kolmogorov complexity is a well-known and useful measure of randomness for binary strings. In recent years, several different quantum generalizations of Kolmogorov complexity have been proposed. The most natural generalization is due to A. Berthiaume et al. (2001), defining the complexity of a quantum bit (qubit) string as the length of the shortest quantum input for a universal quantum computer that outputs the desired string. Except for slight modifications, it is this definition of quantum Kolmogorov complexity that we study in this thesis. We start by analyzing certain aspects of the underlying quantum Turing machine (QTM) model in a more detailed formal rigour than was done previously. Afterwards, we apply these results to quantum Kolmogorov complexity. Our first result is a proof of the existence of a universal QTM which simulates every other QTM for an arbitrary number of time steps and than halts with probability one. In addition, we show that every input that makes a QTM almost halt can be modified to make the universal QTM halt entirely, by adding at most a constant number of qubits. It follows that quantum Kolmogorov complexity has the invariance property, i.e. it depends on the choice of the universal QTM only up to an additive constant. Moreover, the quantum complexity of classical strings agrees with classical complexity, again up to an additive constant. The proofs are based on several analytic estimates. Furthermore, we prove several incompressibility theorems for quantum Kolmogorov complexity. Finally, we show that for ergodic quantum information sources, complexity rate and entropy rate coincide with probability one. The thesis is finished with an outlook on a possible application of quantum Kolmogorov complexity in statistical mechanics. (orig.)

Quantum Bohmian model for financial market

Science.gov (United States)

Choustova, Olga Al.

2007-01-01

We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. The Hamiltonian formalism on the price/price-change phase space describes the classical-like evolution of prices. This classical dynamics of prices is determined by “hard” conditions (natural resources, industrial production, services and so on). These conditions are mathematically described by the classical financial potential V(q), where q=(q1,…,qn) is the vector of prices of various shares. But the information exchange and market psychology play important (and sometimes determining) role in price dynamics. We propose to describe such behavioral financial factors by using the pilot wave (Bohmian) model of quantum mechanics. The theory of financial behavioral waves takes into account the market psychology. The real trajectories of prices are determined (through the financial analogue of the second Newton law) by two financial potentials: classical-like V(q) (“hard” market conditions) and quantum-like U(q) (behavioral market conditions).

Experimental Tests of Quantum Mechanics: Pauli Exclusion Principle and Spontaneous Collapse Models

CERN Document Server

Petrascu, Catalina Curceanu; Bragadireanu, Mario; Clozza, Alberto; Guaraldo, Carlo; Iliescu, Mihai; Rizzo, Alessandro; Vidal, Antonio Romero; Scordo, Alessandro; Sirghi, Diana Laura; Sirghi, Florin; Sperandio, Laura; Doce, Oton Vazquez; Bassi, Angelo; Donadi, Sandro; Milotti, Edoardo; Laubenstein, Matthias; Bertolucci, Sergio; Bragadireanu, Mario; Curceanu, Catalina; Pietreanu, Dorel; Ponta, Titus; Cargnelli, Michael; Ishiwatari, Tomoichi; Marton, Johann; Widmann, Eberhard; Zmeskal, Johann; Matteo, Sergio di; Egger, Jean Pierre

2014-01-01

The Pauli exclusion principle (PEP), as a consequence or the spin-statistics connection, is one of the basic principles of the modern physics. Being at the very basis of our understanding of matter, it spurs a lively debate on its possible limits, deeply rooted as it is in the very foundations of Quantum Field Theory. The VIP (VIolation of the Pauli exclusion principle) experiment is searching for a possible small violation of the PEP for electrons, using the method of searching for Pauli Exclusion Principle forbidden atomic transitions in copper. We describe the experimental method and the obtained results; we briefly present future plans to go beyond the actual limit by upgrading the experiment using vetoed new spectroscopic fast Silicon Drift Detectors. We also mention the possibility of using a similar experimental technique to search for possible X-rays generated in the spontaneous collapse models of quantum mechanics.

Communication: satisfying fermionic statistics in the modeling of open time-dependent quantum systems with one-electron reduced density matrices.

Science.gov (United States)

Head-Marsden, Kade; Mazziotti, David A

2015-02-07

For an open, time-dependent quantum system, Lindblad derived the most general modification of the quantum Liouville equation in the Markovian approximation that models environmental effects while preserving the non-negativity of the system's density matrix. While Lindblad's modification is correct for N-electron density matrices, solution of the Liouville equation with a Lindblad operator causes the one-electron reduced density matrix (1-RDM) to violate the Pauli exclusion principle. Consequently, after a short time, the 1-RDM is not representable by an ensemble N-electron density matrix (not ensemble N-representable). In this communication, we derive the necessary and sufficient constraints on the Lindbladian matrix within the Lindblad operator to ensure that the 1-RDM remains N-representable for all time. The theory is illustrated by considering the relaxation of an excitation in several molecules F2, N2, CO, and BeH2 subject to environmental noise.

