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
Nonequilibrium quantum field theories
International Nuclear Information System (INIS)
Niemi, A.J.
1988-01-01
Combining the Feynman-Vernon influence functional formalism with the real-time formulation of finite-temperature quantum field theories we present a general approach to relativistic quantum field theories out of thermal equilibrium. We clarify the physical meaning of the additional fields encountered in the real-time formulation of quantum statistics and outline diagrammatic rules for perturbative nonequilibrium computations. We derive a generalization of Boltzmann's equation which gives a complete characterization of relativistic nonequilibrium phenomena. (orig.)
Application of nonequilibrium quantum statistical mechanics to homogeneous nucleation
International Nuclear Information System (INIS)
Larson, A.R.; Cantrell, C.D.
1978-01-01
The master equation for cluster growth and evaporation is derived from many-body quantum mechanics and from a modified version of quantum damping theory used in laser physics. For application to nucleation theory, the quantum damping theory has been generalized to include system and reservoir states that are not separate entities. Formulae for rate constants are obtained. Solutions of the master equation yield equations of state and system-averaged quantities recognized as thermodynamic variables. Formulae for Helmholtz free energies of clusters in a Debye approximation are derived. Coexistence-line equations for pressure volume, and number of clusters are obtained from equations-of-state analysis. Coexistence-line and surface-tension data are used to obtain values of parameters for the Debye approximation. These data are employed in calculating both the nucleation current in diffusion cloud chamber experiments and the onset of condensation in expansion nozzle experiments. Theoretical and experimental results are similar for both cloud-chamber and nozzle experiments, which measure water
Homogeneous nucleation: a problem in nonequilibrium quantum statistical mechanics
International Nuclear Information System (INIS)
1978-08-01
The master equation for cluster growth and evaporation is derived for many-body quantum mechanics and from a modified version of quantum damping theory used in laser physics. For application to nucleation theory, the quantum damping theory is generalized to include system and reservoir states that are not separate entities. Formulas for rate constants are obtained. Solutions of the master equation yield equations of state and system-averaged quantities recognized as thermodynamic variables. Formulas for Helmholtz free energies of clusters in a Debye approximation are derived. Coexistence-line equations for pressure, volume, and number of clusters are obtained from equations-of-state analysis. Coexistence-line and surface-tension data are used to obtain values of parameters for the Debye approximation. These data are employed in calculating both the nucleation current in diffusion cloud chamber experiments and the onset of condensation in expansion nozzle experiments. Theoretical and experimental results are similar for both cloud chamber and nozzle experiments, which measure water. Comparison with other theories reveals that classical theory only accidently agrees with experiment and that the Helmholtz free-energy formula used in the Lothe--Pound theory is incomplete. 27 figures, 3 tables, 149 references
Unifying quantum heat transfer in a nonequilibrium spin-boson model with full counting statistics
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.
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.
Nonequilibrium statistical mechanics ensemble method
Eu, Byung Chan
1998-01-01
In this monograph, nonequilibrium statistical mechanics is developed by means of ensemble methods on the basis of the Boltzmann equation, the generic Boltzmann equations for classical and quantum dilute gases, and a generalised Boltzmann equation for dense simple fluids The theories are developed in forms parallel with the equilibrium Gibbs ensemble theory in a way fully consistent with the laws of thermodynamics The generalised hydrodynamics equations are the integral part of the theory and describe the evolution of macroscopic processes in accordance with the laws of thermodynamics of systems far removed from equilibrium Audience This book will be of interest to researchers in the fields of statistical mechanics, condensed matter physics, gas dynamics, fluid dynamics, rheology, irreversible thermodynamics and nonequilibrium phenomena
Statistical mechanics of nonequilibrium liquids
Evans, Denis J; Craig, D P; McWeeny, R
1990-01-01
Statistical Mechanics of Nonequilibrium Liquids deals with theoretical rheology. The book discusses nonlinear response of systems and outlines the statistical mechanical theory. In discussing the framework of nonequilibrium statistical mechanics, the book explains the derivation of a nonequilibrium analogue of the Gibbsian basis for equilibrium statistical mechanics. The book reviews the linear irreversible thermodynamics, the Liouville equation, and the Irving-Kirkwood procedure. The text then explains the Green-Kubo relations used in linear transport coefficients, the linear response theory,
Nonequilibrium quantum fluctuations of work.
Allahverdyan, A E
2014-09-01
The concept of work is basic for statistical thermodynamics. To gain a fuller understanding of work and its (quantum) features, it needs to be represented as an average of a fluctuating quantity. Here I focus on the work done between two moments of time for a thermally isolated quantum system driven by a time-dependent Hamiltonian. I formulate two natural conditions needed for the fluctuating work to be physically meaningful for a system that starts its evolution from a nonequilibrium state. The existing definitions do not satisfy these conditions due to issues that are traced back to noncommutativity. I propose a definition of fluctuating work that is free of previous drawbacks and that applies for a wide class of nonequilibrium initial states. It allows the deduction of a generalized work-fluctuation theorem that applies for an arbitrary (out-of-equilibrium) initial state.
Nonequilibrium statistical physics
Röpke, Gerd
2013-01-01
Authored by one of the top theoretical physicists in Germany, and a well-known authority in the field, this is the only coherent presentation of the subject suitable for masters and PhD students, as well as postdocs in physics and related disciplines.Starting from a general discussion of the nonequilibrium state, different standard approaches such as master equations, and kinetic and linear response theory, are derived after special assumptions. This allows for an insight into the problems of nonequilibrium physics, a discussion of the limits, and suggestions for improvements. Applications
Nonequilibrium statistical averages and thermo field dynamics
International Nuclear Information System (INIS)
Marinaro, A.; Scarpetta, Q.
1984-01-01
An extension of thermo field dynamics is proposed, which permits the computation of nonequilibrium statistical averages. The Brownian motion of a quantum oscillator is treated as an example. In conclusion it is pointed out that the procedure proposed to computation of time-dependent statistical average gives the correct two-point Green function for the damped oscillator. A simple extension can be used to compute two-point Green functions of free particles
Statistical thermodynamics of nonequilibrium processes
Keizer, Joel
1987-01-01
The structure of the theory ofthermodynamics has changed enormously since its inception in the middle of the nineteenth century. Shortly after Thomson and Clausius enunciated their versions of the Second Law, Clausius, Maxwell, and Boltzmann began actively pursuing the molecular basis of thermo dynamics, work that culminated in the Boltzmann equation and the theory of transport processes in dilute gases. Much later, Onsager undertook the elucidation of the symmetry oftransport coefficients and, thereby, established himself as the father of the theory of nonequilibrium thermodynamics. Com bining the statistical ideas of Gibbs and Langevin with the phenomenological transport equations, Onsager and others went on to develop a consistent statistical theory of irreversible processes. The power of that theory is in its ability to relate measurable quantities, such as transport coefficients and thermodynamic derivatives, to the results of experimental measurements. As powerful as that theory is, it is linear and...
Nonequilibrium fermion production in quantum field theory
International Nuclear Information System (INIS)
Pruschke, Jens
2010-01-01
The creation of matter in the early universe or in relativistic heavy-ion collisions is inevitable connected to nonequilibrium physics. One of the key challenges is the explanation of the corresponding thermalization process following nonequilibrium instabilities. The role of fermionic quantum fields in such scenarios is discussed in the literature by using approximations of field theories which neglect important quantum corrections. This thesis goes beyond such approximations. A quantum field theory where scalar bosons interact with Dirac fermions via a Yukawa coupling is analyzed in the 2PI effective action formalism. The chosen approximation allows for a correct description of the dynamics including nonequilibrium instabilities. In particular, fermion-boson loop corrections allow to study the interaction of fermions with large boson fluctuations. The applied initial conditions generate nonequilibrium instabilities like parametric resonance or spinodal instabilities. The equations of motion for correlation functions are solved numerically and major characteristics of the fermion dynamics are described by analytical solutions. New mechanisms for the production of fermions are found. Simulations in the case of spinodal instability show that unstable boson fluctuations induce exponentially growing fermion modes with approximately the same growth rate. If the unstable regime lasts long enough a thermalization of the infrared part of the fermion occupation number occurs on time scales much shorter than the time scale on which bosonic quantum fields thermalize. Fermions acquire an excess of occupation in the ultraviolet regime compared to a Fermi-Dirac statistic characterized by a power-law with exponent two. The fermion production mechanism via parametric resonance is found to be most efficient after the instability ends. Quantum corrections then provide a very efficient particle creation mechanism which is interpreted as an amplification of decay processes. The ratio
Nonequilibrium fermion production in quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Pruschke, Jens
2010-06-16
The creation of matter in the early universe or in relativistic heavy-ion collisions is inevitable connected to nonequilibrium physics. One of the key challenges is the explanation of the corresponding thermalization process following nonequilibrium instabilities. The role of fermionic quantum fields in such scenarios is discussed in the literature by using approximations of field theories which neglect important quantum corrections. This thesis goes beyond such approximations. A quantum field theory where scalar bosons interact with Dirac fermions via a Yukawa coupling is analyzed in the 2PI effective action formalism. The chosen approximation allows for a correct description of the dynamics including nonequilibrium instabilities. In particular, fermion-boson loop corrections allow to study the interaction of fermions with large boson fluctuations. The applied initial conditions generate nonequilibrium instabilities like parametric resonance or spinodal instabilities. The equations of motion for correlation functions are solved numerically and major characteristics of the fermion dynamics are described by analytical solutions. New mechanisms for the production of fermions are found. Simulations in the case of spinodal instability show that unstable boson fluctuations induce exponentially growing fermion modes with approximately the same growth rate. If the unstable regime lasts long enough a thermalization of the infrared part of the fermion occupation number occurs on time scales much shorter than the time scale on which bosonic quantum fields thermalize. Fermions acquire an excess of occupation in the ultraviolet regime compared to a Fermi-Dirac statistic characterized by a power-law with exponent two. The fermion production mechanism via parametric resonance is found to be most efficient after the instability ends. Quantum corrections then provide a very efficient particle creation mechanism which is interpreted as an amplification of decay processes. The ratio
Quantum thermodynamics: a nonequilibrium Green's function approach.
Esposito, Massimiliano; Ochoa, Maicol A; Galperin, Michael
2015-02-27
We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green's functions. The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit.
Nonequilibrium statistical physics a modern perspective
Livi, Roberto
2017-01-01
Statistical mechanics has been proven to be successful at describing physical systems at thermodynamic equilibrium. Since most natural phenomena occur in nonequilibrium conditions, the present challenge is to find suitable physical approaches for such conditions: this book provides a pedagogical pathway that explores various perspectives. The use of clear language, and explanatory figures and diagrams to describe models, simulations and experimental findings makes the book a valuable resource for undergraduate and graduate students, and also for lecturers organizing teaching at varying levels of experience in the field. Written in three parts, it covers basic and traditional concepts of nonequilibrium physics, modern aspects concerning nonequilibrium phase transitions, and application-orientated topics from a modern perspective. A broad range of topics is covered, including Langevin equations, Levy processes, directed percolation, kinetic roughening and pattern formation.
Quantum distribution function of nonequilibrium system
International Nuclear Information System (INIS)
Sogo, Kiyoshi; Fujimoto, Yasushi.
1990-03-01
A path integral representation is derived for the Wigner distribution function of a nonequilibrium system coupled with heat bath. Under appropriate conditions, the Wigner distribution function approaches an equilibrium distribution, which manifests shifting and broadening of spectral lines due to the interaction with heat bath. It is shown that the equilibrium distribution becomes the quantum canonical distribution in the vanishing coupling constant limit. (author)
International Nuclear Information System (INIS)
Yeh, L.
1992-01-01
The phase-space-picture approach to quantum non-equilibrium statistical mechanics via the characteristic function of infinite- mode squeezed coherent states is introduced. We use quantum Brownian motion as an example to show how this approach provides an interesting geometrical interpretation of quantum non-equilibrium phenomena
International Nuclear Information System (INIS)
Schleich, W.; Dobiasch, P.
1986-01-01
A brief review is given of quantum noise in ring laser gyroscopes. Some the basic elements of ring laser theory, such as the Sagnac effect, the locking effect, and the influence of quantumnoise on the mean beat frequency versus rotation rate are discussed. The Langevin equation for the ase difference between the counterpropagating waves in the presence of any periodic and time symmetric dither is cast into a form which alows a qualitative discussion of the resulting lock-in curve as well as an exact expression in terms of infinite matrix continued fractions. The details of the transformation of the stochastic variable and the derivation of the exact expression for f>t may be found in appendices. Exact results are presented for two special cases of the dithering function: the harmonic and the square-wave bias
Quantum gases finite temperature and non-equilibrium dynamics
Szymanska, Marzena; Davis, Matthew; Gardiner, Simon
2013-01-01
The 1995 observation of Bose-Einstein condensation in dilute atomic vapours spawned the field of ultracold, degenerate quantum gases. Unprecedented developments in experimental design and precision control have led to quantum gases becoming the preferred playground for designer quantum many-body systems. This self-contained volume provides a broad overview of the principal theoretical techniques applied to non-equilibrium and finite temperature quantum gases. Covering Bose-Einstein condensates, degenerate Fermi gases, and the more recently realised exciton-polariton condensates, it fills a gap by linking between different methods with origins in condensed matter physics, quantum field theory, quantum optics, atomic physics, and statistical mechanics. Thematically organised chapters on different methodologies, contributed by key researchers using a unified notation, provide the first integrated view of the relative merits of individual approaches, aided by pertinent introductory chapters and the guidance of ed...
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
On quantum statistical inference
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, developments in the theory of quantum measurements have
Nonequilibrium Statistical Operator Method and Generalized Kinetic Equations
Kuzemsky, A. L.
2018-01-01
We consider some principal problems of nonequilibrium statistical thermodynamics in the framework of the Zubarev nonequilibrium statistical operator approach. We present a brief comparative analysis of some approaches to describing irreversible processes based on the concept of nonequilibrium Gibbs ensembles and their applicability to describing nonequilibrium processes. We discuss the derivation of generalized kinetic equations for a system in a heat bath. We obtain and analyze a damped Schrödinger-type equation for a dynamical system in a heat bath. We study the dynamical behavior of a particle in a medium taking the dissipation effects into account. We consider the scattering problem for neutrons in a nonequilibrium medium and derive a generalized Van Hove formula. We show that the nonequilibrium statistical operator method is an effective, convenient tool for describing irreversible processes in condensed matter.
Generalized quantum statistics
International Nuclear Information System (INIS)
Chou, C.
1992-01-01
In the paper, a non-anyonic generalization of quantum statistics is presented, in which Fermi-Dirac statistics (FDS) and Bose-Einstein statistics (BES) appear as two special cases. The new quantum statistics, which is characterized by the dimension of its single particle Fock space, contains three consistent parts, namely the generalized bilinear quantization, the generalized quantum mechanical description and the corresponding statistical mechanics
Annotations to quantum statistical mechanics
Kim, In-Gee
2018-01-01
This book is a rewritten and annotated version of Leo P. Kadanoff and Gordon Bayms lectures that were presented in the book Quantum Statistical Mechanics: Greens Function Methods in Equilibrium and Nonequilibrium Problems. The lectures were devoted to a discussion on the use of thermodynamic Greens 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 Greens 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...
Nonequilibrium electron transport through quantum dots in the Kondo regime
DEFF Research Database (Denmark)
Wölfle, Peter; Paaske, Jens; Rosch, Achim
2005-01-01
Electron transport at large bias voltage through quantum dots in the Kondo regime is described within the perturbative renormalization group extended to nonequilibrium. The conductance, local magnetization, dynamical spin susceptibility and local spectral function are calculated. We show how...
Generalized interpolative quantum statistics
International Nuclear Information System (INIS)
Ramanathan, R.
1992-01-01
A generalized interpolative quantum statistics is presented by conjecturing a certain reordering of phase space due to the presence of possible exotic objects other than bosons and fermions. Such an interpolation achieved through a Bose-counting strategy predicts the existence of an infinite quantum Boltzmann-Gibbs statistics akin to the one discovered by Greenberg recently
On nonequilibrium many-body systems. 1: The nonequilibrium statistical operator method
International Nuclear Information System (INIS)
Algarte, A.C.S.; Vasconcellos, A.R.; Luzzi, R.; Sampaio, A.J.C.
1985-01-01
The theoretical aspects involved in the treatment of many-body systems strongly departed from equilibrium are discussed. The nonequilibrium statistical operator (NSO) method is considered in detail. Using Jaynes' maximum entropy formalism complemented with an ad hoc hypothesis a nonequilibrium statistical operator is obtained. This approach introduces irreversibility from the outset and we recover statistical operators like those of Green-Mori and Zubarev as particular cases. The connection with Generalized Thermodynamics and the construction of nonlinear transport equations are briefly described. (Author) [pt
Coherence enhanced quantum metrology in a nonequilibrium optical molecule
Wang, Zhihai; Wu, Wei; Cui, Guodong; Wang, Jin
2018-03-01
We explore the quantum metrology in an optical molecular system coupled to two environments with different temperatures, using a quantum master equation beyond secular approximation. We discover that the steady-state coherence originating from and sustained by the nonequilibrium condition can enhance quantum metrology. We also study the quantitative measures of the nonequilibrium condition in terms of the curl flux, heat current and entropy production at the steady state. They are found to grow with temperature difference. However, an apparent paradox arises considering the contrary behaviors of the steady-state coherence and the nonequilibrium measures in relation to the inter-cavity coupling strength. This paradox is resolved by decomposing the heat current into a population part and a coherence part. Only the latter, the coherence part of the heat current, is tightly connected to the steady-state coherence and behaves similarly with respect to the inter-cavity coupling strength. Interestingly, the coherence part of the heat current flows from the low-temperature reservoir to the high-temperature reservoir, opposite to the direction of the population heat current. Our work offers a viable way to enhance quantum metrology for open quantum systems through steady-state coherence sustained by the nonequilibrium condition, which can be controlled and manipulated to maximize its utility. The potential applications go beyond quantum metrology and extend to areas such as device designing, quantum computation and quantum technology in general.
On quantum statistical inference
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.
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...
Limiting processes in non-equilibrium classical statistical mechanics
International Nuclear Information System (INIS)
Jancel, R.
1983-01-01
After a recall of the basic principles of the statistical mechanics, the results of ergodic theory, the transient at the thermodynamic limit and his link with the transport theory near the equilibrium are analyzed. The fundamental problems put by the description of non-equilibrium macroscopic systems are investigated and the kinetic methods are stated. The problems of the non-equilibrium statistical mechanics are analyzed: irreversibility and coarse-graining, macroscopic variables and kinetic description, autonomous reduced descriptions, limit processes, BBGKY hierarchy, limit theorems [fr
Projection operator techniques in nonequilibrium statistical mechanics
International Nuclear Information System (INIS)
Grabert, H.
1982-01-01
This book is an introduction to the application of the projection operator technique to the statistical mechanics of irreversible processes. After a general introduction to the projection operator technique and statistical thermodynamics the Fokker-Planck and the master equation approach are described together with the response theory. Then, as applications the damped harmonic oscillator, simple fluids, and the spin relaxation are considered. (HSI)
The Generalized Quantum Statistics
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...
SRB states and nonequilibrium statistical mechanics close to equilibrium
Gallavotti, Giovannni; Ruelle, David
1996-01-01
Nonequilibrium statistical mechanics close to equilibrium is studied using SRB states and a formula for their derivatives with respect to parameters. We write general expressions for the thermodynamic fluxes (or currents) and the transport coefficients, generalizing previous results. In this framework we give a general proof of the Onsager reciprocity relations.
Measures of trajectory ensemble disparity in nonequilibrium statistical dynamics
International Nuclear Information System (INIS)
Crooks, Gavin E; Sivak, David A
2011-01-01
Many interesting divergence measures between conjugate ensembles of nonequilibrium trajectories can be experimentally determined from the work distribution of the process. Herein, we review the statistical and physical significance of several of these measures, in particular the relative entropy (dissipation), Jeffreys divergence (hysteresis), Jensen–Shannon divergence (time-asymmetry), Chernoff divergence (work cumulant generating function), and Rényi divergence
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.
Supersymmetric electroweak baryogenesis, nonequilibrium field theory and quantum Boltzmann equations
Riotto, Antonio
1998-01-01
The closed time-path (CPT) formalism is a powerful Green's function formulation to describe nonequilibrium phenomena in field theory and it leads to a complete nonequilibrium quantum kinetic theory. In this paper we make use of the CPT formalism to write down a set of quantum Boltzmann equations describing the local number density asymmetries of the particles involved in supersymmetric electroweak baryogenesis. These diffusion equations automatically and self-consistently incorporate the CP-violating sources which fuel baryogenesis when transport properties allow the CP-violating charges to diffuse in front of the bubble wall separating the broken from the unbroken phase at the electroweak phase transition. This is a significant improvement with respect to recent approaches where the CP-violating sources are inserted by hand into the diffusion equations. Furthermore, the CP-violating sources and the particle number changing interactions manifest ``memory'' effects which are typical of the quantum transp ort t...
Nonequilibrium Electron Transport Through a Quantum Dot from Kubo Formula
International Nuclear Information System (INIS)
Lue Rong; Zhang Guangming
2005-01-01
Based on the Kubo formula for an electron tunneling junction, we revisit the nonequilibrium transport properties through a quantum dot. Since the Fermi level of the quantum dot is set by the conduction electrons of the leads, we calculate the electron current from the left side by assuming the quantum dot coupled to the right lead as another side of the tunneling junction, and the other way round is used to calculate the current from the right side. By symmetrizing these two currents, an effective local density states on the dot can be obtained, and is discussed at high and low temperatures, respectively.
On Equivalence of Nonequilibrium Thermodynamic and Statistical Entropies
Directory of Open Access Journals (Sweden)
Purushottam D. Gujrati
2015-02-01
Full Text Available We review the concept of nonequilibrium thermodynamic entropy and observables and internal variables as state variables, introduced recently by us, and provide a simple first principle derivation of additive statistical entropy, applicable to all nonequilibrium states by treating thermodynamics as an experimental science. We establish their numerical equivalence in several cases, which includes the most important case when the thermodynamic entropy is a state function. We discuss various interesting aspects of the two entropies and show that the number of microstates in the Boltzmann entropy includes all possible microstates of non-zero probabilities even if the system is trapped in a disjoint component of the microstate space. We show that negative thermodynamic entropy can appear from nonnegative statistical entropy.
Non-equilibrium statistical physics with application to disordered systems
Cáceres, Manuel Osvaldo
2017-01-01
This textbook is the result of the enhancement of several courses on non-equilibrium statistics, stochastic processes, stochastic differential equations, anomalous diffusion and disorder. The target audience includes students of physics, mathematics, biology, chemistry, and engineering at undergraduate and graduate level with a grasp of the basic elements of mathematics and physics of the fourth year of a typical undergraduate course. The little-known physical and mathematical concepts are described in sections and specific exercises throughout the text, as well as in appendices. Physical-mathematical motivation is the main driving force for the development of this text. It presents the academic topics of probability theory and stochastic processes as well as new educational aspects in the presentation of non-equilibrium statistical theory and stochastic differential equations.. In particular it discusses the problem of irreversibility in that context and the dynamics of Fokker-Planck. An introduction on fluc...
Glushak, P. A.; Markiv, B. B.; Tokarchuk, M. V.
2018-01-01
We present a generalization of Zubarev's nonequilibrium statistical operator method based on the principle of maximum Renyi entropy. In the framework of this approach, we obtain transport equations for the basic set of parameters of the reduced description of nonequilibrium processes in a classical system of interacting particles using Liouville equations with fractional derivatives. For a classical systems of particles in a medium with a fractal structure, we obtain a non-Markovian diffusion equation with fractional spatial derivatives. For a concrete model of the frequency dependence of a memory function, we obtain generalized Kettano-type diffusion equation with the spatial and temporal fractality taken into account. We present a generalization of nonequilibrium thermofield dynamics in Zubarev's nonequilibrium statistical operator method in the framework of Renyi statistics.
Non-equilibrium quantum heat machines
Alicki, Robert; Gelbwaser-Klimovsky, David
2015-11-01
Standard heat machines (engine, heat pump, refrigerator) are composed of a system (working fluid) coupled to at least two equilibrium baths at different temperatures and periodically driven by an external device (piston or rotor) sometimes called the work reservoir. The aim of this paper is to go beyond this scheme by considering environments which are stationary but cannot be decomposed into a few baths at thermal equilibrium. Such situations are important, for example in solar cells, chemical machines in biology, various realizations of laser cooling or nanoscopic machines driven by laser radiation. We classify non-equilibrium baths depending on their thermodynamic behavior and show that the efficiency of heat machines powered by them is limited by the generalized Carnot bound.
Non-equilibrium quantum heat machines
International Nuclear Information System (INIS)
Alicki, Robert; Gelbwaser-Klimovsky, David
2015-01-01
Standard heat machines (engine, heat pump, refrigerator) are composed of a system (working fluid) coupled to at least two equilibrium baths at different temperatures and periodically driven by an external device (piston or rotor) sometimes called the work reservoir. The aim of this paper is to go beyond this scheme by considering environments which are stationary but cannot be decomposed into a few baths at thermal equilibrium. Such situations are important, for example in solar cells, chemical machines in biology, various realizations of laser cooling or nanoscopic machines driven by laser radiation. We classify non-equilibrium baths depending on their thermodynamic behavior and show that the efficiency of heat machines powered by them is limited by the generalized Carnot bound. (paper)
Memory Effects and Nonequilibrium Correlations in the Dynamics of Open Quantum Systems
Morozov, V. G.
2018-01-01
We propose a systematic approach to the dynamics of open quantum systems in the framework of Zubarev's nonequilibrium statistical operator method. The approach is based on the relation between ensemble means of the Hubbard operators and the matrix elements of the reduced statistical operator of an open quantum system. This key relation allows deriving master equations for open systems following a scheme conceptually identical to the scheme used to derive kinetic equations for distribution functions. The advantage of the proposed formalism is that some relevant dynamical correlations between an open system and its environment can be taken into account. To illustrate the method, we derive a non-Markovian master equation containing the contribution of nonequilibrium correlations associated with energy conservation.
Chaotic Dynamical Ferromagnetic Phase Induced by Nonequilibrium Quantum Fluctuations
Lerose, Alessio; Marino, Jamir; Žunkovič, Bojan; Gambassi, Andrea; Silva, Alessandro
2018-03-01
We investigate the robustness of a dynamical phase transition against quantum fluctuations by studying the impact of a ferromagnetic nearest-neighbor spin interaction in one spatial dimension on the nonequilibrium dynamical phase diagram of the fully connected quantum Ising model. In particular, we focus on the transient dynamics after a quantum quench and study the prethermal state via a combination of analytic time-dependent spin wave theory and numerical methods based on matrix product states. We find that, upon increasing the strength of the quantum fluctuations, the dynamical critical point fans out into a chaotic dynamical phase within which the asymptotic ordering is characterized by strong sensitivity to the parameters and initial conditions. We argue that such a phenomenon is general, as it arises from the impact of quantum fluctuations on the mean-field out of equilibrium dynamics of any system which exhibits a broken discrete symmetry.
Nonequilibrium Green function techniques applied to hot electron quantum transport
International Nuclear Information System (INIS)
Jauho, A.P.
1989-01-01
During the last few years considerable effort has been devoted to deriving quantum transport equations for semiconductors under extreme conditions (high electric fields, spatial quantization in one or two directions). Here we review the results obtained with nonequilibrium Green function techniques as formulated by Baym and Kadanoff, or by Keldysh. In particular, the following topics will be discussed: (i) Systematic approaches to reduce the transport equation governing the correlation function to a transport equation for the Wigner function; (ii) Approximations reducing the nonmarkovian quantum transport equation to a numerically tractable form, and results for model semiconductors; (iii) Recent progress in extending the formalism to inhomogeneous systems; and (iv) Nonequilibrium screening. In all sections we try to direct the reader's attention to points where the present understanding is (at best) incomplete, and indicate possible lines for future work. (orig.)
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
Towards a nonequilibrium quantum field theory approach to electroweak baryogenesis
International Nuclear Information System (INIS)
Riotto, A.
1996-01-01
We propose a general method to compute CP violating observables from extensions of the standard model in the context of electroweak baryogenesis. It is an alternative to the one recently developed by Huet and Nelson and relies on a nonequilibrium quantum field theory approach. The method is valid for all shapes and sizes of the bubble wall expanding in the thermal bath during a first-order electroweak phase transition. The quantum physics of CP violation and its suppression coming from the incoherent nature of thermal processes are also made explicit. copyright 1996 The American Physical Society
What can we learn from noise? - Mesoscopic nonequilibrium statistical physics.
Kobayashi, Kensuke
2016-01-01
Mesoscopic systems - small electric circuits working in quantum regime - offer us a unique experimental stage to explorer quantum transport in a tunable and precise way. The purpose of this Review is to show how they can contribute to statistical physics. We introduce the significance of fluctuation, or equivalently noise, as noise measurement enables us to address the fundamental aspects of a physical system. The significance of the fluctuation theorem (FT) in statistical physics is noted. We explain what information can be deduced from the current noise measurement in mesoscopic systems. As an important application of the noise measurement to statistical physics, we describe our experimental work on the current and current noise in an electron interferometer, which is the first experimental test of FT in quantum regime. Our attempt will shed new light in the research field of mesoscopic quantum statistical physics.
Quantum Statistics and Entanglement Problems
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.
Nonequilibrium statistical mechanics and stochastic thermodynamics of small systems
International Nuclear Information System (INIS)
Tu Zhanchun
2014-01-01
Thermodynamics is an old subject. The research objects in conventional thermodynamics are macroscopic systems with huge number of particles. In recent 30 years, thermodynamics of small systems is a frontier topic in physics. Here we introduce nonequilibrium statistical mechanics and stochastic thermodynamics of small systems. As a case study, we construct a Canot-like cycle of a stochastic heat engine with a single particle controlled by a time-dependent harmonic potential. We find that the efficiency at maximum power is 1 - √T c /T h , where Tc and Th are the temperatures of cold bath and hot bath, respectively. (author)
Lecture notes on quantum statistics
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
Nonequilibrium steady states of ideal bosonic and fermionic quantum gases.
Vorberg, Daniel; Wustmann, Waltraut; Schomerus, Henning; Ketzmerick, Roland; Eckardt, André
2015-12-01
We investigate nonequilibrium steady states of driven-dissipative ideal quantum gases of both bosons and fermions. We focus on systems of sharp particle number that are driven out of equilibrium either by the coupling to several heat baths of different temperature or by time-periodic driving in combination with the coupling to a heat bath. Within the framework of (Floquet-)Born-Markov theory, several analytical and numerical methods are described in detail. This includes a mean-field theory in terms of occupation numbers, an augmented mean-field theory taking into account also nontrivial two-particle correlations, and quantum-jump-type Monte Carlo simulations. For the case of the ideal Fermi gas, these methods are applied to simple lattice models and the possibility of achieving exotic states via bath engineering is pointed out. The largest part of this work is devoted to bosonic quantum gases and the phenomenon of Bose selection, a nonequilibrium generalization of Bose condensation, where multiple single-particle states are selected to acquire a large occupation [Phys. Rev. Lett. 111, 240405 (2013)]. In this context, among others, we provide a theory for transitions where the set of selected states changes, describe an efficient algorithm for finding the set of selected states, investigate beyond-mean-field effects, and identify the dominant mechanisms for heat transport in the Bose-selected state.
Nonequilibrium steady states of ideal bosonic and fermionic quantum gases
Vorberg, Daniel; Wustmann, Waltraut; Schomerus, Henning; Ketzmerick, Roland; Eckardt, André
2015-12-01
We investigate nonequilibrium steady states of driven-dissipative ideal quantum gases of both bosons and fermions. We focus on systems of sharp particle number that are driven out of equilibrium either by the coupling to several heat baths of different temperature or by time-periodic driving in combination with the coupling to a heat bath. Within the framework of (Floquet-)Born-Markov theory, several analytical and numerical methods are described in detail. This includes a mean-field theory in terms of occupation numbers, an augmented mean-field theory taking into account also nontrivial two-particle correlations, and quantum-jump-type Monte Carlo simulations. For the case of the ideal Fermi gas, these methods are applied to simple lattice models and the possibility of achieving exotic states via bath engineering is pointed out. The largest part of this work is devoted to bosonic quantum gases and the phenomenon of Bose selection, a nonequilibrium generalization of Bose condensation, where multiple single-particle states are selected to acquire a large occupation [Phys. Rev. Lett. 111, 240405 (2013), 10.1103/PhysRevLett.111.240405]. In this context, among others, we provide a theory for transitions where the set of selected states changes, describe an efficient algorithm for finding the set of selected states, investigate beyond-mean-field effects, and identify the dominant mechanisms for heat transport in the Bose-selected state.
Nonequilibrium statistical operator in hot-electron transport theory
International Nuclear Information System (INIS)
Xing, D.Y.; Liu, M.
1991-09-01
The Nonequilibrium Statistical Operator method developed by Zubarev is generalized and applied to the study of hot-electron transport in semiconductors. The steady-state balance equations for momentum and energy are derived to the lowest order in the electron-lattice coupling. We show that the derived balance equations are exactly the same as those obtained by Lei and Ting. This equivalence stems from the fact that to the linear order in the electron-lattice coupling, two statistical density matrices have identical effect when they are used to calculate the average value of a dynamical operator. The application to the steady-state and transient hot-electron transport in multivalley semiconductors is also discussed. (author). 28 refs, 1 fig
Nonequilibrium quantum mechanics: A "hot quantum soup" of paramagnons
Scammell, H. D.; Sushkov, O. P.
2017-01-01
Motivated by recent measurements of the lifetime (decay width) of paramagnons in quantum antiferromagnet TlCuCl3, we investigate paramagnon decay in a heat bath and formulate an appropriate quantum theory. Our formulation can be split into two regimes: (i) a nonperturbative, "hot quantum soup" regime where the paramagnon width is comparable to its energy; (ii) a usual perturbative regime where the paramagnon width is significantly lower than its energy. Close to the Neel temperature, the paramagnon width becomes comparable to its energy and falls into the hot quantum soup regime. To describe this regime, we develop a new finite frequency, finite temperature technique for a nonlinear quantum field theory; the "golden rule of quantum kinetics." The formulation is generic and applicable to any three-dimensional quantum antiferromagnet in the vicinity of a quantum critical point. Specifically, we apply our results to TlCuCl3 and find agreement with experimental data. Additionally, we show that logarithmic running of the coupling constant in the upper critical dimension changes the commonly accepted picture of the quantum disordered and quantum critical regimes.
Non-equilibrium transport in the quantum dot: quench dynamics and non-equilibrium steady state
Culver, Adrian; Andrei, Natan
We present an exact method of calculating the non-equilibrium current driven by a voltage drop across a quantum dot. The system is described by the two lead Anderson model at zero temperature with on-site Coulomb repulsion and non-interacting, linearized leads. We prepare the system in an initial state consisting of a free Fermi sea in each lead with the voltage drop given as the difference between the two Fermi levels. We quench the system by coupling the dot to the leads at t = 0 and following the time evolution of the wavefunction. In the long time limit a new type of Bethe Ansatz wavefunction emerges, which satisfies the Lippmann-Schwinger equation with the two Fermi seas serving as the boundary conditions. This exact, non-perturbative solution describes the non-equilibrium steady state of the system. We describe how to use this solution to compute the infinite time limit of the expectation value of the current operator at a given voltage, which would yield the I-V characteristic of the dot. Research supported by NSF Grant DMR 1410583.
Non-equilibrium dynamics near a quantum multicritical point
International Nuclear Information System (INIS)
Patra, Ayoti; Mukherjee, Victor; Dutta, Amit
2011-01-01
We study the non-equilibrium dynamics of a quantum system close to a quantum multi-critical point (MCP) using the example of a one-dimensional spin-1/2 transverse XY spin chain. We summarize earlier results of defect generenation and fidelity susceptibility for quenching through MCP and close to the MCP, respectively. For a quenching scheme which enables the system to hit the MCP along different paths, we emphasize the role of path on exponents associated with quasicritical points which appear in the scaling relations. Finally, we explicitly derive the scaling of concurrence and negativity for two spin entanglement generated following a slow quenching across the MCP and enlist the results for different quenching schemes. We explicity show the dependence of the scaling on the quenching path and dicuss the limiting situations.
Quantum Coherent Dynamics Enhanced by Synchronization with Nonequilibrium Environments
Ishikawa, Akira; Okada, Ryo; Uchiyama, Kazuharu; Hori, Hirokazu; Kobayashi, Kiyoshi
2018-05-01
We report the discovery of the anomalous enhancement of quantum coherent dynamics (CD) due to a non-Markovian mechanism originating from not thermal-equilibrium phonon baths but nonequilibrium coherent phonons. CD is an elementary process for quantum phenomena in nanosystems, such as excitation transfer (ET) in semiconductor nanostructures and light-harvesting systems. CD occurs in homogeneous nanosystems because system inhomogeneity typically destroys coherence. In real systems, however, nanosystems behave as open systems surrounded by environments such as phonon systems. Typically, CD in inhomogeneous nanosystems is enhanced by the absorption and emission of thermal-equilibrium phonons, and the enhancement is described by the conventional master equation. On the other hand, CD is also enhanced by synchronization between population dynamics in nanosystems and coherent phonons; namely, coherent phonons, which are self-consistently induced by phase matching with Rabi oscillation, are fed back to enhance CD. This anomalous enhancement of CD essentially originates from the nonequilibrium and dynamical non-Markovian nature of coherent phonon environments, and the enhancement is firstly predicted by applying time-dependent projection operators to nonequilibrium and dynamical environments. Moreover, CD is discussed by considering ET from a donor to an acceptor. It is found that the enhancement of ET by synchronization with coherent phonons depends on the competition between the output time from a system to an acceptor and the formation time of coherent phonons. These findings in this study will stimulate the design and manipulation of CD via structured environments from the viewpoint of application to nano-photoelectronic devices.
Fractional statistics and quantum theory
Khare, Avinash
1997-01-01
This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced research workers with a reasonable background in quantum and statistical mechanics. The main emphasis will be on explaining new concepts. Topics in the first part of the book includes the flux tube model of anyons, the braid group and quantum and statistical mechanics of noninteracting anyon gas. The second part of the book provides a detailed discussion about f
What Can Reinforcement Learning Teach Us About Non-Equilibrium Quantum Dynamics
Bukov, Marin; Day, Alexandre; Sels, Dries; Weinberg, Phillip; Polkovnikov, Anatoli; Mehta, Pankaj
Equilibrium thermodynamics and statistical physics are the building blocks of modern science and technology. Yet, our understanding of thermodynamic processes away from equilibrium is largely missing. In this talk, I will reveal the potential of what artificial intelligence can teach us about the complex behaviour of non-equilibrium systems. Specifically, I will discuss the problem of finding optimal drive protocols to prepare a desired target state in quantum mechanical systems by applying ideas from Reinforcement Learning [one can think of Reinforcement Learning as the study of how an agent (e.g. a robot) can learn and perfect a given policy through interactions with an environment.]. The driving protocols learnt by our agent suggest that the non-equilibrium world features possibilities easily defying intuition based on equilibrium physics.
Quantum mechanics from classical statistics
International Nuclear Information System (INIS)
Wetterich, C.
2010-01-01
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. 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. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. 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. As an illustration, we discuss a classical statistical implementation of a quantum computer.
Nonequilibrium Transport through a Spinful Quantum Dot with Superconducting Leads
DEFF Research Database (Denmark)
Andersen, Brian Møller; Flensberg, Karsten; Koerting, Verena
2011-01-01
We study the nonlinear cotunneling current through a spinful quantum dot contacted by two superconducting leads. Applying a general nonequilibrium Green function formalism to an effective Kondo model, we study the rich variation in the IV characteristics with varying asymmetry in the tunnel...... coupling to source and drain electrodes. The current is found to be carried, respectively, by multiple Andreev reflections in the symmetric limit, and by spin-induced Yu-Shiba-Rusinov bound states in the strongly asymmetric limit. The interplay between these two mechanisms leads to qualitatively different...... IV characteristics in the crossover regime of intermediate symmetry, consistent with recent experimental observations of negative differential conductance and repositioned conductance peaks in subgap cotunneling spectroscopy....
On Quantum Statistical Inference, II
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...
Nonequilibrium forces between neutral atoms mediated by a quantum field
International Nuclear Information System (INIS)
Behunin, Ryan O.; Hu, Bei-Lok
2010-01-01
We study forces between two neutral atoms, modeled as three-dimensional harmonic oscillators, arising from mutual influences mediated by an electromagnetic field but not from their direct interactions. We allow as dynamical variables the center-of-mass motion of the atom, its internal degrees of freedom, and the quantum field treated relativistically. We adopt the method of nonequilibrium quantum field theory which can provide a first-principles, systematic, and unified description including the intrinsic and induced dipole fluctuations. The inclusion of self-consistent back-actions makes possible a fully dynamical description of these forces valid for general atom motion. In thermal equilibrium we recover the known forces--London, van der Waals, and Casimir-Polder--between neutral atoms in the long-time limit. We also reproduce a recently reported force between atoms when the system is out of thermal equilibrium at late times. More noteworthy is the discovery of the existence of a type of (or identification of the source of some known) interatomic force which we call the ''entanglement force,'' originating from the quantum correlations of the internal degrees of freedom of entangled atoms.