The Generalized Quantum Episodic Memory Model.

Science.gov (United States)

Trueblood, Jennifer S; Hemmer, Pernille

2017-11-01

Recent evidence suggests that experienced events are often mapped to too many episodic states, including those that are logically or experimentally incompatible with one another. For example, episodic over-distribution patterns show that the probability of accepting an item under different mutually exclusive conditions violates the disjunction rule. A related example, called subadditivity, occurs when the probability of accepting an item under mutually exclusive and exhaustive instruction conditions sums to a number >1. Both the over-distribution effect and subadditivity have been widely observed in item and source-memory paradigms. These phenomena are difficult to explain using standard memory frameworks, such as signal-detection theory. A dual-trace model called the over-distribution (OD) model (Brainerd & Reyna, 2008) can explain the episodic over-distribution effect, but not subadditivity. Our goal is to develop a model that can explain both effects. In this paper, we propose the Generalized Quantum Episodic Memory (GQEM) model, which extends the Quantum Episodic Memory (QEM) model developed by Brainerd, Wang, and Reyna (2013). We test GQEM by comparing it to the OD model using data from a novel item-memory experiment and a previously published source-memory experiment (Kellen, Singmann, & Klauer, 2014) examining the over-distribution effect. Using the best-fit parameters from the over-distribution experiments, we conclude by showing that the GQEM model can also account for subadditivity. Overall these results add to a growing body of evidence suggesting that quantum probability theory is a valuable tool in modeling recognition memory. Copyright © 2016 Cognitive Science Society, Inc.

Quantum synchronization of the Schrödinger–Lohe model

International Nuclear Information System (INIS)

Choi, Sun-Ho; Ha, Seung-Yeal

2014-01-01

We present a quantum synchronization estimate of the Schrödinger–Lohe (S–L) model introduced by Lohe (2010 J. Phys. A: Math. Theor. 43 465301). The S–L model describes the dynamics of quantum oscillators on the nodes of a quantum network. When the coupling strength is positive and the maximal L 2 distances between normalized initial wave functions are smaller than (1/2), we show that the L 2 distances between wave functions converge to zero exponentially fast. Our result generalizes earlier work by Chi et al (2014 J. Math. Phys. 55 052703) for the Lohe model. (paper)

Quantum graphs: a simple model for chaotic scattering

International Nuclear Information System (INIS)

Kottos, Tsampikos; Smilansky, Uzy

2003-01-01

We connect quantum graphs with infinite leads, and turn them into scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay time and conductance distributions, Ericson fluctuations, and when considered statistically, the ensemble of scattering matrices reproduces quite well the predictions of the appropriately defined random matrix ensembles. The underlying classical dynamics can be defined, and it provides important parameters which are needed for the quantum theory. In particular, we derive exact expressions for the scattering matrix, and an exact trace formula for the density of resonances, in terms of classical orbits, analogous to the semiclassical theory of chaotic scattering. We use this in order to investigate the origin of the connection between random matrix theory and the underlying classical chaotic dynamics. Being an exact theory, and due to its relative simplicity, it offers new insights into this problem which is at the forefront of the research in chaotic scattering and related fields

A Dirac sea pilot-wave model for quantum field theory

International Nuclear Information System (INIS)

Colin, S; Struyve, W

2007-01-01

We present a pilot-wave model for quantum field theory in which the Dirac sea is taken seriously. The model ascribes particle trajectories to all the fermions, including the fermions filling the Dirac sea. The model is deterministic and applies to the regime in which fermion number is superselected. This work is a further elaboration of work by Colin, in which a Dirac sea pilot-wave model is presented for quantum electrodynamics. We extend his work to non-electromagnetic interactions, we discuss a cut-off regularization of the pilot-wave model and study how it reproduces the standard quantum predictions. The Dirac sea pilot-wave model can be seen as a possible continuum generalization of a lattice model by Bell. It can also be seen as a development and generalization of the ideas by Bohm, Hiley and Kaloyerou, who also suggested the use of the Dirac sea for the development of a pilot-wave model for quantum electrodynamics

Quantum transport in a ring of quantum dots

Energy Technology Data Exchange (ETDEWEB)