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
Quantum information theory and quantum statistics
International Nuclear Information System (INIS)
Petz, D.
2008-01-01
Based on lectures given by the author, this book focuses on providing reliable introductory explanations of key concepts of quantum information theory and quantum statistics - rather than on results. The mathematically rigorous presentation is supported by numerous examples and exercises and by an appendix summarizing the relevant aspects of linear analysis. Assuming that the reader is familiar with the content of standard undergraduate courses in quantum mechanics, probability theory, linear algebra and functional analysis, the book addresses graduate students of mathematics and physics as well as theoretical and mathematical physicists. Conceived as a primer to bridge the gap between statistical physics and quantum information, a field to which the author has contributed significantly himself, it emphasizes concepts and thorough discussions of the fundamental notions to prepare the reader for deeper studies, not least through the selection of well chosen exercises. (orig.)
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 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
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)
Quantum formalism for classical statistics
Wetterich, C.
2018-06-01
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg picture for this problem, we develop here the associated Schrödinger picture that keeps track of the local probabilistic information. The transport of the probabilistic information between neighboring hypersurfaces obeys a linear evolution equation, and therefore the superposition principle for the possible solutions. Operators are associated to local observables, with rules for the computation of expectation values similar to quantum mechanics. We discuss how non-commutativity naturally arises in this setting. Also other features characteristic of quantum mechanics, such as complex structure, change of basis or symmetry transformations, can be found in classical statistics once formulated in terms of wave functions or density matrices. We construct for every quantum system an equivalent classical statistical system, such that time in quantum mechanics corresponds to the location of hypersurfaces in the classical probabilistic ensemble. For suitable choices of local observables in the classical statistical system one can, in principle, compute all expectation values and correlations of observables in the quantum system from the local probabilistic information of the associated classical statistical system. Realizing a static memory material as a quantum simulator for a given quantum system is not a matter of principle, but rather of practical simplicity.
International Nuclear Information System (INIS)
Hsiang, J.-T.; Hu, B.L.
2015-01-01
The existence and uniqueness of a steady state for nonequilibrium systems (NESS) is a fundamental subject and a main theme of research in statistical mechanics for decades. For Gaussian systems, such as a chain of classical harmonic oscillators connected at each end to a heat bath, and for classical anharmonic oscillators under specified conditions, definitive answers exist in the form of proven theorems. Answering this question for quantum many-body systems poses a challenge for the present. In this work we address this issue by deriving the stochastic equations for the reduced system with self-consistent backaction from the two baths, calculating the energy flow from one bath to the chain to the other bath, and exhibiting a power balance relation in the total (chain + baths) system which testifies to the existence of a NESS in this system at late times. Its insensitivity to the initial conditions of the chain corroborates to its uniqueness. The functional method we adopt here entails the use of the influence functional, the coarse-grained and stochastic effective actions, from which one can derive the stochastic equations and calculate the average values of physical variables in open quantum systems. This involves both taking the expectation values of quantum operators of the system and the distributional averages of stochastic variables stemming from the coarse-grained environment. This method though formal in appearance is compact and complete. It can also easily accommodate perturbative techniques and diagrammatic methods from field theory. Taken all together it provides a solid platform for carrying out systematic investigations into the nonequilibrium dynamics of open quantum systems and quantum thermodynamics. -- Highlights: •Nonequilibrium steady state (NESS) for interacting quantum many-body systems. •Derivation of stochastic equations for quantum oscillator chain with two heat baths. •Explicit calculation of the energy flow from one bath to the
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.)
Directory of Open Access Journals (Sweden)
P.Kostrobii
2006-01-01
Full Text Available Nonequilibrium properties of an inhomogeneous electron gas are studied using the method of the nonequilibrium statistical operator by D.N. Zubarev. Generalized transport equations for the mean values of inhomogeneous operators of the electron number density, momentum density, and total energy density for weakly and strongly nonequilibrium states are obtained. We derive a chain of equations for the Green's functions, which connects commutative time-dependent Green's functions "density-density", "momentum-momentum", "enthalpy-enthalpy" with reduced Green's functions of the generalized transport coefficients and with Green's functions for higher order memory kernels in the case of a weakly nonequilibrium spatially inhomogeneous electron gas.
A calculational scheme for nonequilibrium quantum field system
International Nuclear Information System (INIS)
Yamanaka, Y.
1991-01-01
A new calculational scheme is presented for interacting nonequi-librium time dependent quantum field systems within the framework of thermo field dynamics (TFD), taking account of the fact that the thermal vacuum should go through many inequivalent state vector spaces. A para-meter parametrizing various state vector spaces has to be introduced and plays a role of new time-variable. Thus we have double-time TFD. The 2 requirements in this double-time TFD are imposed to establish a quasi-particle picture to get an attainable scheme of perturbative calculation : the existence of the spectral representation for the full propagator and the diagonalization of the quasi-particle Hamiltonian. The 1st condition turns out to amount to the existence of local-time tempera-ture. The 2nd condition leads to the master equation for the number density. This formalism is applied to high-energy heavy ion collision process. The very fundamental question is then how the thermodynamical properties such as heat and temperature appear in such an isolated system. This double-time TFD, suitable for isolated thermal systems of quantum fields, can handle the situation from the beginning of the process. (author). 24 refs.; 1 fig
Some recent developments in non-equilibrium statistical physics
Indian Academy of Sciences (India)
: ... This canonical prescription is the starting point for studying a system in ... abilistic approach to non-equilibrium dynamics by treating the case of Markovian ..... equation in this network between the incoming flux and the outgoing flux at each.
Non-equilibrium effects upon the non-Markovian Caldeira-Leggett quantum master equation
International Nuclear Information System (INIS)
Bolivar, A.O.
2011-01-01
Highlights: → Classical Brownian motion described by a non-Markovian Fokker-Planck equation. → Quantization process. → Quantum Brownian motion described by a non-Markovian Caldeira-Leggett equation. → A non-equilibrium quantum thermal force is predicted. - Abstract: We obtain a non-Markovian quantum master equation directly from the quantization of a non-Markovian Fokker-Planck equation describing the Brownian motion of a particle immersed in a generic environment (e.g. a non-thermal fluid). As far as the especial case of a heat bath comprising of quantum harmonic oscillators is concerned, we derive a non-Markovian Caldeira-Leggett master equation on the basis of which we work out the concept of non-equilibrium quantum thermal force exerted by the harmonic heat bath upon the Brownian motion of a free particle. The classical limit (or dequantization process) of this sort of non-equilibrium quantum effect is scrutinized, as well.
Quantum local asymptotic normality and other questions of quantum statistics
Kahn, Jonas
2008-01-01
This thesis is entitled Quantum Local Asymptotic Normality and other questions of Quantum Statistics ,. Quantum statistics are statistics on quantum objects. In classical statistics, we usually start from the data. Indeed, if we want to predict the weather, and can measure the wind or the
Nonequilibrium quantum solvation with a time-dependent Onsager cavity
Kirchberg, H.; Nalbach, P.; Thorwart, M.
2018-04-01
We formulate a theory of nonequilibrium quantum solvation in which parameters of the solvent are explicitly depending on time. We assume in a simplest approach a spherical molecular Onsager cavity with a time-dependent radius. We analyze the relaxation properties of a test molecular point dipole in a dielectric solvent and consider two cases: (i) a shrinking Onsager sphere and (ii) a breathing Onsager sphere. Due to the time-dependent solvent, the frequency-dependent response function of the dipole becomes time-dependent. For a shrinking Onsager sphere, the dipole relaxation is in general enhanced. This is reflected in a temporally increasing linewidth of the absorptive part of the response. Furthermore, the effective frequency-dependent response function shows two peaks in the absorptive part which are symmetrically shifted around the eigenfrequency. By contrast, a breathing sphere reduces damping as compared to the static sphere. Interestingly, we find a non-monotonous dependence of the relaxation rate on the breathing rate and a resonant suppression of damping when both rates are comparable. Moreover, the linewidth of the absorptive part of the response function is strongly reduced for times when the breathing sphere reaches its maximal extension.
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
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or
Open problems in non-equilibrium physics
International Nuclear Information System (INIS)
Kusnezov, D.
1997-01-01
The report contains viewgraphs on the following: approaches to non-equilibrium statistical mechanics; classical and quantum processes in chaotic environments; classical fields in non-equilibrium situations: real time dynamics at finite temperature; and phase transitions in non-equilibrium conditions
Open problems in non-equilibrium physics
Energy Technology Data Exchange (ETDEWEB)
Kusnezov, D.
1997-09-22
The report contains viewgraphs on the following: approaches to non-equilibrium statistical mechanics; classical and quantum processes in chaotic environments; classical fields in non-equilibrium situations: real time dynamics at finite temperature; and phase transitions in non-equilibrium conditions.
Introduction to quantum statistical mechanics
Bogolyubov, N N
2010-01-01
Introduction to Quantum Statistical Mechanics (Second Edition) may be used as an advanced textbook by graduate students, even ambitious undergraduates in physics. It is also suitable for non experts in physics who wish to have an overview of some of the classic and fundamental quantum models in the subject. The explanation in the book is detailed enough to capture the interest of the reader, and complete enough to provide the necessary background material needed to dwell further into the subject and explore the research literature.
Nonequilibrium Green's function method for quantum thermal transport
Wang, Jian-Sheng; Agarwalla, Bijay Kumar; Li, Huanan; Thingna, Juzar
2014-12-01
This review deals with the nonequilibrium Green's function (NEGF) method applied to the problems of energy transport due to atomic vibrations (phonons), primarily for small junction systems. We present a pedagogical introduction to the subject, deriving some of the well-known results such as the Laudauer-like formula for heat current in ballistic systems. The main aim of the review is to build the machinery of the method so that it can be applied to other situations, which are not directly treated here. In addition to the above, we consider a number of applications of NEGF, not in routine model system calculations, but in a few new aspects showing the power and usefulness of the formalism. In particular, we discuss the problems of multiple leads, coupled left-right-lead system, and system without a center. We also apply the method to the problem of full counting statistics. In the case of nonlinear systems, we make general comments on the thermal expansion effect, phonon relaxation time, and a certain class of mean-field approximations. Lastly, we examine the relationship between NEGF, reduced density matrix, and master equation approaches to thermal transport.
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.
Quantum Statistical Mechanics on a Quantum Computer
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
Directory of Open Access Journals (Sweden)
L. Fusco
2014-08-01
Full Text Available We analyze the nature of the statistics of the work done on or by a quantum many-body system brought out of equilibrium. We show that, for the sudden quench and for an initial state that commutes with the initial Hamiltonian, it is possible to retrieve the whole nonequilibrium thermodynamics via single projective measurements of observables. We highlight, in a physically clear way, the qualitative implications for the statistics of work coming from considering processes described by operators that either commute or do not commute with the unperturbed Hamiltonian of a given system. We consider a quantum many-body system and derive an expression that allows us to give a physical interpretation, for a thermal initial state, to all of the cumulants of the work in the case of quenched operators commuting with the unperturbed Hamiltonian. In the commuting case, the observables that we need to measure have an intuitive physical meaning. Conversely, in the noncommuting case, we show that, although it is possible to operate fully within the single-measurement framework irrespectively of the size of the quench, some difficulties are faced in providing a clear-cut physical interpretation to the cumulants. This circumstance makes the study of the physics of the system nontrivial and highlights the nonintuitive phenomenology of the emergence of thermodynamics from the fully quantum microscopic description. We illustrate our ideas with the example of the Ising model in a transverse field showing the interesting behavior of the high-order statistical moments of the work distribution for a generic thermal state and linking them to the critical nature of the model itself.
Exploring the nonequilibrium dynamics of ultracold quantum gases by using numerical tools
Heidrich-Meisner, Fabian
Numerical tools such as exact diagonalization or the density matrix renormalization group method have been vital for the study of the nonequilibrium dynamics of strongly correlated many-body systems. Moreover, they provided unique insight for the interpretation of quantum gas experiments, whenever a direct comparison with theory is possible. By considering the example of the experiment by Ronzheimer et al., in which both an interaction quench and the release of bosons from a trap into an empty optical lattice (sudden expansion) was realized, I discuss several nonequilibrium effects of strongly interacting quantum gases. These include the thermalization of a closed quantum system and its connection to the eigenstate thermalization hypothesis, nonequilibrium mass transport, dynamical fermionization, and transient phenomena such as quantum distillation or dynamical quasicondensation. I highlight the role of integrability in giving rise to ballistic transport in strongly interacting 1D systems and in determining the asymptotic state after a quantum quench. The talk concludes with a perspective on open questions concerning 2D systems and the numerical simulation of their nonequilibrium dynamics. Supported by Deutsche Forschungsgemeinschaft (DFG) via FOR 801.
Fluctuation and dissipation in nonequilibrium quantum field theory
International Nuclear Information System (INIS)
Ramos, Rudnei O.
1994-01-01
The nonequilibrium dynamics of a scalar field is studied using perturbation theory and a real time finite temperature formulation. The evolution equation for the scalar field is explicitly obtained, and terms responsible for noise (fluctuations) and dissipation are identified and studied in the high temperature limit. (author)
Non-equilibrium statistical thermodynamics of neutron gas in reactor
International Nuclear Information System (INIS)
Hayasaka, Hideo
1977-01-01
The thermodynamic structures of non-equilibrium steady states of highly rarefied neutron gas in various media are considered for the irreversible processes owing to creative and destructive reactions of neutrons with nuclei of these media and supply from the external sources. Under the so-called clean and cold condition in reactor, the medium is regarded virtually as offering the different chemical potential fields for each subsystem of a steady neutron gas system. The fluctuations around a steady state are considered in a Markovian-Gaussian process. The generalized Einstein relations are derived for stationary neutron gas systems. The forces and flows of neutron gases in a medium are defined upon the general stationary solution of the Fokker-Planck equation. There exist the symmetry of the kinetic coefficients, and the minimum entropy production upon neutron-nuclear reactions. The distribution functions in various media are determined by each corresponding extremum condition under the vanishing of changes of the respective total entropies in the Gibbs equation. (auth.)
Quantum Statistical Mechanics on a Quantum Computer
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.
Probabilistic and Statistical Aspects of Quantum Theory
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
2013-01-01
This book offers a comprehensive picture of nonequilibrium phenomena in nanoscale systems. Written by internationally recognized experts in the field, this book strikes a balance between theory and experiment, and includes in-depth introductions to nonequilibrium fluctuation relations, nonlinear dynamics and transport, single molecule experiments, and molecular diffusion in nanopores. The authors explore the application of these concepts to nano- and biosystems by cross-linking key methods and ideas from nonequilibrium statistical physics, thermodynamics, stochastic theory, and dynamical s
Conserving GW scheme for nonequilibrium quantum transport in molecular contacts
DEFF Research Database (Denmark)
Thygesen, Kristian Sommer; Rubio, Angel
2008-01-01
We give a detailed presentation of our recent scheme to include correlation effects in molecular transport calculations using the nonequilibrium Keldysh formalism. The scheme is general and can be used with any quasiparticle self-energy, but for practical reasons, we mainly specialize to the so......-called GW self-energy, widely used to describe the quasiparticle band structures and spectroscopic properties of extended and low-dimensional systems. We restrict the GW self-energy to a finite, central region containing the molecule, and we describe the leads by density functional theory (DFT). A minimal...
Nonequilibrium statistical mechanics of systems with long-range interactions
Energy Technology Data Exchange (ETDEWEB)
Levin, Yan, E-mail: levin@if.ufrgs.br; Pakter, Renato, E-mail: pakter@if.ufrgs.br; Rizzato, Felipe B., E-mail: rizzato@if.ufrgs.br; Teles, Tarcísio N., E-mail: tarcisio.teles@fi.infn.it; Benetti, Fernanda P.C., E-mail: fbenetti@if.ufrgs.br
2014-02-01
Systems with long-range (LR) forces, for which the interaction potential decays with the interparticle distance with an exponent smaller than the dimensionality of the embedding space, remain an outstanding challenge to statistical physics. The internal energy of such systems lacks extensivity and additivity. Although the extensivity can be restored by scaling the interaction potential with the number of particles, the non-additivity still remains. Lack of additivity leads to inequivalence of statistical ensembles. Before relaxing to thermodynamic equilibrium, isolated systems with LR forces become trapped in out-of-equilibrium quasi-stationary states (qSSs), the lifetime of which diverges with the number of particles. Therefore, in the thermodynamic limit LR systems will not relax to equilibrium. The qSSs are attained through the process of collisionless relaxation. Density oscillations lead to particle–wave interactions and excitation of parametric resonances. The resonant particles escape from the main cluster to form a tenuous halo. Simultaneously, this cools down the core of the distribution and dampens out the oscillations. When all the oscillations die out the ergodicity is broken and a qSS is born. In this report, we will review a theory which allows us to quantitatively predict the particle distribution in the qSS. The theory is applied to various LR interacting systems, ranging from plasmas to self-gravitating clusters and kinetic spin models.
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 ...
Majorana fermion modulated nonequilibrium transport through double quantum dots
International Nuclear Information System (INIS)
Deng, Ming-Xun; Wang, Rui-Qiang; Ai, Bao-Quan; Yang, Mou; Hu, Liang-Bin; Zhong, Qing-Hu; Wang, Guang-Hui
2014-01-01
Nonequilibrium electronic transports through a double-QD-Majorana coupling system are studied with a purpose to extract the information to identify Majorana bound states (MBSs). It is found that MBSs can help form various transport processes, including the nonlocal crossed Andreev reflection, local resonant Andreev reflection, and cotunneling, depending on the relative position of two dot levels. These processes enrich the signature of average currents and noise correlations to probe the nature of MBSs. We further demonstrate the switching between the current peaks of crossed Andreev reflection and cotunneling, which is closely related to the nonlocal nature of Majorana fermions. We also propose effective physical pictures to understand these Majorana-assisted transports. - Highlights: • Majorana fermions are characterized in the signature of currents and noises. • Three types of tunneling mechanisms are realized separately. • The switching of crossed Andreev reflection and cotunneling is realized. • Concrete physical pictures are proposed to understand Majorana-assisted transports
Majorana fermion modulated nonequilibrium transport through double quantum dots
Energy Technology Data Exchange (ETDEWEB)
Deng, Ming-Xun [Laboratory of Quantum Engineering and Quantum Materials, ICMP and SPTE, South China Normal University, Guangzhou 510006 (China); Wang, Rui-Qiang, E-mail: rqwanggz@163.com [Laboratory of Quantum Engineering and Quantum Materials, ICMP and SPTE, South China Normal University, Guangzhou 510006 (China); Ai, Bao-Quan; Yang, Mou; Hu, Liang-Bin; Zhong, Qing-Hu [Laboratory of Quantum Engineering and Quantum Materials, ICMP and SPTE, South China Normal University, Guangzhou 510006 (China); Wang, Guang-Hui [Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510006 (China)
2014-06-13
Nonequilibrium electronic transports through a double-QD-Majorana coupling system are studied with a purpose to extract the information to identify Majorana bound states (MBSs). It is found that MBSs can help form various transport processes, including the nonlocal crossed Andreev reflection, local resonant Andreev reflection, and cotunneling, depending on the relative position of two dot levels. These processes enrich the signature of average currents and noise correlations to probe the nature of MBSs. We further demonstrate the switching between the current peaks of crossed Andreev reflection and cotunneling, which is closely related to the nonlocal nature of Majorana fermions. We also propose effective physical pictures to understand these Majorana-assisted transports. - Highlights: • Majorana fermions are characterized in the signature of currents and noises. • Three types of tunneling mechanisms are realized separately. • The switching of crossed Andreev reflection and cotunneling is realized. • Concrete physical pictures are proposed to understand Majorana-assisted transports.
Effects of quantum coherence on work statistics
Xu, Bao-Ming; Zou, Jian; Guo, Li-Sha; Kong, Xiang-Mu
2018-05-01
In the conventional two-point measurement scheme of quantum thermodynamics, quantum coherence is destroyed by the first measurement. But as we know the coherence really plays an important role in the quantum thermodynamics process, and how to describe the work statistics for a quantum coherent process is still an open question. In this paper, we use the full counting statistics method to investigate the effects of quantum coherence on work statistics. First, we give a general discussion and show that for a quantum coherent process, work statistics is very different from that of the two-point measurement scheme, specifically the average work is increased or decreased and the work fluctuation can be decreased by quantum coherence, which strongly depends on the relative phase, the energy level structure, and the external protocol. Then, we concretely consider a quenched one-dimensional transverse Ising model and show that quantum coherence has a more significant influence on work statistics in the ferromagnetism regime compared with that in the paramagnetism regime, so that due to the presence of quantum coherence the work statistics can exhibit the critical phenomenon even at high temperature.
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.
Energy Technology Data Exchange (ETDEWEB)
Haertle, Rainer [Institut fuer Theoretische Physik, Georg-August-Universitaet Goettingen, Goettingen (Germany); Millis, Andrew J. [Department of Physics, Columbia University, New York (United States)
2016-07-01
We present a new impurity solver for real-time and nonequilibrium dynamical mean field theory applications, based on the recently developed hierarchical quantum master equation approach. Our method employs a hybridization expansion of the time evolution operator, including an advanced, systematic truncation scheme. Convergence to exact results for not too low temperatures has been demonstrated by a direct comparison to quantum Monte Carlo simulations. The approach is time-local, which gives us access to slow dynamics such as, e.g., in the presence of magnetic fields or exchange interactions and to nonequilibrium steady states. Here, we present first results of this new scheme for the description of strongly correlated materials in the framework of dynamical mean field theory, including benchmark and new results for the Hubbard and periodic Anderson model.
Röpke, G.
2018-01-01
One of the fundamental problems in physics that are not yet rigorously solved is the statistical mechanics of nonequilibrium processes. An important contribution to describing irreversible behavior starting from reversible Hamiltonian dynamics was given by D. N. Zubarev, who invented the method of the nonequilibrium statistical operator. We discuss this approach, in particular, the extended von Neumann equation, and as an example consider the electrical conductivity of a system of charged particles. We consider the selection of the set of relevant observables. We show the relation between kinetic theory and linear response theory. Using thermodynamic Green's functions, we present a systematic treatment of correlation functions, but the convergence needs investigation. We compare different expressions for the conductivity and list open questions.
Statistical mechanics for a class of quantum statistics
International Nuclear Information System (INIS)
Isakov, S.B.
1994-01-01
Generalized statistical distributions for identical particles are introduced for the case where filling a single-particle quantum state by particles depends on filling states of different momenta. The system of one-dimensional bosons with a two-body potential that can be solved by means of the thermodynamic Bethe ansatz is shown to be equivalent thermodynamically to a system of free particles obeying statistical distributions of the above class. The quantum statistics arising in this way are completely determined by the two-particle scattering phases of the corresponding interacting systems. An equation determining the statistical distributions for these statistics is derived
Nonequilibrium transport through molecular junctions in the quantum regime
Czech Academy of Sciences Publication Activity Database
Koch, T.; Loos, Jan; Alvermann, A.; Fehske, H.
2011-01-01
Roč. 84, č. 12 (2011), 125131/1-125131/16 ISSN 1098-0121 Institutional research plan: CEZ:AV0Z10100521 Keywords : the ory of electron ic transport * scattering mechanisms * polarons and electron -phonon interactions * quantum dots Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.691, year: 2011
Depletion of superfluidity in a disordered non-equilibrium quantum condensate
Energy Technology Data Exchange (ETDEWEB)
Janot, Alexander; Rosenow, Bernd [Institut fuer Theoretische Physik, Universitaet Leipzig, 04009 Leipzig (Germany); Hyart, Timo [Institute of Physics, Leiden University, Niels Bohrweg 2, 2333 CA Leiden (Netherlands); Eastham, Paul [School of Physics, Trinity College, Dublin 2 (Ireland)
2013-07-01
Observations of quantum coherence in driven systems, e.g. polariton condensates, have strongly stimulated experimental as well as theoretical efforts during the last decade. We analyze the superfluid stiffness of a non-equilibrium quantum-condensate in a disordered environment taking gain and loss of particles into account. To this end a modified effective Gross-Pitaevskii equation is employed. We find that the disorder-driven depletion of superfluidity is strongly enhanced due to the gain-loss mechanism. It turns out that the condensate remains stiff at finite length scales only.
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.
Quantum Statistical Testing of a Quantum Random Number Generator
Energy Technology Data Exchange (ETDEWEB)
Humble, Travis S [ORNL
2014-01-01
The unobservable elements in a quantum technology, e.g., the quantum state, complicate system verification against promised behavior. Using model-based system engineering, we present methods for verifying the opera- tion of a prototypical quantum random number generator. We begin with the algorithmic design of the QRNG followed by the synthesis of its physical design requirements. We next discuss how quantum statistical testing can be used to verify device behavior as well as detect device bias. We conclude by highlighting how system design and verification methods must influence effort to certify future quantum technologies.
Hsiang, J-T; Chou, C H; Subaşı, Y; Hu, B L
2018-01-01
In a series of papers, we intend to take the perspective of open quantum systems and examine from their nonequilibrium dynamics the conditions when the physical quantities, their relations, and the laws of thermodynamics become well defined and viable for quantum many-body systems. We first describe how an open-system nonequilibrium dynamics (ONEq) approach is different from the closed combined system + environment in a global thermal state (CGTs) setup. Only after the open system equilibrates will it be amenable to conventional thermodynamics descriptions, thus quantum thermodynamics (QTD) comes at the end rather than assumed in the beginning. The linkage between the two comes from the reduced density matrix of ONEq in that stage having the same form as that of the system in the CGTs. We see the open-system approach having the advantage of dealing with nonequilibrium processes as many experiments in the near future will call for. Because it spells out the conditions of QTD's existence, it can also aid us in addressing the basic issues in quantum thermodynamics from first principles in a systematic way. We then study one broad class of open quantum systems where the full nonequilibrium dynamics can be solved exactly, that of the quantum Brownian motion of N strongly coupled harmonic oscillators, interacting strongly with a scalar-field environment. In this paper, we focus on the internal energy, heat capacity, and the third law. We show for this class of physical models, amongst other findings, the extensive property of the internal energy, the positivity of the heat capacity, and the validity of the third law from the perspective of the behavior of the heat capacity toward zero temperature. These conclusions obtained from exact solutions and quantitative analysis clearly disprove claims of negative specific heat in such systems and dispel allegations that in such systems the validity of the third law of thermodynamics relies on quantum entanglement. They are
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 ...
Nonequilibrium dynamic critical scaling of the quantum Ising chain.
Kolodrubetz, Michael; Clark, Bryan K; Huse, David A
2012-07-06
We solve for the time-dependent finite-size scaling functions of the one-dimensional transverse-field Ising chain during a linear-in-time ramp of the field through the quantum critical point. We then simulate Mott-insulating bosons in a tilted potential, an experimentally studied system in the same equilibrium universality class, and demonstrate that universality holds for the dynamics as well. We find qualitatively athermal features of the scaling functions, such as negative spin correlations, and we show that they should be robustly observable within present cold atom experiments.
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.
International Nuclear Information System (INIS)
Zhao, Peiji; Horing, Norman J.M.; Woolard, Dwight L.; Cui, H.L.
2003-01-01
We present a nonequilibrium Green's function formulation of many-body quantum transport theory for multi-band semiconductor systems with a phonon bath. The equations are expressed exactly in terms of single particle nonequilibrium Green's functions and self-energies, treating the open electron-hole system in weak interaction with the bath. A decoupling technique is employed to separate the individual band Green's function equations of motion from one another, with the band-band interaction effects embedded in ''cross-band'' self-energies. This nonequilibrium Green's function formulation of quantum transport theory is amenable to solution by parallel computing because of its formal decoupling with respect to inter-band interactions. Moreover, this formulation also permits coding the simulator of an n-band semiconductor in terms of that for an (n-1)-band system, in step with the current tendency and development of programming technology. Finally, the focus of these equations on individual bands provides a relatively direct route for the determination of carrier motion in energy bands, and to delineate the influence of intra- and inter-band interactions. A detailed description is provided for three-band semiconductor systems
Nonequilibrium forces between atoms and dielectrics mediated by a quantum field
International Nuclear Information System (INIS)
Behunin, Ryan O.; Hu, Bei-Lok
2011-01-01
In this paper we give a first principles microphysics derivation of the nonequilibrium forces between an atom, treated as a three-dimensional harmonic oscillator, and a bulk dielectric medium modeled as a continuous lattice of oscillators coupled to a reservoir. We assume no direct interaction between the atom and the medium but there exist mutual influences transmitted via a common electromagnetic field. By employing concepts and techniques of open quantum systems we introduce coarse-graining to the physical variables--the medium, the quantum field, and the atom's internal degrees of freedom, in that order--to extract their averaged effects from the lowest tier progressively to the top tier. The first tier of coarse-graining provides the averaged effect of the medium upon the field, quantified by a complex permittivity (in the frequency domain) describing the response of the dielectric to the field in addition to its back action on the field through a stochastic forcing term. The last tier of coarse-graining over the atom's internal degrees of freedom results in an equation of motion for the atom's center of mass from which we can derive the force on the atom. Our nonequilibrium formulation provides a fully dynamical description of the atom's motion including back-action effects from all other relevant variables concerned. In the long-time limit we recover the known results for the atom-dielectric force when the combined system is in equilibrium or in a nonequilibrium stationary state.
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
A quantum information approach to statistical mechanics
International Nuclear Information System (INIS)
Cuevas, G.
2011-01-01
The field of quantum information and computation harnesses and exploits the properties of quantum mechanics to perform tasks more efficiently than their classical counterparts, or that may uniquely be possible in the quantum world. Its findings and techniques have been applied to a number of fields, such as the study of entanglement in strongly correlated systems, new simulation techniques for many-body physics or, generally, to quantum optics. This thesis aims at broadening the scope of quantum information theory by applying it to problems in statistical mechanics. We focus on classical spin models, which are toy models used in a variety of systems, ranging from magnetism, neural networks, to quantum gravity. We tackle these models using quantum information tools from three different angles. First, we show how the partition function of a class of widely different classical spin models (models in different dimensions, different types of many-body interactions, different symmetries, etc) can be mapped to the partition function of a single model. We prove this by first establishing a relation between partition functions and quantum states, and then transforming the corresponding quantum states to each other. Second, we give efficient quantum algorithms to estimate the partition function of various classical spin models, such as the Ising or the Potts model. The proof is based on a relation between partition functions and quantum circuits, which allows us to determine the quantum computational complexity of the partition function by studying the corresponding quantum circuit. Finally, we outline the possibility of applying quantum information concepts and tools to certain models of dis- crete quantum gravity. The latter provide a natural route to generalize our results, insofar as the central quantity has the form of a partition function, and as classical spin models are used as toy models of matter. (author)
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
Semi-Poisson statistics in quantum chaos.
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.
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
Itineration of the Internet over nonequilibrium stationary states in Tsallis statistics.
Abe, Sumiyoshi; Suzuki, Norikazu
2003-01-01
The cumulative probability distribution of sparseness time interval in the Internet is studied by the method of data analysis. Round-trip time between a local host and a destination host through ten odd routers is measured using the ping command, i.e., doing an echo experiment. The data are found to be well described by q-exponential distributions, which maximize the Tsallis entropy indexed by q less or larger than unity, showing a scale-invariant feature of the system. The network is observed to itinerate over a series of the nonequilibrium stationary states characterized by Tsallis statistics.
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 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.
Hidden Statistics Approach to Quantum Simulations
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
Non-equilibrium statistical theory about microscopic fatigue cracks of metal in magnetic field
International Nuclear Information System (INIS)
Zhao-Long, Liu; Hai-Yun, Hu; Tian-You, Fan; Xiu-San, Xing
2010-01-01
This paper develops the non-equilibrium statistical fatigue damage theory to study the statistical behaviour of micro-crack for metals in magnetic field. The one-dimensional homogeneous crack system is chosen for study. To investigate the effect caused by magnetic field on the statistical distribution of micro-crack in the system, the theoretical analysis on microcrack evolution equation, the average length of micro-crack, density distribution function of micro-crack and fatigue fracture probability have been performed. The derived results relate the changes of some quantities, such as average length, density distribution function and fatigue fracture probability, to the applied magnetic field, the magnetic and mechanical properties of metals. It gives a theoretical explanation on the change of fatigue damage due to magnetic fields observed by experiments, and presents an analytic approach on studying the fatigue damage of metal in magnetic field. (cross-disciplinary physics and related areas of science and technology)
Microcavity quantum-dot systems for non-equilibrium Bose-Einstein condensation
International Nuclear Information System (INIS)
Piper, I M; Ediger, M; Wilson, A M; Wu, Y; Phillips, R T; Eastham, P R; Hugues, M; Hopkinson, M
2010-01-01
We review the practical conditions required to achieve a non-equilibrium BEC driven by quantum dynamics in a system comprising a microcavity field mode and a distribution of localised two-level systems driven to a step-like population inversion profile. A candidate system based on eight 3.8nm layers of In 0.23 Ga 0.77 As in GaAs shows promising characteristics with regard to the total dipole strength which can be coupled to the field mode.
Microcavity quantum-dot systems for non-equilibrium Bose-Einstein condensation
Energy Technology Data Exchange (ETDEWEB)
Piper, I M; Ediger, M; Wilson, A M; Wu, Y; Phillips, R T [Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE (United Kingdom); Eastham, P R [School of Physics, Trinity College Dublin, Dublin 2 (Ireland); Hugues, M; Hopkinson, M, E-mail: imp24@cam.ac.u [Department of Electronic and Electrical Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD (United Kingdom)
2010-09-01
We review the practical conditions required to achieve a non-equilibrium BEC driven by quantum dynamics in a system comprising a microcavity field mode and a distribution of localised two-level systems driven to a step-like population inversion profile. A candidate system based on eight 3.8nm layers of In{sub 0.23}Ga{sub 0.77}As in GaAs shows promising characteristics with regard to the total dipole strength which can be coupled to the field mode.
Zeno dynamics in quantum statistical mechanics
International Nuclear Information System (INIS)
Schmidt, Andreas U
2003-01-01
We study the quantum Zeno effect in quantum statistical mechanics within the operator algebraic framework. We formulate a condition for the appearance of the effect in W*-dynamical systems, in terms of the short-time behaviour of the dynamics. Examples of quantum spin systems show that this condition can be effectively applied to quantum statistical mechanical models. Furthermore, we derive an explicit form of the Zeno generator, and use it to construct Gibbs equilibrium states for the Zeno dynamics. As a concrete example, we consider the X-Y model, for which we show that a frequent measurement at a microscopic level, e.g. a single lattice site, can produce a macroscopic effect in changing the global equilibrium
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
Statistical distribution of quantum particles
Indian Academy of Sciences (India)
S B Khasare
2018-02-08
Feb 8, 2018 ... In this work, the statistical distribution functions for boson, fermions and their mixtures have been ... index is greater than unity, then it is easy in the present approach to ... ability W. Section 3 gives the derivation and graphical.
Statistical transmutation in doped quantum dimer models.
Lamas, C A; Ralko, A; Cabra, D C; Poilblanc, D; Pujol, P
2012-07-06
We prove a "statistical transmutation" symmetry of doped quantum dimer models on the square, triangular, and kagome lattices: the energy spectrum is invariant under a simultaneous change of statistics (i.e., bosonic into fermionic or vice versa) of the holes and of the signs of all the dimer resonance loops. This exact transformation enables us to define the duality equivalence between doped quantum dimer Hamiltonians and provides the analytic framework to analyze dynamical statistical transmutations. We investigate numerically the doping of the triangular quantum dimer model with special focus on the topological Z(2) dimer liquid. Doping leads to four (instead of two for the square lattice) inequivalent families of Hamiltonians. Competition between phase separation, superfluidity, supersolidity, and fermionic phases is investigated in the four families.
Nonequilibrium Quantum Phase Transition in a Hybrid Atom-Optomechanical System
Mann, Niklas; Bakhtiari, M. Reza; Pelster, Axel; Thorwart, Michael
2018-02-01
We consider a hybrid quantum many-body system formed by a vibrational mode of a nanomembrane, which interacts optomechanically with light in a cavity, and an ultracold atom gas in the optical lattice of the out-coupled light. The adiabatic elimination of the light field yields an effective Hamiltonian which reveals a competition between the force localizing the atoms and the membrane displacement. At a critical atom-membrane interaction, we find a nonequilibrium quantum phase transition from a localized symmetric state of the atom cloud to a shifted symmetry-broken state, the energy of the lowest collective excitation vanishes, and a strong atom-membrane entanglement arises. The effect occurs when the atoms and the membrane are nonresonantly coupled.
Error suppression and error correction in adiabatic quantum computation: non-equilibrium dynamics
International Nuclear Information System (INIS)
Sarovar, Mohan; Young, Kevin C
2013-01-01
While adiabatic quantum computing (AQC) has some robustness to noise and decoherence, it is widely believed that encoding, error suppression and error correction will be required to scale AQC to large problem sizes. Previous works have established at least two different techniques for error suppression in AQC. In this paper we derive a model for describing the dynamics of encoded AQC and show that previous constructions for error suppression can be unified with this dynamical model. In addition, the model clarifies the mechanisms of error suppression and allows the identification of its weaknesses. In the second half of the paper, we utilize our description of non-equilibrium dynamics in encoded AQC to construct methods for error correction in AQC by cooling local degrees of freedom (qubits). While this is shown to be possible in principle, we also identify the key challenge to this approach: the requirement of high-weight Hamiltonians. Finally, we use our dynamical model to perform a simplified thermal stability analysis of concatenated-stabilizer-code encoded many-body systems for AQC or quantum memories. This work is a companion paper to ‘Error suppression and error correction in adiabatic quantum computation: techniques and challenges (2013 Phys. Rev. X 3 041013)’, which provides a quantum information perspective on the techniques and limitations of error suppression and correction in AQC. In this paper we couch the same results within a dynamical framework, which allows for a detailed analysis of the non-equilibrium dynamics of error suppression and correction in encoded AQC. (paper)
Quantum entanglement at high temperatures? Bosonic systems in nonequilibrium steady state
International Nuclear Information System (INIS)
Hsiang, Jen-Tsung; Hu, B.L.
2015-01-01
This is the second of a series of three papers examining how viable it is for entanglement to be sustained at high temperatures for quantum systems in thermal equilibrium (Case A), in nonequilibrium (Case B) and in nonequilibrium steady state (NESS) conditions (Case C). The system we analyze here consists of two coupled quantum harmonic oscillators each interacting with its own bath described by a scalar field, set at temperatures T_1>T_2. For constant bilinear inter-oscillator coupling studied here (Case C1) owing to the Gaussian nature, the problem can be solved exactly at arbitrary temperatures even for strong coupling. We find that the valid entanglement criterion in general is not a function of the bath temperature difference, in contrast to thermal transport in the same NESS setting http://arxiv.org/abs/1405.7642. Thus lowering the temperature of one of the thermal baths does not necessarily help to safeguard the entanglement between the oscillators. Indeed, quantum entanglement will disappear if any one of the thermal baths has a temperature higher than the critical temperature T_c, defined as the temperature above which quantum entanglement vanishes. With the Langevin equations derived we give a full display of how entanglement dynamics in this system depends on T_1, T_2, the inter-oscillator coupling and the system-bath coupling strengths. For weak oscillator-bath coupling the critical temperature T_c is about the order of the inverse oscillator frequency, but for strong oscillator-bath coupling it will depend on the bath cutoff frequency. We conclude that in most realistic circumstances, for bosonic systems in NESS with constant bilinear coupling, ‘hot entanglement’ is largely a fiction.
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.
Quantum Statistical Approach to Superconductivity
Nam, Eunsoo
The Frohlich Hamiltonian representing an interaction between electron and phonon is derived. By exchanging a virtual phonon, a system of two electrons can lower the system's total energy if the difference of their kinetic energies is less than the energy of the phonon exchanged. This is shown by using quantum mechanical perturbation theory, which is fully developed. A general theory of superconductivity is developed, starting with a BCS Hamiltonian in which the interaction strengths (V_{11}, V_{22 }, V_{12}) among and between "electron" (1) and "hole" (2) Cooper pairs are differentiated. The supercondensate is shown to be composed of equal numbers of "electron" and "hole" ground (zero-momentum) Cooper pairs with charges mp 2e.. Based on the Hamiltonian, the normal-to-super phase transition is investigated, approaching the critical temperature T_{c} from the high temperature side. Non zero momentum Cooper pairs, that is, pairs of electrons (holes) with antiparallel spins and nearly opposite momenta above T_{c } in the bulk limit, are shown to move like independent bosons with the energy momentum relation varepsilon = (1/2)upsilon_ {F}p, where upsilon_ {F} represents the Fermi velocity. We have investigated the Bose-Einstein condensation of pairons. The system of free Cooper pairs in a 3D superconductors undergoes a phase transition of the second order with the critical temperature T_{c} given byk_{B}T_{c } = (1/2)(pi^2hbar^3v_sp {F}{3}n/1.20257)^{1over3 }where n is the number density of Cooper pairs. We calculate various properties associated with superconductivity at finite temperature. We derive general expressions for the energy gaps for both quasi electrons and pairons. Based on the independent pairon model, we explain the flux quantization, London's equation and the Josephson effects, stressing the importance of the macroscopic wave -function which represents the supercondensate in motion. We derived the basic equations governing the behavior of the
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
International Nuclear Information System (INIS)
Wu, C.-H.; Lee, D.-S.