Sena Junior, Marcone I.; Macedo, Antonio M.C. [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil). Dept. de Fisica

2012-07-01

Full text: Quantum dots play a central role in the recent technological efforts to build efficient devices to storage, process and transmit information in the quantum regime [1]. One of the reasons for this interest is the relative simplicity with which its control parameters can be changed by experimentalists. Systems with one, two and even arrays of quantum dots have been intensively studied with respect to their efficiency in processing information carried by charge, spin and heat [1]. A particularly useful realization of a quantum dot is a ballistic electron cavity formed by electrostatic potentials in a two-dimensional electron gas. In the chaotic regime, the shape of the dot is statistically irrelevant and the ability to change its form via external gates can be used to generate members of an ensemble of identical systems. From a theoretical point of view, such quantum dots are ideal electron systems in which to study theoretical models combining phase-coherence, chaotic dynamics and Coulomb interactions. In this work, we use the Keldysh non-linear sigma model [2] with a counting field to study electron transport through a ring of four chaotic quantum dots pierced by an Aharonov-Bohm flux. This system is particularly well suited for studying ways to use the weak-localization effect to process quantum information. We derive the quantum circuit equations for this system from the saddle-point condition of the Keldysh action. The results are used to build the action of the corresponding supersymmetric (SUSY) non-linear sigma model. The connection with the random scattering matrix approach is then made via the color-flavor transformation. In the perturbative regime, where weak-localization effects appear, the Keldysh, SUSY and random scattering matrix approaches can be compared by means of independent analytical calculations. We conclude by pointing out the many advantages of our unified approach. [1] For a review, see Yu. V. Nazarov, and Ya. M. Blanter, Quantum

Correlation inequalities for the Yukawa2 quantum field theory

International Nuclear Information System (INIS)

Rosen, L.

1981-01-01

Correlation inequalities have been useful in statistical mechanics and quantum field theory. In particular, in the case of strongly coupled bose quantum field models such as P(phi) 2 , correlation inequalities provide the best control of the infinite volume limit. The author reports on work in which the FKG inequality was established in the Yukawa 2 quantum field theory. An elementary proof of the first Griffiths inequality is also given. (Auth.)

Finite-size fluctuations and photon statistics near the polariton condensation transition in a single-mode microcavity

International Nuclear Information System (INIS)

Eastham, P. R.; Littlewood, P. B.

2006-01-01

We consider polariton condensation in a generalized Dicke model, describing a single-mode cavity containing quantum dots, and extend our previous mean-field theory to allow for finite-size fluctuations. Within the fluctuation-dominated regime the correlation functions differ from their (trivial) mean-field values. We argue that the low-energy physics of the model, which determines the photon statistics in this fluctuation-dominated crossover regime, is that of the (quantum) anharmonic oscillator. The photon statistics at the crossover are different in the high-temperature and low-temperature limits. When the temperature is high enough for quantum effects to be neglected we recover behavior similar to that of a conventional laser. At low enough temperatures, however, we find qualitatively different behavior due to quantum effects

Detected-jump-error-correcting quantum codes, quantum error designs, and quantum computation

International Nuclear Information System (INIS)

Alber, G.; Mussinger, M.; Beth, Th.; Charnes, Ch.; Delgado, A.; Grassl, M.

2003-01-01

The recently introduced detected-jump-correcting quantum codes are capable of stabilizing qubit systems against spontaneous decay processes arising from couplings to statistically independent reservoirs. These embedded quantum codes exploit classical information about which qubit has emitted spontaneously and correspond to an active error-correcting code embedded in a passive error-correcting code. The construction of a family of one-detected-jump-error-correcting quantum codes is shown and the optimal redundancy, encoding, and recovery as well as general properties of detected-jump-error-correcting quantum codes are discussed. By the use of design theory, multiple-jump-error-correcting quantum codes can be constructed. The performance of one-jump-error-correcting quantum codes under nonideal conditions is studied numerically by simulating a quantum memory and Grover's algorithm

Quasilocal conservation laws in the quantum Hirota model

International Nuclear Information System (INIS)

Zadnik, Lenart; Prosen, Tomaž

2017-01-01

The extensivity of the quantum Hirota model’s conservation laws on a 1  +  1 dimensional lattice is considered. This model can be interpreted in terms of an integrable many-body quantum Floquet dynamics. We establish the procedure to generate a continuous family of quasilocal conservation laws from the conserved operators proposed by Faddeev and Volkov. The Hilbert–Schmidt kernel which allows the calculation of inner products of these new conservation laws is explicitly computed. This result has potential applications in quantum quench and transport problems in integrable quantum field theories. (paper)