2005-01-01
We employ the Schwinger-Keldysh formalism to study the nonequilibrium dynamics of the mirror with perfect reflection moving in a quantum field. In the case where the mirror undergoes the small displacement, the coarse-grained effective action is obtained by integrating out the quantum field with the method of influence functional. The semiclassical Langevin equation is derived, and is found to involve two levels of backreaction effects on the dynamics of mirrors: radiation reaction induced by the motion of the mirror and backreaction dissipation arising from fluctuations in quantum field via a fluctuation-dissipation relation. Although the corresponding theorem of fluctuation and dissipation for the case with the small mirror's displacement is of model independence, the study from the first principles derivation shows that the theorem is also independent of the regulators introduced to deal with short-distance divergences from the quantum field. Thus, when the method of regularization is introduced to compute the dissipation and fluctuation effects, this theorem must be fulfilled as the results are obtained by taking the short-distance limit in the end of calculations. The backreaction effects from vacuum fluctuations on moving mirrors are found to be hardly detected while those effects from thermal fluctuations may be detectable
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
Conceptual developments of non-equilibrium statistical mechanics in the early days of Japan
Ichiyanagi, Masakazu
1995-11-01
This paper reviews the research in nonequilibrium statistical mechanics made in Japan in the period between 1930 and 1960. Nearly thirty years have passed since the discovery of the exact formula for the electrical conductivity. With the rise of the linear response theory, the methods and results of which are quickly grasped by anyone, its rationale was pushed aside and even at the stage where the formulation was still incomplete some authors hurried to make physical applications. Such an attitude robbed it of most of its interest for the average physicist, who would approach an understanding of some basic concept, not through abstract and logical analysis but by simply increasing his technical experiences with the concept. The purpose of this review is to rescue the linear response theory from being labeled a mathematical tool and to show that it has considerable physical content. Many key papers, originally written in Japanese, are reproduced.
Lower bounds for ballistic current and noise in non-equilibrium quantum steady states
Directory of Open Access Journals (Sweden)
Benjamin Doyon
2015-03-01
Full Text Available Let an infinite, homogeneous, many-body quantum system be unitarily evolved for a long time from a state where two halves are independently thermalized. One says that a non-equilibrium steady state emerges if there are nonzero steady currents in the central region. In particular, their presence is a signature of ballistic transport. We analyze the consequences of the current observable being a conserved density; near equilibrium this is known to give rise to linear wave propagation and a nonzero Drude peak. Using the Lieb–Robinson bound, we derive, under a certain regularity condition, a lower bound for the non-equilibrium steady-state current determined by equilibrium averages. This shows and quantifies the presence of ballistic transport far from equilibrium. The inequality suggests the definition of “nonlinear sound velocities”, which specialize to the sound velocity near equilibrium in non-integrable models, and “generalized sound velocities”, which encode generalized Gibbs thermalization in integrable models. These are bounded by the Lieb–Robinson velocity. The inequality also gives rise to a bound on the energy current noise in the case of pure energy transport. We show that the inequality is satisfied in many models where exact results are available, and that it is saturated at one-dimensional criticality.
Emergence of currents as a transient quantum effect in nonequilibrium systems
Energy Technology Data Exchange (ETDEWEB)
Granot, Er' el; Marchewka, Avi [Department of Electrical and Electronics Engineering, Ariel University Center of Samaria, Ariel (Israel)
2011-09-15
Most current calculations are based on equilibrium or semi-equilibrium models. However, except for very special scenarios (like ring configuration), the current cannot exist in equilibrium. Moreover, unlike with equilibrium scenarios, there is no generic approach to confront out-of-equilibrium currents. In this paper we used recent studies on transient quantum mechanics to solve the current, which appears in the presence of very high density gradients and fast transients. It shows that the emerging current appears instantaneously, and although the density beyond the discontinuity is initially negligible the currents there have a finite value, and remain constant for a finite period. It is shown that this nonequilibrium effect can be measured in real experiments (such as cooled rubidium atoms), where the discontinuity is replaced with a finite width (hundreds of nanometers) gradient.
Emergence of currents as a transient quantum effect in nonequilibrium systems
International Nuclear Information System (INIS)
Granot, Er'el; Marchewka, Avi
2011-01-01
Most current calculations are based on equilibrium or semi-equilibrium models. However, except for very special scenarios (like ring configuration), the current cannot exist in equilibrium. Moreover, unlike with equilibrium scenarios, there is no generic approach to confront out-of-equilibrium currents. In this paper we used recent studies on transient quantum mechanics to solve the current, which appears in the presence of very high density gradients and fast transients. It shows that the emerging current appears instantaneously, and although the density beyond the discontinuity is initially negligible the currents there have a finite value, and remain constant for a finite period. It is shown that this nonequilibrium effect can be measured in real experiments (such as cooled rubidium atoms), where the discontinuity is replaced with a finite width (hundreds of nanometers) gradient.
Emergence of currents as a transient quantum effect in nonequilibrium systems
Granot, Er'El; Marchewka, Avi
2011-09-01
Most current calculations are based on equilibrium or semi-equilibrium models. However, except for very special scenarios (like ring configuration), the current cannot exist in equilibrium. Moreover, unlike with equilibrium scenarios, there is no generic approach to confront out-of-equilibrium currents. In this paper we used recent studies on transient quantum mechanics to solve the current, which appears in the presence of very high density gradients and fast transients. It shows that the emerging current appears instantaneously, and although the density beyond the discontinuity is initially negligible the currents there have a finite value, and remain constant for a finite period. It is shown that this nonequilibrium effect can be measured in real experiments (such as cooled rubidium atoms), where the discontinuity is replaced with a finite width (hundreds of nanometers) gradient.
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
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
Spezia, Riccardo; Martínez-Nuñez, Emilio; Vazquez, Saulo; Hase, William L
2017-04-28
In this Introduction, we show the basic problems of non-statistical and non-equilibrium phenomena related to the papers collected in this themed issue. Over the past few years, significant advances in both computing power and development of theories have allowed the study of larger systems, increasing the time length of simulations and improving the quality of potential energy surfaces. In particular, the possibility of using quantum chemistry to calculate energies and forces 'on the fly' has paved the way to directly study chemical reactions. This has provided a valuable tool to explore molecular mechanisms at given temperatures and energies and to see whether these reactive trajectories follow statistical laws and/or minimum energy pathways. This themed issue collects different aspects of the problem and gives an overview of recent works and developments in different contexts, from the gas phase to the condensed phase to excited states.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'. © 2017 The Author(s).
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.
der, R.
1987-01-01
The various approaches to nonequilibrium statistical mechanics may be subdivided into convolution and convolutionless (time-local) ones. While the former, put forward by Zwanzig, Mori, and others, are used most commonly, the latter are less well developed, but have proven very useful in recent applications. The aim of the present series of papers is to develop the time-local picture (TLP) of nonequilibrium statistical mechanics on a new footing and to consider its physical implications for topics such as the formulation of irreversible thermodynamics. The most natural approach to TLP is seen to derive from the Fourier-Laplace transformwidetilde{C}(z)) of pertinent time correlation functions, which on the physical sheet typically displays an essential singularity at z=∞ and a number of macroscopic and microscopic poles in the lower half-plane corresponding to long- and short-lived modes, respectively, the former giving rise to the autonomous macrodynamics, whereas the latter are interpreted as doorway modes mediating the transfer of information from relevant to irrelevant channels. Possible implications of this doorway mode concept for socalled extended irreversible thermodynamics are briefly discussed. The pole structure is used for deriving new kinds of generalized Green-Kubo relations expressing macroscopic quantities, transport coefficients, e.g., by contour integrals over current-current correlation functions obeying Hamiltonian dynamics, the contour integration replacing projection. The conventional Green-Kubo relations valid for conserved quantities only are rederived for illustration. Moreover,widetilde{C}(z) may be expressed by a Laurent series expansion in positive and negative powers of z, from which a rigorous, general, and straightforward method is developed for extracting all macroscopic quantities from so-called secularly divergent expansions ofwidetilde{C}(z) as obtained from the application of conventional many-body techniques to the calculation
Perakis, Ilias; Kapetanakis, Myron; Lingos, Panagiotis; Barmparis, George; Patz, A.; Li, T.; Wang, Jigang
We study the role of spin quantum fluctuations driven by photoelectrons during 100fs photo-excitation of colossal magneto-resistive manganites in anti-ferromagnetic (AFM) charge-ordered insulating states with Jahn-Teller distortions. Our mean-field calculation of composite fermion excitations demonstrates that spin fluctuations reduce the energy gap by quasi-instantaneously deforming the AFM background, thus opening a conductive electronic pathway via FM correlation. We obtain two quasi-particle bands with distinct spin-charge dynamics and dependence on lattice distortions. To connect with fs-resolved spectroscopy experiments, we note the emergence of fs magnetization in the low-temperature magneto-optical signal, with threshold dependence on laser intensity characteristic of a photo-induced phase transition. Simultaneously, the differential reflectivity shows bi-exponential relaxation, with fs component, small at low intensity, exceeding ps component above threshold for fs AFM-to-FM switching. This suggests the emergence of a non-equilibrium metallic FM phase prior to establishment of a new lattice structure, linked with quantum magnetism via spin/charge/lattice couplings for weak magnetic fields.
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
Adib, Artur B.
In the last two decades or so, a collection of results in nonequilibrium statistical mechanics that departs from the traditional near-equilibrium framework introduced by Lars Onsager in 1931 has been derived, yielding new fundamental insights into far-from-equilibrium processes in general. Apart from offering a more quantitative statement of the second law of thermodynamics, some of these results---typified by the so-called "Jarzynski equality"---have also offered novel means of estimating equilibrium quantities from nonequilibrium processes, such as free energy differences from single-molecule "pulling" experiments. This thesis contributes to such efforts by offering three novel results in nonequilibrium statistical mechanics: (a) The entropic analog of the Jarzynski equality; (b) A methodology for estimating free energies from "clamp-and-release" nonequilibrium processes; and (c) A directly measurable symmetry relation in chemical kinetics similar to (but more general than) chemical detailed balance. These results share in common the feature of remaining valid outside Onsager's near-equilibrium regime, and bear direct applicability in protein folding kinetics as well as in single-molecule free energy estimation.
An Optimization Principle for Deriving Nonequilibrium Statistical Models of Hamiltonian Dynamics
Turkington, Bruce
2013-08-01
A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. Given a vector of resolved variables, selected to describe the macroscopic state of the system, a family of quasi-equilibrium probability densities on phase space corresponding to the resolved variables is employed as a statistical model, and the evolution of the mean resolved vector is estimated by optimizing over paths of these densities. Specifically, a cost function is constructed to quantify the lack-of-fit to the microscopic dynamics of any feasible path of densities from the statistical model; it is an ensemble-averaged, weighted, squared-norm of the residual that results from submitting the path of densities to the Liouville equation. The path that minimizes the time integral of the cost function determines the best-fit evolution of the mean resolved vector. The closed reduced equations satisfied by the optimal path are derived by Hamilton-Jacobi theory. When expressed in terms of the macroscopic variables, these equations have the generic structure of governing equations for nonequilibrium thermodynamics. In particular, the value function for the optimization principle coincides with the dissipation potential that defines the relation between thermodynamic forces and fluxes. The adjustable closure parameters in the best-fit reduced equations depend explicitly on the arbitrary weights that enter into the lack-of-fit cost function. Two particular model reductions are outlined to illustrate the general method. In each example the set of weights in the optimization principle contracts into a single effective closure parameter.
International Nuclear Information System (INIS)
Yu, J.; Sommer, W.F.; Bradbury, J.N.
1986-01-01
Microstructural evolution in metals under particle irradiation is described by a non-equilibrium statistics method. This method gives a set of equations for the evolution of bubbles and an approximate solution for a distribution function of bubble size as a function of fluence and temperature. The distribution function gives the number of bubbles of radius r at time t, N(r,t)dr, as a function of size, r/r 0 (r 0 is the radius of a bubble nucleus). It is found that N(r,t)dr increases with fluence. Also, the peak value of N(r,t)dt shifts to higher r/r 0 with increasing fluence. Nucleation depends mainly on helium concentration and defect cluster concentration while bubble growth is controlled mainly by the vacancy concentration and a fluctuation coefficient. If suitable material parameters are chosen, a reasonable distribution function for bubble size is obtained. The helium diffusion coefficient is found to be less than that for vacancies by five orders of magnitude. The fraction of helium remaining in matrix is less than 10 -2 ; the majority of the helium is associated with the bubbles
Lattice ellipsoidal statistical BGK model for thermal non-equilibrium flows
Meng, Jianping; Zhang, Yonghao; Hadjiconstantinou, Nicolas G.; Radtke, Gregg A.; Shan, Xiaowen
2013-03-01
A thermal lattice Boltzmann model is constructed on the basis of the ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK model uses a single distribution function and features an adjustable Prandtl number. Numerical simulations show that using a moderate discrete velocity set, this model can accurately recover steady and transient solutions of the ES-BGK equation in the slip-flow and early transition regimes in the small Mach number limit that is typical of microscale problems of practical interest. In the transition regime in particular, comparisons with numerical solutions of the ES-BGK model, direct Monte Carlo and low-variance deviational Monte Carlo simulations show good accuracy for values of the Knudsen number up to approximately 0.5. On the other hand, highly non-equilibrium phenomena characterized by high Mach numbers, such as viscous heating and force-driven Poiseuille flow for large values of the driving force, are more difficult to capture quantitatively in the transition regime using discretizations chosen with computational efficiency in mind such as the one used here, although improved accuracy is observed as the number of discrete velocities is increased.
Nonequilibrium statistical mechanics in the general theory of relativity. I. A general formalism
International Nuclear Information System (INIS)
Israel, W.; Kandrup, H.E.
1984-01-01
This is the first in a series of papers, the overall objective of which is the formulation of a new covariant approach to nonequilibrium statistical mechanics in classical general relativity. The objecct here is the development of a tractable theory for self-gravitating systems. It is argued that the ''state'' of an N-particle system may be characterized by an N-particle distribution function, defined in an 8N-dimensional phase space, which satisfies a collection of N conservation equations. By mapping the true physics onto a fictitious ''background'' spacetime, which may be chosen to satisfy some ''average'' field equations, one then obtains a useful covariant notion of ''evolution'' in response to a fluctuating ''gravitational force.'' For many cases of practical interest, one may suppose (i) that these fluctuating forces satisfy linear field equations and (ii) that they may be modeled by a direct interaction. In this case, one can use a relativistic projection operator formalism to derive exact closed equations for the evolution of such objects as an appropriately defined reduced one-particle distribution function. By capturing, in a natural way, the notion of a dilute gas, or impulse, approximation, one is then led to a comparatively simple equation for the one-particle distribution. If, furthermore, one treats the effects of the fluctuating forces as ''localized'' in space and time, one obtains a tractable kinetic equation which reduces, in the Newtonian limit, to the stardard Landau equation
The non-equilibrium statistical mechanics of a simple geophysical fluid dynamics model
Verkley, Wim; Severijns, Camiel
2014-05-01
Lorenz [1] has devised a dynamical system that has proved to be very useful as a benchmark system in geophysical fluid dynamics. The system in its simplest form consists of a periodic array of variables that can be associated with an atmospheric field on a latitude circle. The system is driven by a constant forcing, is damped by linear friction and has a simple advection term that causes the model to behave chaotically if the forcing is large enough. Our aim is to predict the statistics of Lorenz' model on the basis of a given average value of its total energy - obtained from a numerical integration - and the assumption of statistical stationarity. Our method is the principle of maximum entropy [2] which in this case reads: the information entropy of the system's probability density function shall be maximal under the constraints of normalization, a given value of the average total energy and statistical stationarity. Statistical stationarity is incorporated approximately by using `stationarity constraints', i.e., by requiring that the average first and possibly higher-order time-derivatives of the energy are zero in the maximization of entropy. The analysis [3] reveals that, if the first stationarity constraint is used, the resulting probability density function rather accurately reproduces the statistics of the individual variables. If the second stationarity constraint is used as well, the correlations between the variables are also reproduced quite adequately. The method can be generalized straightforwardly and holds the promise of a viable non-equilibrium statistical mechanics of the forced-dissipative systems of geophysical fluid dynamics. [1] E.N. Lorenz, 1996: Predictability - A problem partly solved, in Proc. Seminar on Predictability (ECMWF, Reading, Berkshire, UK), Vol. 1, pp. 1-18. [2] E.T. Jaynes, 2003: Probability Theory - The Logic of Science (Cambridge University Press, Cambridge). [3] W.T.M. Verkley and C.A. Severijns, 2014: The maximum entropy
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
International Nuclear Information System (INIS)
Ma, Minjie; Jalil, Mansoor Bin Abdul; Tan, Seng Gee
2013-01-01
The spin-dependent transport through a diluted magnetic semiconductor quantum dot (QD) which is coupled via magnetic tunnel junctions to two ferromagnetic leads is studied theoretically. A noncollinear system is considered, where the QD is magnetized at an arbitrary angle with respect to the leads’ magnetization. The tunneling current is calculated in the coherent regime via the Keldysh nonequilibrium Green’s function (NEGF) formalism, incorporating the electron–electron interaction in the QD. We provide the first analytical solution for the Green’s function of the noncollinear DMS quantum dot system, solved via the equation of motion method under Hartree–Fock approximation. The transport characteristics (charge and spin currents, and tunnel magnetoresistance (TMR)) are evaluated for different voltage regimes. The interplay between spin-dependent tunneling and single-charge effects results in three distinct voltage regimes in the spin and charge current characteristics. The voltage range in which the QD is singly occupied corresponds to the maximum spin current and greatest sensitivity of the spin current to the QD magnetization orientation. The QD device also shows transport features suitable for sensor applications, i.e., a large charge current coupled with a high TMR ratio. - Highlights: ► The spin polarized transport through a diluted magnetic quantum dot is studied. ► The model is based on the Green’s function and the equation of motion method.► The charge and spin currents and tunnel magnetoresistance (TMR) are investigated. ► The system is suitable for current-induced spin-transfer torque application. ► A large tunneling current and a high TMR are possible for sensor application.
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)
International Nuclear Information System (INIS)
Li, Guanchen; Al-Abbasi, Omar; Von Spakovsky, Michael R
2014-01-01
This paper outlines an atomistic-level framework for modeling the non-equilibrium behavior of chemically reactive systems. The framework called steepest- entropy-ascent quantum thermodynamics (SEA-QT) is based on the paradigm of intrinsic quantum thermodynamic (IQT), which is a theory that unifies quantum mechanics and thermodynamics into a single discipline with wide applications to the study of non-equilibrium phenomena at the atomistic level. SEA-QT is a novel approach for describing the state of chemically reactive systems as well as the kinetic and dynamic features of the reaction process without any assumptions of near-equilibrium states or weak-interactions with a reservoir or bath. Entropy generation is the basis of the dissipation which takes place internal to the system and is, thus, the driving force of the chemical reaction(s). The SEA-QT non-equilibrium model is able to provide detailed information during the reaction process, providing a picture of the changes occurring in key thermodynamic properties (e.g., the instantaneous species concentrations, entropy and entropy generation, reaction coordinate, chemical affinities, reaction rate, etc). As an illustration, the SEA-QT framework is applied to an atomistic-level chemically reactive system governed by the reaction mechanism F + H 2 ↔ FH + H
International Nuclear Information System (INIS)
Hotta, Ryuuichi; Morozumi, Takuya; Takata, Hiroyuki
2012-01-01
We develop the method analyzing particle number non-conserving phenomena with non-equilibrium quantum field-theory. In this study, we consider a CP violating model with interaction Hamiltonian that breaks particle number conservation. To derive the quantum Boltzmann equation for the particle number, we solve Schwinger-Dyson equation, which are obtained from two particle irreducible closed-time-path (2PI CTP) effective action. In this calculation, we show the contribution from interaction Hamiltonian to the time evolution of expectation value of particle number.
Nonequilibrium statistical mechanics of shear flow: invariant quantities and current relations
International Nuclear Information System (INIS)
Baule, A; Evans, R M L
2010-01-01
In modeling nonequilibrium systems one usually starts with a definition of the microscopic dynamics, e.g., in terms of transition rates, and then derives the resulting macroscopic behavior. We address the inverse question for a class of steady state systems, namely complex fluids under continuous shear flow: how does an externally imposed shear current affect the microscopic dynamics of the fluid? The answer can be formulated in the form of invariant quantities, exact relations for the transition rates in the nonequilibrium steady state, as discussed in a recent letter (Baule and Evans, 2008 Phys. Rev. Lett. 101 240601). Here, we present a more pedagogical account of the invariant quantities and the theory underlying them, known as the nonequilibrium counterpart to detailed balance (NCDB). Furthermore, we investigate the relationship between the transition rates and the shear current in the steady state. We show that a fluctuation relation of the Gallavotti–Cohen type holds for systems satisfying NCDB
Quantum statistical model for hot dense matter
International Nuclear Information System (INIS)
Rukhsana Kouser; Tasneem, G.; Saleem Shahzad, M.; Shafiq-ur-Rehman; Nasim, M.H.; Amjad Ali
2015-01-01
In solving numerous applied problems, one needs to know the equation of state, photon absorption coefficient and opacity of substances employed. We present a code for absorption coefficient and opacity calculation based on quantum statistical model. A self-consistent method for the calculation of potential is used. By solving Schrödinger equation with self-consistent potential we find energy spectrum of quantum mechanical system and corresponding wave functions. In addition we find mean occupation numbers of electron states and average charge state of the substance studied. The main processes of interaction of radiation with matter included in our opacity calculation are photon absorption in spectral lines (Bound-bound), photoionization (Bound-free), inverse bremsstrahlung (Free-free), Compton and Thomson scattering. Bound-bound line shape function has contribution from natural, Doppler, fine structure, collisional and stark broadening. To illustrate the main features of the code and its capabilities, calculation of average charge state, absorption coefficient, Rosseland and Planck mean and group opacities of aluminum and iron are presented. Results are satisfactorily compared with the published data. (authors)
Current algebra, statistical mechanics and quantum models
Vilela Mendes, R.
2017-11-01
Results obtained in the past for free boson systems at zero and nonzero temperatures are revisited to clarify the physical meaning of current algebra reducible functionals which are associated to systems with density fluctuations, leading to observable effects on phase transitions. To use current algebra as a tool for the formulation of quantum statistical mechanics amounts to the construction of unitary representations of diffeomorphism groups. Two mathematical equivalent procedures exist for this purpose. One searches for quasi-invariant measures on configuration spaces, the other for a cyclic vector in Hilbert space. Here, one argues that the second approach is closer to the physical intuition when modelling complex systems. An example of application of the current algebra methodology to the pairing phenomenon in two-dimensional fermion systems is discussed.
Directory of Open Access Journals (Sweden)
Krzysztof Jόzwikowska
2015-06-01
Full Text Available The main goal of this work is to determine a statistical non-equilibrium distribution function for the electron and holes in semiconductor heterostructures in steady-state conditions. Based on the postulates of local equilibrium, as well as on the integral form of the weighted Gyarmati’s variational principle in the force representation, using an alternative method, we have derived general expressions, which have the form of the Fermi–Dirac distribution function with four additional components. The physical interpretation of these components has been carried out in this paper. Some numerical results of a non-equilibrium distribution function for an electron in HgCdTe structures are also presented.
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.
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...
Belof, Jonathan; Orlikowski, Daniel; Wu, Christine; McLaughlin, Keith
2013-06-01
Shock and ramp compression experiments are allowing us to probe condensed matter under extreme conditions where phase transitions and other non-equilibrium aspects can now be directly observed, but first principles simulation of kinetics remains a challenge. A multi-scale approach is presented here, with non-equilibrium statistical mechanical quantities calculated by molecular dynamics (MD) and then leveraged to inform a classical nucleation and growth kinetics model at the hydrodynamic scale. Of central interest is the free energy barrier for the formation of a critical nucleus, with direct NEMD presenting the challenge of relatively long timescales necessary to resolve nucleation. Rather than attempt to resolve the time-dependent nucleation sequence directly, the methodology derived here is built upon the non-equilibrium work theorem in order to bias the formation of a critical nucleus and thus construct the nucleation and growth rates. Having determined these kinetic terms from MD, a hydrodynamics implementation of Kolmogorov-Johnson-Mehl-Avrami (KJMA) kinetics and metastabilty is applied to the dynamic compressive freezing of water and compared with recent ramp compression experiments [Dolan et al., Nature (2007)] Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the U.S. Department of Energy, National Nuclear Security Administration under Contract DE-AC52-07NA27344.
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)
Energy Technology Data Exchange (ETDEWEB)
Pokhabov, D. A., E-mail: pokhabov@isp.nsc.ru; Pogosov, A. G.; Budantsev, M. V.; Zhdanov, E. Yu.; Bakarov, A. K. [Russian Academy of Sciences, Rzhanov Institute of Semiconductor Physics, Siberian Branch (Russian Federation)
2016-08-15
The nonequilibrium state of a two-dimensional electron gas in the quantum-Hall-effect regime is studied in Hall bars equipped with additional inner contacts situated within the bar. The magnetic-field dependence of the voltage drop between different contact pairs are studied at various temperatures. It was found that the voltage between the inner and outer contacts exhibits peaks of significant amplitude in narrow magnetic-field intervals near integer filling factors. Furthermore, the magnetic-field dependence of the voltage in these intervals exhibits a hysteresis, whereas the voltage between the outer contacts remains zero in the entire magnetic-field range. The appearance of the observed voltage peaks and their hysteretic behavior can be explained by an imbalance between the chemical potentials of edge and bulk states, resulting from nonequilibrium charge redistribution between the edge and bulk states when the magnetic field sweeps under conditions of the quantum Hall effect. The results of the study significantly complement the conventional picture of the quantum Hall effect, explicitly indicating the existence of a significant imbalance at the edge of the two-dimensional electron gas: the experimentally observed difference between the electrochemical potentials of the edge and bulk exceeds the distance between Landau levels by tens of times.
Yasuda, H.; Kubis, T.; Hosako, I.; Hirakawa, K.
2012-04-01
We theoretically investigated GaN-based resonant phonon terahertz-quantum cascade laser (QCL) structures for possible high-temperature operation by using the non-equilibrium Green's function method. It was found that the GaN-based THz-QCL structures do not necessarily have a gain sufficient for lasing, even though the thermal backfilling and the thermally activated phonon scattering are effectively suppressed. The main reason for this is the broadening of the subband levels caused by a very strong interaction between electrons and longitudinal optical (LO) phonons in GaN.
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 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
Žunkovič, Bojan; Heyl, Markus; Knap, Michael; Silva, Alessandro
2018-03-01
We theoretically study the dynamics of a transverse-field Ising chain with power-law decaying interactions characterized by an exponent α , which can be experimentally realized in ion traps. We focus on two classes of emergent dynamical critical phenomena following a quantum quench from a ferromagnetic initial state: The first one manifests in the time-averaged order parameter, which vanishes at a critical transverse field. We argue that such a transition occurs only for long-range interactions α ≤2 . The second class corresponds to the emergence of time-periodic singularities in the return probability to the ground-state manifold which is obtained for all values of α and agrees with the order parameter transition for α ≤2 . We characterize how the two classes of nonequilibrium criticality correspond to each other and give a physical interpretation based on the symmetry of the time-evolved quantum states.
Levy, Tal J; Rabani, Eran
2013-04-28
We study steady state transport through a double quantum dot array using the equation-of-motion approach to the nonequilibrium Green functions formalism. This popular technique relies on uncontrolled approximations to obtain a closure for a hierarchy of equations; however, its accuracy is questioned. We focus on 4 different closures, 2 of which were previously proposed in the context of the single quantum dot system (Anderson impurity model) and were extended to the double quantum dot array, and develop 2 new closures. Results for the differential conductance are compared to those attained by a master equation approach known to be accurate for weak system-leads couplings and high temperatures. While all 4 closures provide an accurate description of the Coulomb blockade and other transport properties in the single quantum dot case, they differ in the case of the double quantum dot array, where only one of the developed closures provides satisfactory results. This is rationalized by comparing the poles of the Green functions to the exact many-particle energy differences for the isolate system. Our analysis provides means to extend the equation-of-motion technique to more elaborate models of large bridge systems with strong electronic interactions.
Schwarz, F.; Goldstein, M.; Dorda, A.; Arrigoni, E.; Weichselbaum, A.; von Delft, J.
2016-10-01
The description of interacting quantum impurity models in steady-state nonequilibrium is an open challenge for computational many-particle methods: the numerical requirement of using a finite number of lead levels and the physical requirement of describing a truly open quantum system are seemingly incompatible. One possibility to bridge this gap is the use of Lindblad-driven discretized leads (LDDL): one couples auxiliary continuous reservoirs to the discretized lead levels and represents these additional reservoirs by Lindblad terms in the Liouville equation. For quadratic models governed by Lindbladian dynamics, we present an elementary approach for obtaining correlation functions analytically. In a second part, we use this approach to explicitly discuss the conditions under which the continuum limit of the LDDL approach recovers the correct representation of thermal reservoirs. As an analytically solvable example, the nonequilibrium resonant level model is studied in greater detail. Lastly, we present ideas towards a numerical evaluation of the suggested Lindblad equation for interacting impurities based on matrix product states. In particular, we present a reformulation of the Lindblad equation, which has the useful property that the leads can be mapped onto a chain where both the Hamiltonian dynamics and the Lindblad driving are local at the same time. Moreover, we discuss the possibility to combine the Lindblad approach with a logarithmic discretization needed for the exploration of exponentially small energy scales.
Teaching at the edge of knowledge: Non-equilibrium statistical physics
Schmittmann, Beate
2007-03-01
As physicists become increasingly interested in biological problems, we frequently find ourselves confronted with complex open systems, involving many interacting constituents and characterized by non-vanishing fluxes of mass or energy. Faced with the task of predicting macroscopic behaviors from microscopic information for these non-equilibrium systems, the familiar Gibbs-Boltzmann framework fails. The development of a comprehensive theoretical characterization of non-equilibrium behavior is one of the key challenges of modern condensed matter physics. In its absence, several approaches have been developed, from master equations to thermostatted molecular dynamics, which provide key insights into the rich and often surprising phenomenology of systems far from equilibrium. In my talk, I will address some of these methods, selecting those that are most relevant for a broad range of interdisciplinary problems from biology to traffic, finance, and sociology. The ``portability'' of these methods makes them valuable for graduate students from a variety of disciplines. To illustrate how different methods can complement each other when probing a problem from, e.g., the life sciences, I will discuss some recent attempts at modeling translation, i.e., the process by which the genetic information encoded on an mRNA is translated into the corresponding protein.
DEFF Research Database (Denmark)
Chen, Jingzhe; Thygesen, Kristian S.; Jacobsen, Karsten W.
2012-01-01
We present an efficient implementation of a nonequilibrium Green's function method for self-consistent calculations of electron transport and forces in nanostructured materials. The electronic structure is described at the level of density functional theory using the projector augmented wave method...... over k points and real space makes the code highly efficient and applicable to systems containing several hundreds of atoms. The method is applied to a number of different systems, demonstrating the effects of bias and gate voltages, multiterminal setups, nonequilibrium forces, and spin transport....
Vorberger, J.; Chapman, D. A.
2018-01-01
We present a quantum theory for the dynamic structure factors in nonequilibrium, correlated, two-component systems such as plasmas or warm dense matter. The polarization function, which is needed as the input for the calculation of the structure factors, is calculated in nonequilibrium based on a perturbation expansion in the interaction strength. To make our theory applicable for x-ray scattering, a generalized Chihara decomposition for the total electron structure factor in nonequilibrium is derived. Examples are given and the influence of correlations and exchange on the structure and the x-ray-scattering spectrum are discussed for a model nonequilibrium distribution, as often encountered during laser heating of materials, as well as for two-temperature systems.
Vorberger, J; Chapman, D A
2018-01-01
We present a quantum theory for the dynamic structure factors in nonequilibrium, correlated, two-component systems such as plasmas or warm dense matter. The polarization function, which is needed as the input for the calculation of the structure factors, is calculated in nonequilibrium based on a perturbation expansion in the interaction strength. To make our theory applicable for x-ray scattering, a generalized Chihara decomposition for the total electron structure factor in nonequilibrium is derived. Examples are given and the influence of correlations and exchange on the structure and the x-ray-scattering spectrum are discussed for a model nonequilibrium distribution, as often encountered during laser heating of materials, as well as for two-temperature systems.
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.
Directory of Open Access Journals (Sweden)
E. A. Tatokchin
2017-01-01
Full Text Available Development of the modern educational technologies caused by broad introduction of comput-er testing and development of distant forms of education does necessary revision of methods of an examination of pupils. In work it was shown, need transition to mathematical criteria, exami-nations of knowledge which are deprived of subjectivity. In article the review of the problems arising at realization of this task and are offered approaches for its decision. The greatest atten-tion is paid to discussion of a problem of objective transformation of rated estimates of the ex-pert on to the scale estimates of the student. In general, the discussion this question is was con-cluded that the solution to this problem lies in the creation of specialized intellectual systems. The basis for constructing intelligent system laid the mathematical model of self-organizing nonequilibrium dissipative system, which is a group of students. This article assumes that the dissipative system is provided by the constant influx of new test items of the expert and non-equilibrium – individual psychological characteristics of students in the group. As a result, the system must self-organize themselves into stable patterns. This patern will allow for, relying on large amounts of data, get a statistically significant assessment of student. To justify the pro-posed approach in the work presents the data of the statistical analysis of the results of testing a large sample of students (> 90. Conclusions from this statistical analysis allowed to develop intelligent system statistically significant examination of student performance. It is based on data clustering algorithm (k-mean for the three key parameters. It is shown that this approach allows you to create of the dynamics and objective expertise evaluation.
Satyendranath Bose: Co-Founder of Quantum Statistics
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)
Chernyak, Vladimir Y.; Chertkov, Michael; Bierkens, Joris; Kappen, Hilbert J.
2014-01-01
In stochastic optimal control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive), for a system participating in forced and controlled Langevin dynamics. We extend the SOC problem by introducing an additional cost-of-dynamics, characterized by a vector potential. We propose derivation of the generalized gauge-invariant Hamilton-Jacobi-Bellman equation as a variation over density and current, suggest hydrodynamic interpretation and discuss examples, e.g., ergodic control of a particle-within-a-circle, illustrating non-equilibrium space-time complexity.
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
International Nuclear Information System (INIS)
Maes, Christian
2012-01-01
In contrast to the quite unique entropy concept useful for systems in (local) thermodynamic equilibrium, there is a variety of quite distinct nonequilibrium entropies, reflecting different physical points. We disentangle these entropies as they relate to heat, fluctuations, response, time asymmetry, variational principles, monotonicity, volume contraction or statistical forces. However, not all of those extensions yield state quantities as understood thermodynamically. At the end we sketch how aspects of dynamical activity can take over for obtaining an extended Clausius relation.
Craven, Galen T.; Nitzan, Abraham
2018-01-01
Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level are derived. This selective analysis is applied to examine transport properties of a nonequilibrium Brownian process that is coupled to multiple thermal sources characterized by different temperatures. Distributions, moments, and correlation functions of a free particle that occur during upside and downside events are investigated for energy activation and energy relaxation processes and also for positive and negative energy fluctuations from the average energy. The presented results are sufficiently general and can be applied without modification to the standard Brownian motion. This article focuses on the mathematical basis of this selective analysis. In subsequent articles in this series, we apply this general formalism to processes in which heat transfer between thermal reservoirs is mediated by activated rate processes that take place in a system bridging them.
A simple non-equilibrium, statistical-physics toy model of thin-film growth
International Nuclear Information System (INIS)
Ochab, Jeremi K; Nagel, Hannes; Janke, Wolfhard; Waclaw, Bartlomiej
2015-01-01
We present a simple non-equilibrium model of mass condensation with Lennard–Jones interactions between particles and the substrate. We show that when some number of particles is deposited onto the surface and the system is left to equilibrate, particles condense into an island if the density of particles becomes higher than some critical density. We illustrate this with numerically obtained phase diagrams for three-dimensional systems. We also solve a two-dimensional counterpart of this model analytically and show that not only the phase diagram but also the shape of the cross-sections of three-dimensional condensates qualitatively matches the two-dimensional predictions. Lastly, we show that when particles are being deposited with a constant rate, the system has two phases: a single condensate for low deposition rates, and multiple condensates for fast deposition. The behaviour of our model is thus similar to that of thin film growth processes, and in particular to Stranski–Krastanov growth. (paper)
Hudson, Phillip S; Woodcock, H Lee; Boresch, Stefan
2015-12-03
Carrying out free energy simulations (FES) using quantum mechanical (QM) Hamiltonians remains an attractive, albeit elusive goal. Renewed efforts in this area have focused on using "indirect" thermodynamic cycles to connect "low level" simulation results to "high level" free energies. The main obstacle to computing converged free energy results between molecular mechanical (MM) and QM (ΔA(MM→QM)), as recently demonstrated by us and others, is differences in the so-called "stiff" degrees of freedom (e.g., bond stretching) between the respective energy surfaces. Herein, we demonstrate that this problem can be efficiently circumvented using nonequilibrium work (NEW) techniques, i.e., Jarzynski's and Crooks' equations. Initial applications of computing ΔA(NEW)(MM→QM), for blocked amino acids alanine and serine as well as to generate butane's potentials of mean force via the indirect QM/MM FES method, showed marked improvement over traditional FES approaches.
Experimental statistical signature of many-body quantum interference
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.
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)
Statistical physics of black holes as quantum-mechanical systems
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...
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
The scientifiv way of thinking in statistics, statistical physics and quantum mechanics
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
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...
Stability and equilibrium in quantum statistical mechanics
International Nuclear Information System (INIS)
Kastler, Daniel.
1975-01-01
A derivation of the Gibbs Ansatz, base of the equilibrium statistical mechanics is provided from a stability requirements, in technical connection with the harmonic analysis of non-commutative dynamical systems. By the same token a relation is established between stability and the positivity of Hamiltonian in the zero temperature case [fr
The quantum theory of statistical multistep nucleus reactions
Zhivopistsev, F A
2002-01-01
The phenomenological models and quantum approaches to the description of the statistical multistep nuclear reactions are discussed. The basic advantages and deficiencies of various modifications of the quantum theory of the statistical multistep direct reactions: Feshbach-Kerman-Koonin formalism, the generalized model of the statistical multistep reactions (GMSMR) are considered in detail. The possibility of obtaining the consistent description of the experimental spectra for the reactions with nucleons is shown by the particular examples. Further improvement and development of the quantum formalism for the more complete and consecutive description of various mechanisms of the component particle formalism in the output channel, the correct of the unbound state densities of the intermediate and finite nuclei are needed for the analysis of the inclusive reactions with participation of the component particles, (and with an account of the contributions to the cross sections of the nucleus cluster and shell areas)...
Nonequilibrium carrier dynamics in self-assembled InGaAs quantum dots
International Nuclear Information System (INIS)
Wesseli, M.; Ruppert, C.; Trumm, S.; Betz, M.; Krenner, H.J.; Finley, J.J.
2006-01-01
Carrier dynamics in InGaAs/GaAs quantum dots is analyzed with highly sensitive femtosecond transmission spectroscopy. In a first step, measurements on a large ensemble of nanoislands reveal the dynamical electronic filling of quantum dots from the surrounding wetting layer. Most interestingly, we find a spin-preserving phonon mediated scattering into fully localized states within a few picoseconds. Then, individual artificial atoms are isolated with metallic shadow masks. For the first time, a single self-assembled quantum dot is addressed in an ultrafast transmission experiment. We find bleaching signals in the order of 10 -5 that arise from individual interband transitions of one quantum dot. As a result, we have developed an ultrafast optical tool for both manipulation and read-out of a single self-assembled quantum dot. (copyright 2006 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
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
Quantum statistical metastability for a finite spin
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)].
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)
Curvature, zero modes and quantum statistics
Energy Technology Data Exchange (ETDEWEB)
Calixto, M [Departamento de Matematica Aplicada y EstadIstica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de AstrofIsica de AndalucIa, Apartado Postal 3004, 18080 Granada (Spain)
2006-08-18
We explore an intriguing connection between the Fermi-Dirac and Bose-Einstein statistics and the thermal baths obtained from a vacuum radiation of coherent states of zero modes in a second quantized (many-particle) theory on the compact O(3) and noncompact O(2, 1) isometry subgroups of the de Sitter and anti-de Sitter spaces, respectively. The high frequency limit is retrieved as a (zero-curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the vacuum energy density and the cosmological constant problem. (letter to the editor)
Dynamics and statistics of unstable quantum states
International Nuclear Information System (INIS)
Sokolov, V.V.; Zelevinsky, V.G.
1989-01-01
The statistical theory of spectra formulated in terms of random matrices is extended to unstable states. The energies and widths of these states are treated as real and imaginary parts of complex eigenvalues for an effective non-hermitian hamiltonian. Eigenvalue statistics are investigated under simple assumptions. If the coupling through common decay channels is weak we obtain a Wigner distribution for the level spacings and a Porter-Thomas one for the widths, with the only exception for spacings less than widths where level repulsion fades out. Meanwhile in the complex energy plane the repulsion of eigenvalues is quadratic in accordance with the T-noninvariant character of decaying systems. In the opposite case of strong coupling with the continuum, k short-lived states are formed (k is the number of open decay channels). These states accumulate almost the whole total width, the rest of the states becoming long-lived. Such a perestroika corresponds to separation of direct processes (a nuclear analogue of Dicke coherent superradiance). At small channel number, Ericson fluctuations of the cross sections are found to be suppressed. The one-channel case is considered in detail. The joint distribution of energies and widths is obtained. The average cross sections and density of unstable states are calculated. (orig.)
Nonequilibrium Green's function theory for nonadiabatic effects in quantum electron transport
Kershaw, Vincent F.; Kosov, Daniel S.
2017-12-01
We develop nonequilibrium Green's function-based transport theory, which includes effects of nonadiabatic nuclear motion in the calculation of the electric current in molecular junctions. Our approach is based on the separation of slow and fast time scales in the equations of motion for Green's functions by means of the Wigner representation. Time derivatives with respect to central time serve as a small parameter in the perturbative expansion enabling the computation of nonadiabatic corrections to molecular Green's functions. Consequently, we produce a series of analytic expressions for non-adiabatic electronic Green's functions (up to the second order in the central time derivatives), which depend not solely on the instantaneous molecular geometry but likewise on nuclear velocities and accelerations. An extended formula for electric current is derived which accounts for the non-adiabatic corrections. This theory is concisely illustrated by the calculations on a model molecular junction.
Rodrigues, Clóves G.; Silva, Antônio A. P.; Silva, Carlos A. B.; Vasconcellos, Áurea R.; Ramos, J. Galvão; Luzzi, Roberto
2010-01-01
The nowadays notable development of all the modern technology, fundamental for the progress and well being of world society, imposes a great deal of stress in the realm of basic Physics, more precisely on Thermo-Statistics. We do face situations in electronics and optoelectronics involving physical-chemical systems far-removed-from equilibrium, where ultrafast (in pico- and femto-second scale) and non-linear processes are present. Further, we need to be aware of the rapid unfolding of nano-te...
Electron Energy Level Statistics in Graphene Quantum Dots
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
Counting statistics of many-particle quantum walks
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.
Electron systems out of equilibrium: nonequilibrium Green's function approach
Czech Academy of Sciences Publication Activity Database
Špička, Václav; Velický, Bedřich; Kalvová, Anděla
2014-01-01
Roč. 28, č. 23 (2014), "1430013-1"-"1430013-103" ISSN 0217-9792 R&D Projects: GA ČR GAP204/12/0897 Institutional support: RVO:68378271 Keywords : nonequilibrium statistical physics * transients * quantum transport the ory Subject RIV: BE - The oretical Physics Impact factor: 0.937, year: 2014
Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states
International Nuclear Information System (INIS)
Gamba, Irene M.; Tharkabhushanam, Sri Harsha
2009-01-01
We propose a new spectral Lagrangian based deterministic solver for the non-linear Boltzmann transport equation (BTE) in d-dimensions for variable hard sphere (VHS) collision kernels with conservative or non-conservative binary interactions. The method is based on symmetries of the Fourier transform of the collision integral, where the complexity in its computation is reduced to a separate integral over the unit sphere S d-1 . The conservation of moments is enforced by Lagrangian constraints. The resulting scheme, implemented in free space, is very versatile and adjusts in a very simple manner to several cases that involve energy dissipation due to local micro-reversibility (inelastic interactions) or elastic models of slowing down process. Our simulations are benchmarked with available exact self-similar solutions, exact moment equations and analytical estimates for the homogeneous Boltzmann equation, both for elastic and inelastic VHS interactions. Benchmarking of the simulations involves the selection of a time self-similar rescaling of the numerical distribution function which is performed using the continuous spectrum of the equation for Maxwell molecules as studied first in Bobylev et al. [A.V. Bobylev, C. Cercignani, G. Toscani, Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials, Journal of Statistical Physics 111 (2003) 403-417] and generalized to a wide range of related models in Bobylev et al. [A.V. Bobylev, C. Cercignani, I.M. Gamba, On the self-similar asymptotics for generalized non-linear kinetic Maxwell models, Communication in Mathematical Physics, in press. URL: ( )]. The method also produces accurate results in the case of inelastic diffusive Boltzmann equations for hard spheres (inelastic collisions under thermal bath), where overpopulated non-Gaussian exponential tails have been conjectured in computations by stochastic methods [T.V. Noije, M. Ernst, Velocity distributions in homogeneously
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.)
Machine learning Z2 quantum spin liquids with quasiparticle statistics
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.
Algebraic methods in statistical mechanics and quantum field theory
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
Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics
Energy Technology Data Exchange (ETDEWEB)
Montoya-Castillo, Andrés, E-mail: am3720@columbia.edu; Reichman, David R., E-mail: drr2103@columbia.edu [Department of Chemistry, Columbia University, New York, New York 10027 (United States)
2016-05-14
We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion to circumvent the difficulty of projected dynamics, we obtain a self-consistent equation for the memory kernel which requires only knowledge of normally evolved auxiliary kernels. To illustrate the properties of the current approach, we focus on the spin-boson model and limit our attention to the use of a simple and inexpensive quasi-classical dynamics, given by the Ehrenfest method, for the calculation of the auxiliary kernels. For the first time, we provide a detailed analysis of the dependence of the properties of the memory kernels obtained via different projection operators, namely, the thermal (Redfield-type) and population based (NIBA-type) projection operators. We further elucidate the conditions that lead to short-lived memory kernels and the regions of parameter space to which this program is best suited. Via a thorough analysis of the different closures available for the auxiliary kernels and the convergence properties of the self-consistently extracted memory kernel, we identify the mechanisms whereby the current approach leads to a significant improvement over the direct usage of standard semi- and quasi-classical dynamics.
Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics
International Nuclear Information System (INIS)
Montoya-Castillo, Andrés; Reichman, David R.
2016-01-01
We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion to circumvent the difficulty of projected dynamics, we obtain a self-consistent equation for the memory kernel which requires only knowledge of normally evolved auxiliary kernels. To illustrate the properties of the current approach, we focus on the spin-boson model and limit our attention to the use of a simple and inexpensive quasi-classical dynamics, given by the Ehrenfest method, for the calculation of the auxiliary kernels. For the first time, we provide a detailed analysis of the dependence of the properties of the memory kernels obtained via different projection operators, namely, the thermal (Redfield-type) and population based (NIBA-type) projection operators. We further elucidate the conditions that lead to short-lived memory kernels and the regions of parameter space to which this program is best suited. Via a thorough analysis of the different closures available for the auxiliary kernels and the convergence properties of the self-consistently extracted memory kernel, we identify the mechanisms whereby the current approach leads to a significant improvement over the direct usage of standard semi- and quasi-classical dynamics.
International Nuclear Information System (INIS)
Ness, H.; Dash, L. K.
2014-01-01
We study the non-equilibrium (NE) fluctuation-dissipation (FD) relations in the context of quantum thermoelectric transport through a two-terminal nanodevice in the steady-state. The FD relations for the one- and two-particle correlation functions are derived for a model of the central region consisting of a single electron level. Explicit expressions for the FD relations of the Green's functions (one-particle correlations) are provided. The FD relations for the current-current and charge-charge (two-particle) correlations are calculated numerically. We use self-consistent NE Green's functions calculations to treat the system in the absence and in the presence of interaction (electron-phonon) in the central region. We show that, for this model, there is no single universal FD theorem for the NE steady state. There are different FD relations for each different class of problems. We find that the FD relations for the one-particle correlation function are strongly dependent on both the NE conditions and the interactions, while the FD relations of the current-current correlation function are much less dependent on the interaction. The latter property suggests interesting applications for single-molecule and other nanoscale transport experiments
Greenberg, Benjamin L; Ganguly, Shreyashi; Held, Jacob T; Kramer, Nicolaas J; Mkhoyan, K Andre; Aydil, Eray S; Kortshagen, Uwe R
2015-12-09
Metal oxide semiconductor nanocrystals (NCs) exhibit localized surface plasmon resonances (LSPRs) tunable within the infrared (IR) region of the electromagnetic spectrum by vacancy or impurity doping. Although a variety of these NCs have been produced using colloidal synthesis methods, incorporation and activation of dopants in the liquid phase has often been challenging. Herein, using Al-doped ZnO (AZO) NCs as an example, we demonstrate the potential of nonthermal plasma synthesis as an alternative strategy for the production of doped metal oxide NCs. Exploiting unique, thoroughly nonequilibrium synthesis conditions, we obtain NCs in which dopants are not segregated to the NC surfaces and local doping levels are high near the NC centers. Thus, we achieve overall doping levels as high as 2 × 10(20) cm(-3) in NCs with diameters ranging from 12.6 to 3.6 nm, and for the first time experimentally demonstrate a clear quantum confinement blue shift of the LSPR energy in vacancy- and impurity-doped semiconductor NCs. We propose that doping of central cores and heavy doping of small NCs are achievable via nonthermal plasma synthesis, because chemical potential differences between dopant and host atoms-which hinder dopant incorporation in colloidal synthesis-are irrelevant when NC nucleation and growth proceed via irreversible interactions among highly reactive gas-phase ions and radicals and ligand-free NC surfaces. We explore how the distinctive nucleation and growth kinetics occurring in the plasma influences dopant distribution and activation, defect structure, and impurity phase formation.
Crossover physics in the nonequilibrium dynamics of quenched quantum impurity systems.
Vasseur, Romain; Trinh, Kien; Haas, Stephan; Saleur, Hubert
2013-06-14
A general framework is proposed to tackle analytically local quantum quenches in integrable impurity systems, combining a mapping onto a boundary problem with the form factor approach to boundary-condition-changing operators introduced by Lesage and Saleur [Phys. Rev. Lett. 80, 4370 (1998)]. We discuss how to compute exactly the following two central quantities of interest: the Loschmidt echo and the distribution of the work done during the quantum quench. Our results display an interesting crossover physics characterized by the energy scale T(b) of the impurity corresponding to the Kondo temperature. We discuss in detail the noninteracting case as a paradigm and benchmark for more complicated integrable impurity models and check our results using numerical methods.
Many-body Tunneling and Nonequilibrium Dynamics of Doublons in Strongly Correlated Quantum Dots.
Hou, WenJie; Wang, YuanDong; Wei, JianHua; Zhu, ZhenGang; Yan, YiJing
2017-05-30
Quantum tunneling dominates coherent transport at low temperatures in many systems of great interest. In this work we report a many-body tunneling (MBT), by nonperturbatively solving the Anderson multi-impurity model, and identify it a fundamental tunneling process on top of the well-acknowledged sequential tunneling and cotunneling. We show that the MBT involves the dynamics of doublons in strongly correlated systems. Proportional to the numbers of dynamical doublons, the MBT can dominate the off-resonant transport in the strongly correlated regime. A T 3/2 -dependence of the MBT current on temperature is uncovered and can be identified as a fingerprint of the MBT in experiments. We also prove that the MBT can support the coherent long-range tunneling of doublons, which is well consistent with recent experiments on ultracold atoms. As a fundamental physical process, the MBT is expected to play important roles in general quantum systems.
Thermodynamic description of non-Markovian information flux of nonequilibrium open quantum systems
Chen, Hong-Bin; Chen, Guang-Yin; Chen, Yueh-Nan
2017-12-01
One of the fundamental issues in the field of open quantum systems is the classification and quantification of non-Markovianity. In the contest of quantity-based measures of non-Markovianity, the intuition of non-Markovianity in terms of information backflow is widely discussed. However, it is not easy to characterize the information flux for a given system state and show its connection to non-Markovianity. Here, by using the concepts from thermodynamics and information theory, we discuss a potential definition of information flux of an open quantum system, valid for static environments. We present a simple protocol to show how a system attempts to share information with its environment and how it builds up system-environment correlations. We also show that the information returned from the correlations characterizes the non-Markovianity and a hierarchy of indivisibility of the system dynamics.
Definition of Nonequilibrium Entropy of General Systems
Mei, Xiaochun
1999-01-01
The definition of nonequilibrium entropy is provided for the general nonequilibrium processes by connecting thermodynamics with statistical physics, and the principle of entropy increment in the nonequilibrium processes is also proved in the paper. The result shows that the definition of nonequilibrium entropy is not unique.
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
The thermodynamic meaning of local temperature of nonequilibrium open quantum systems
Ye, LvZhou; Zheng, Xiao; Yan, YiJing; Di Ventra, Massimiliano
2016-01-01
Measuring the local temperature of nanoscale systems out of equilibrium has emerged as a new tool to study local heating effects and other local thermal properties of systems driven by external fields. Although various experimental protocols and theoretical definitions have been proposed to determine the local temperature, the thermodynamic meaning of the measured or defined quantities remains unclear. By performing analytical and numerical analysis of bias-driven quantum dot systems both in ...
Kusaba, Akira; Li, Guanchen; von Spakovsky, Michael R; Kangawa, Yoshihiro; Kakimoto, Koichi
2017-08-15
Clearly understanding elementary growth processes that depend on surface reconstruction is essential to controlling vapor-phase epitaxy more precisely. In this study, ammonia chemical adsorption on GaN(0001) reconstructed surfaces under metalorganic vapor phase epitaxy (MOVPE) conditions (3Ga-H and N ad -H + Ga-H on a 2 × 2 unit cell) is investigated using steepest-entropy-ascent quantum thermodynamics (SEAQT). SEAQT is a thermodynamic-ensemble based, first-principles framework that can predict the behavior of non-equilibrium processes, even those far from equilibrium where the state evolution is a combination of reversible and irreversible dynamics. SEAQT is an ideal choice to handle this problem on a first-principles basis since the chemical adsorption process starts from a highly non-equilibrium state. A result of the analysis shows that the probability of adsorption on 3Ga-H is significantly higher than that on N ad -H + Ga-H. Additionally, the growth temperature dependence of these adsorption probabilities and the temperature increase due to the heat of reaction is determined. The non-equilibrium thermodynamic modeling applied can lead to better control of the MOVPE process through the selection of preferable reconstructed surfaces. The modeling also demonstrates the efficacy of DFT-SEAQT coupling for determining detailed non-equilibrium process characteristics with a much smaller computational burden than would be entailed with mechanics-based, microscopic-mesoscopic approaches.
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.
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)
Is quantum theory a form of statistical mechanics?
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.
Negative values of quasidistributions and quantum wave and number statistics
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 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
Lifetime statistics of quantum chaos studied by a multiscale analysis
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.
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
DEFF Research Database (Denmark)
Jørgensen, Jacob Lykkebo
Abstract The idea of using single-molecules as components in electronic devices is fas- cinating. For this idea to come into fruition, a number of technical and theo- retical challenges must be overcome. In this PhD thesis, the electron-phonon interaction is studied for a special class of molecules......, which is characterised by destructive quantum interference. The molecules are cross-conjugated, which means that the two parts of the molecules are conjugated to a third part, but not to each other. This gives rise to an anti-resonance in the trans- mission. In the low bias and low temperature regime......-conjugated molecules. We nd that the vibrational modes that would be expected to dominate, following the propensity, rules are very weak. Instead, other modes are found to be the dominant ones. We study this phenomenon for a number of cross-conjugated molecules, and link these ndings to the anti...
International Nuclear Information System (INIS)
Ojima, Izumi
1989-01-01
With aid of the so-called dilation method, a concise formula is obtained for the entropy production in the algebraic formulation of quantum dynamical systems. In this framework, the initial ergodic state of an external force system plays a pivotal role in generating dissipativity as a conditional expectation. The physical meaning of van Hove limit is clarified through the scale-changing transformation to control transitions between microscopic and macroscopic levels. It plays a crucial role in realizing the macroscopic stationary in the presence of microscopic fluctuations as well as in the transition from non-Markovian (groupoid) dynamics to Markovian dissipative processes of state changes. The extension of the formalism to cases with spatial and internal inhomogeneity is indicated in the light of the groupoid dynamical systems and noncommutative integration theory
Nonequilibrium Phenomena in Plasmas
Sharma, A Surjalal
2005-01-01
The complexity of plasmas arises mainly from their inherent nonlinearity and far from equilibrium nature. The nonequilibrium behavior of plasmas is evident in the natural settings, for example, in the Earth's magnetosphere. Similarly, laboratory plasmas such as fusion bottles also have their fair share of complex behavior. Nonequilibrium phenomena are intimately connected with statistical dynamics and form one of the growing research areas in modern nonlinear physics. These studies encompass the ideas of self-organization, phase transition, critical phenomena, self-organized criticality and turbulence. This book presents studies of complexity in the context of nonequilibrium phenomena using theory, modeling, simulations, and experiments, both in the laboratory and in nature.
Quantum theory and statistical thermodynamics principles and worked examples
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...
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
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
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
Statistical quasi-particle theory for open quantum systems
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.
Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes
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.
International Nuclear Information System (INIS)
Hermanns, S; Bonitz, M; Balzer, K
2013-01-01
The nonequilibrium description of quantum systems requires, for more than two or three particles, the use of a reduced description to be numerically tractable. Two possible approaches are based on either reduced density matrices or nonequilibrium Green functions (NEGF). Both concepts are formulated in terms of hierarchies of coupled equations—the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for the reduced density operators and the Martin-Schwinger-hierarchy (MS) for the Green functions, respectively. In both cases, similar approximations are introduced to decouple the hierarchy, yet still many questions regarding the correspondence of both approaches remain open. Here we analyze this correspondence by studying the generalized Kadanoff–Baym ansatz (GKBA) that reduces the NEGF to a single-time theory. Starting from the BBGKY-hierarchy we present the approximations that are necessary to recover the GKBA result both, with Hartree-Fock propagators (HF-GKBA) and propagators in second Born approximation. To test the quality of the HF-GKBA, we study the dynamics of a 4-electron Hubbard nanocluster starting from a strong nonequilibrium initial state and compare to exact results and the Wang-Cassing approximation to the BBGKY hierarchy presented recently by Akbari et al. [1].
Dupoyet, B.; Fiebig, H. R.; Musgrove, D. P.
2010-01-01
We report on initial studies of a quantum field theory defined on a lattice with multi-ladder geometry and the dilation group as a local gauge symmetry. The model is relevant in the cross-disciplinary area of econophysics. A corresponding proposal by Ilinski aimed at gauge modeling in non-equilibrium pricing is implemented in a numerical simulation. We arrive at a probability distribution of relative gains which matches the high frequency historical data of the NASDAQ stock exchange index.
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.)
Agents with left and right dominant hemispheres and quantum statistics
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.
Radiation from quantum weakly dynamical horizons in loop quantum gravity.
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.
Schwabl, Franz
2006-01-01
The completely revised new edition of the classical book on Statistical Mechanics covers the basic concepts of equilibrium and non-equilibrium statistical physics. In addition to a deductive approach to equilibrium statistics and thermodynamics based on a single hypothesis - the form of the microcanonical density matrix - this book treats the most important elements of non-equilibrium phenomena. Intermediate calculations are presented in complete detail. Problems at the end of each chapter help students to consolidate their understanding of the material. Beyond the fundamentals, this text demonstrates the breadth of the field and its great variety of applications. Modern areas such as renormalization group theory, percolation, stochastic equations of motion and their applications to critical dynamics, kinetic theories, as well as fundamental considerations of irreversibility, are discussed. The text will be useful for advanced students of physics and other natural sciences; a basic knowledge of quantum mechan...
Statistical benchmarking for orthogonal electrostatic quantum dot qubit devices
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.
Quantum statistics of dense gases and nonideal plasmas
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...
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
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)
Energy flow in non-equilibrium conformal field theory
Bernard, Denis; Doyon, Benjamin
2012-09-01
We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperatures and glued together at a point contact. We prove that these systems converge towards steady states, and give a general description of such non-equilibrium steady states in terms of quantum field theory data. We compute the large deviation function, also called the full counting statistics, of energy transfer through the contact. These are universal and satisfy fluctuation relations. We provide a simple representation of these quantum fluctuations in terms of classical Poisson processes whose intensities are proportional to Boltzmann weights.
International Nuclear Information System (INIS)
Eslami, Leila; Esmaeilzadeh, Mahdi
2014-01-01
Spin-dependent electron transport in an open double quantum ring, when each ring is made up of four quantum dots and threaded by a magnetic flux, is studied. Two independent and tunable gate voltages are applied to induce Rashba spin-orbit effect in the quantum rings. Using non-equilibrium Green's function formalism, we study the effects of electron-electron interaction on spin-dependent electron transport and show that although the electron-electron interaction induces an energy gap, it has no considerable effect when the bias voltage is sufficiently high. We also show that the double quantum ring can operate as a spin-filter for both spin up and spin down electrons. The spin-polarization of transmitted electrons can be tuned from −1 (pure spin-down current) to +1 (pure spin-up current) by changing the magnetic flux and/or the gates voltage. Also, the double quantum ring can act as AND and NOR gates when the system parameters such as Rashba coefficient are properly adjusted
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
Role of quantum statistics in multi-particle decay dynamics
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.
Directory of Open Access Journals (Sweden)
V.V.Ignatyuk
2004-01-01
Full Text Available Non-Markovian kinetic equations in the second Born approximation are derived for a two-zone semiconductor excited by a short laser pulse. Both collision dynamics and running nonequilibrium correlations are taken into consideration. The energy balance and relaxation of the system to equilibrium are discussed. Results of numerical solution of the kinetic equations for carriers and phonons are presented.
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
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 some boundary value problems in quantum statistical mechanics
International Nuclear Information System (INIS)
Angelescu, N.
1978-01-01
The following two topics of equilibrium quantum statistical mechanics are discussed in this thesis: (i) the independence of the thermodynamic limit of grand-canonical pressure on the boundary conditions; (ii) the magnetic properties of free quantum gases. Problem (i) is handled with a functional integration technique. Wiener-type conditional measures are constructed for a given domain and a general class of mixed conditions on its boundary, these measures are used to write down Feynman-Kac formulae for the kernels of exp(-βH), where H is the Hamiltonian of N interacting particles in the given domain. These measures share the property that they assign the same mass as the usual Wiener measure to any set of trajectories not intersecting the boundary. Local estimates on the kernels of exp(-βH) are derived, which imply independence of the pressure on the boundary conditions in the thermodynamic limit. Problem (ii) has a historical development: since Landau's work (1930), much discussion has been devoted to the influence of the finite size on the susceptibility. In finite volume, Dirichlet boundary conditions are imposed, on the ground that they ensure gauge invariance. The thermodynamic limit of the pressure is proved, using again functional integration. The functional measure is now complex but absolutely continuous with respect to Wiener measure, so the usual local estimates hold true. The controversy in the literature was concentrated on the commutativity of the operations of H-derivation and thermodynamic limit, so the existence of this limit for the zero-field susceptibility and its surface term are proved separately, demonstrating this commutativity. The proof relies on the following result of independent interest: the perturbation theory of self-adjoint trace-class semigroups is trace-class convergent and analytic. (author)
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
International Nuclear Information System (INIS)
Horing, Norman J Morgenstern; Popov, Vyacheslav V
2006-01-01
Recent experimental observations by X.G. Peralta and S.J. Allen, et al. of dc photoconductivity resonances in steady source-drain current subject to terahertz radiation in a grid-gated double-quantum well FET suggested an association with plasmon resonances. This association was definitively confirmed for some parameter ranges in our detailed electrodynamic absorbance calculations. In this paper we propose that the reason that the dc photoconductance resonances match the plasmon resonances in semiconductors is based on a nonlinear dynamic screening mechanism. In this, we employ a shielded potential approximation that is nonlinear in the terahertz field to determine the nonequilibrium Green's function and associated density perturbation that govern the nonequilibrium dielectric polarization of the medium. This 'conditioning' of the system by the incident THz radiation results in resonant polarization response at the plasmon frequencies which, in turn, causes a sharp drop of the resistive shielded impurity scattering potentials and attendant increase of the dc source-drain current. This amounts to disabling the impurity scattering mechanism by plasmon resonant behavior in nonlinear screening
International Nuclear Information System (INIS)
Krönke, Sven; Cao, Lushuai; Schmelcher, Peter; Vendrell, Oriol
2013-01-01
We develop and apply the multi-layer multi-configuration time-dependent Hartree method for bosons, which represents an ab initio method for investigating the non-equilibrium quantum dynamics of multi-species bosonic systems. Its multi-layer feature allows for tailoring the wave function ansatz to describe intra- and inter-species correlations accurately and efficiently. To demonstrate the beneficial scaling and efficiency of the method, we explored the correlated tunneling dynamics of two species with repulsive intra- and inter-species interactions, to which a third species with vanishing intra-species interaction was weakly coupled. The population imbalances of the first two species can feature a temporal equilibration and their time evolution significantly depends on the coupling to the third species. Bosons of the first and second species exhibit a bunching tendency, whose strength can be influenced by their coupling to the third species. (paper)
DEFF Research Database (Denmark)
De Souza, Fabricio; Jauho, Antti-Pekka; Egues, J.C.
2008-01-01
Using nonequilibrium Green's functions we calculate the spin-polarized current and shot noise in a ferromagnet-quantum-dot-ferromagnet system. Both parallel (P) and antiparallel (AP) magnetic configurations are considered. Coulomb interaction and coherent spin flip (similar to a transverse magnetic...... field) are taken into account within the dot. We find that the interplay between Coulomb interaction and spin accumulation in the dot can result in a bias-dependent current polarization p. In particular, p can be suppressed in the P alignment and enhanced in the AP case depending on the bias voltage....... The coherent spin flip can also result in a switch of the current polarization from the emitter to the collector lead. Interestingly, for a particular set of parameters it is possible to have a polarized current in the collector and an unpolarized current in the emitter lead. We also found a suppression...
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.
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.
Quantum origin of the primordial fluctuation spectrum and its statistics
Landau, Susana; León, Gabriel; Sudarsky, Daniel
2013-07-01
The usual account for the origin of cosmic structure during inflation is not fully satisfactory, as it lacks a physical mechanism capable of generating the inhomogeneity and anisotropy of our Universe, from an exactly homogeneous and isotropic initial state associated with the early inflationary regime. The proposal in [A. Perez, H. Sahlmann, and D. Sudarsky, Classical Quantum Gravity 23, 2317 (2006)] considers the spontaneous dynamical collapse of the wave function as a possible answer to that problem. In this work, we review briefly the difficulties facing the standard approach, as well as the answers provided by the above proposal and explore their relevance to the investigations concerning the characterization of the primordial spectrum and other statistical aspects of the cosmic microwave background and large-scale matter distribution. We will see that the new approach leads to novel ways of considering some of the relevant questions, and, in particular, to distinct characterizations of the non-Gaussianities that might have left imprints on the available data.
Statistical mechanics view of quantum chromodynamics: Lattice gauge theory
International Nuclear Information System (INIS)
Kogut, J.B.
1984-01-01
Recent developments in lattice gauge theory are discussed from a statistial mechanics viewpoint. The basic physics problems of quantum chromodynamics (QCD) are reviewed for an audience of critical phenomena theorists. The idea of local gauge symmetry and color, the connection between statistical mechanics and field theory, asymptotic freedom and the continuum limit of lattice gauge theories, and the order parameters (confinement and chiral symmetry) of QCD are reviewed. Then recent developments in the field are discussed. These include the proof of confinement in the lattice theory, numerical evidence for confinement in the continuum limit of lattice gauge theory, and perturbative improvement programs for lattice actions. Next, we turn to the new challenges facing the subject. These include the need for a better understanding of the lattice Dirac equation and recent progress in the development of numerical methods for fermions (the pseudofermion stochastic algorithm and the microcanonical, molecular dynamics equation of motion approach). Finally, some of the applications of lattice gauge theory to QCD spectrum calculations and the thermodynamics of QCD will be discussed and a few remarks concerning future directions of the field will be made
International Nuclear Information System (INIS)
Hyldgaard, P
2012-01-01
The standard formulation of tunneling transport rests on an open-boundary modeling. There, conserving approximations to nonequilibrium Green function or quantum statistical mechanics provide consistent but computational costly approaches; alternatively, the use of density-dependent ballistic-transport calculations (e.g., Lang 1995 Phys. Rev. B 52 5335), here denoted ‘DBT’, provides computationally efficient (approximate) atomistic characterizations of the electron behavior but has until now lacked a formal justification. This paper presents an exact, variational nonequilibrium thermodynamic theory for fully interacting tunneling and provides a rigorous foundation for frozen-nuclei DBT calculations as a lowest-order approximation to an exact nonequilibrium thermodynamic density functional evaluation. The theory starts from the complete electron nonequilibrium quantum statistical mechanics and I identify the operator for the nonequilibrium Gibbs free energy which, generally, must be treated as an implicit solution of the fully interacting many-body dynamics. I demonstrate a minimal property of a functional for the nonequilibrium thermodynamic grand potential which thus uniquely identifies the solution as the exact nonequilibrium density matrix. I also show that the uniqueness-of-density proof from a closely related Lippmann-Schwinger collision density functional theory (Hyldgaard 2008 Phys. Rev. B 78 165109) makes it possible to express the variational nonequilibrium thermodynamic description as a single-particle formulation based on universal electron-density functionals; the full nonequilibrium single-particle formulation improves the DBT method, for example, by a more refined account of Gibbs free energy effects. I illustrate a formal evaluation of the zero-temperature thermodynamic grand potential value which I find is closely related to the variation in the scattering phase shifts and hence to Friedel density oscillations. This paper also discusses the
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
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.
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
Toward a Parastatistics in Quantum Nonextensive Statistical Mechanics
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.
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.)
A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.
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
International Nuclear Information System (INIS)
Haken, H.
1980-01-01
In the development of statistical mechanics we can more or less distinguish between two steps. First of all the main objective of statistical mechanics had been to give thermodynamics a solid theoretical basis starting from the microscopic world. The next step has then been performed in parallel with the development of irreversible thermodynamics dealing with processes close to thermal equilibrium. The problems dealt with here are mainly transport and relaxation processes. Over the past years it has become apparent that there is a third field, namely processes far away from thermal equilibrium. The particular interest in those processes stems from the fact that in such situations order can be generated on a macroscopic scale. The ordered states can be maintained by a flux of energy or matter through, these systems. In the realm of synergetjcs we have studied numerous examples and we now know that the occurrence of many of the ordered structures is governed by the same basic principles. (author)
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
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.
Quantum statistical mechanics of dense partially ionized hydrogen.
Dewitt, H. E.; Rogers, F. J.
1972-01-01
The theory of dense hydrogenic plasmas beginning with the two component quantum grand partition function is reviewed. It is shown that ionization equilibrium and molecular dissociation equilibrium can be treated in the same manner with proper consideration of all two-body states. A quantum perturbation expansion is used to give an accurate calculation of the equation of state of the gas for any degree of dissociation and ionization. In this theory, the effective interaction between any two charges is the dynamic screened potential obtained from the plasma dielectric function. We make the static approximation; and we carry out detailed numerical calculations with the bound and scattering states of the Debye potential, using the Beth-Uhlenbeck form of the quantum second virial coefficient. We compare our results with calculations from the Saha equation.
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....
On stability and symmetries in quantum statistical mechanics
Hoekman, Frank
1977-01-01
In deze studie wordt de aard van toestanden van systemen in de quantum statistische mechanica onderzocht vanuit het gezichtspunt van stabiliteit voor kleine storingen van de dynamica en vanuit het gezichtspunt van invariantie voor een geschikte ondergroep van de symmetrieën van de dynamica. Systemen
Counting statistics of non-markovian quantum stochastic processes
DEFF Research Database (Denmark)
Flindt, Christian; Novotny, T.; Braggio, A.
2008-01-01
We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants...
Topological and statistical properties of quantum control transition landscapes
International Nuclear Information System (INIS)
Hsieh, Michael; Wu Rebing; Rabitz, Herschel; Rosenthal, Carey
2008-01-01
A puzzle arising in the control of quantum dynamics is to explain the relative ease with which high-quality control solutions can be found in the laboratory and in simulations. The emerging explanation appears to lie in the nature of the quantum control landscape, which is an observable as a function of the control variables. This work considers the common case of the observable being the transition probability between an initial and a target state. For any controllable quantum system, this landscape contains only global maxima and minima, and no local extrema traps. The probability distribution function for the landscape value is used to calculate the relative volume of the region of the landscape corresponding to good control solutions. The topology of the global optima of the landscape is analysed and the optima are shown to have inherent robustness to variations in the controls. Although the relative landscape volume of good control solutions is found to shrink rapidly as the system Hilbert space dimension increases, the highly favourable landscape topology at and away from the global optima provides a rationale for understanding the relative ease of finding high-quality, stable quantum optimal control solutions
Important contributions of M.C. Wang and C.S. Wang Chang to non-equilibrium statistical physics
International Nuclear Information System (INIS)
Liu Jixing
2004-01-01
In the middle of the 20th century two Chinese women physicists, Ming-Chen Wang and Cheng-Shu Wang Chang made great contributions to statistical physics. The famous review article 'On the theory of the Brownian motion II' by Ming-Chen Wang and G.E. Uhlenbeck published in Rev. of Mod. Phys. in 1945 provided a complete scientific classification of stochastic processes which is still adopted by the scientific community as the standard classification. The Wang-Chang-Uhlenbeck (WCU) equation proposed jointly by C.S. Wang-Chang and Uhlenbeck became the fundamental kinetic equation for the treatment of transport properties of multi-atomic gases with internal degrees of freedom in the physics literature. These important scientific contributions are analyzed and reviewed
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
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)
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.
Gessner, Manuel; Breuer, Heinz-Peter
2013-04-01
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of complex open quantum systems, employing arguments from ensemble theory. We further generalize these results to arbitrary eigenvalue distributions, allowing a detailed comparison of typical regular and chaotic systems with the help of concepts from random matrix theory. To illustrate the physical relevance and the general applicability of our results we present a series of examples related to the fields of open quantum systems and nonequilibrium quantum thermodynamics. These include the effect of initial correlations, the average quantum dynamical maps, the generic dynamics of system-environment pure state entanglement and, finally, the equilibration of generic open and closed quantum systems.
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.
Nonequilibrium mesoscopic transport: a genealogy
International Nuclear Information System (INIS)
Das, Mukunda P; Green, Frederick
2012-01-01
Models of nonequilibrium quantum transport underpin all modern electronic devices, from the largest scales to the smallest. Past simplifications such as coarse graining and bulk self-averaging served well to understand electronic materials. Such particular notions become inapplicable at mesoscopic dimensions, edging towards the truly quantum regime. Nevertheless a unifying thread continues to run through transport physics, animating the design of small-scale electronic technology: microscopic conservation and nonequilibrium dissipation. These fundamentals are inherent in quantum transport and gain even greater and more explicit experimental meaning in the passage to atomic-sized devices. We review their genesis, their theoretical context, and their governing role in the electronic response of meso- and nanoscopic systems. (topical review)
No information flow using statistical fluctuations and quantum cryptography
Larsson, Jan-Åke
2004-04-01
The communication protocol of Home and Whitaker [Phys. Rev. A 67, 022306 (2003)] is examined in some detail, and found to work equally well using a separable state. The protocol is in fact completely classical, based on postselection of suitable experimental runs. The quantum-cryptography protocol proposed in the same publication is also examined, and this protocol uses entanglement, a strictly quantum property of the system. An individual eavesdropping attack on each qubit pair would be detected by the security test proposed in the mentioned paper. However, the key is provided by groups of qubits, and there exists a coherent attack, internal to these groups, that will go unnoticed in that security test. A modified test is proposed here that will ensure security, even against such a coherent attack.
No information flow using statistical fluctuations and quantum cryptography
International Nuclear Information System (INIS)
Larsson, Jan-Aake
2004-01-01
The communication protocol of Home and Whitaker [Phys. Rev. A 67, 022306 (2003)] is examined in some detail, and found to work equally well using a separable state. The protocol is in fact completely classical, based on postselection of suitable experimental runs. The quantum-cryptography protocol proposed in the same publication is also examined, and this protocol uses entanglement, a strictly quantum property of the system. An individual eavesdropping attack on each qubit pair would be detected by the security test proposed in the mentioned paper. However, the key is provided by groups of qubits, and there exists a coherent attack, internal to these groups, that will go unnoticed in that security test. A modified test is proposed here that will ensure security, even against such a coherent attack
Liu, Tao; Kubis, Tillmann; Jie Wang, Qi; Klimeck, Gerhard
2012-03-01
The nonequilibrium Green's function approach is applied to the design of three-well indirect pumping terahertz (THz) quantum cascade lasers (QCLs) based on a resonant phonon depopulation scheme. The effects of the anticrossing of the injector states and the dipole matrix element of the laser levels on the optical gain of THz QCLs are studied. The results show that a design that results in a more pronounced anticrossing of the injector states will achieve a higher optical gain in the indirect pumping scheme compared to the traditional resonant-tunneling injection scheme. This offers in general a more efficient coherent resonant-tunneling transport of electrons in the indirect pumping scheme. It is also shown that, for operating temperatures below 200 K and low lasing frequencies, larger dipole matrix elements, i.e., vertical optical transitions, offer a higher optical gain. In contrast, in the case of high lasing frequencies, smaller dipole matrix elements, i.e., diagonal optical transitions are better for achieving a higher optical gain.
Uchida, Satoshi; Yoshida, Taketo; Tochikubo, Fumiyoshi
2017-10-01
Plasma medicine is one of the most attractive applications using atmospheric pressure nonequilibrium plasma. With respect to direct contact of the discharge plasma with a biological membrane, reactive oxygen species play an important role in induction of medical effects. However, complicated interactions between the plasma radicals and membrane have not been understood well. In the present work, we simulated elemental processes at the first stage of physicochemical interactions between oxygen atom and phosphatidylcholine using the quantum mechanical molecular dynamics code in a general software AMBER. The change in the above processes was classified according to the incident energy of oxygen atom. At an energy of 1 eV, the abstraction of a hydrogen atom and recombination to phosphatidylcholine were simultaneously occurred in chemical attachment of incident oxygen atom. The exothermal energy of the reaction was about 80% of estimated one based on the bond energies of ethane. An oxygen atom over 10 eV separated phosphatidylcholine partially. The behaviour became increasingly similar to physical sputtering. The reaction probability of oxygen atom was remarkably high in comparison with that of hydrogen peroxide. These results suggest that we can uniformly estimate various physicochemical dynamics of reactive oxygen species against membrane lipids.
Yang, Quan; Achenie, Luke E K
2018-04-18
Ionic liquids (ILs) show brilliant performance in separating gas impurities, but few researchers have performed an in-depth exploration of the bulk and interface behavior of penetrants and ILs thoroughly. In this research, we have performed a study on both molecular dynamics (MD) simulation and quantum chemical (QC) calculation to explore the transport of acetylene and ethylene in the bulk and interface regions of 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM]-[BF4]). The diffusivity, solubility and permeability of gas molecules in the bulk were researched with MD simulation first. The subdiffusion behavior of gas molecules is induced by coupling between the motion of gas molecules and the ions, and the relaxation processes of the ions after the disturbance caused by gas molecules. Then, QC calculation was performed to explore the optical geometry of ions, ion pairs and complexes of ions and penetrants, and interaction potential for pairs and complexes. Finally, nonequilibrium MD simulation was performed to explore the interface structure and properties of the IL-gas system and gas molecule behavior in the interface region. The research results may be used in the design of IL separation media.
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�...
International Nuclear Information System (INIS)
Harbola, U.; Mukamel, S.
2008-01-01
Nonequilibrium Green's functions provide a powerful tool for computing the dynamical response and particle exchange statistics of coupled quantum systems. We formulate the theory in terms of the density matrix in Liouville space and introduce superoperator algebra that greatly simplifies the derivation and the physical interpretation of all quantities. Expressions for various observables are derived directly in real time in terms of superoperator nonequilibrium Green's functions (SNGF), rather than the artificial time-loop required in Schwinger's Hilbert-space formulation. Applications for computing interaction energies, charge densities, average currents, current induced fluorescence, electroluminescence and current fluctuation (electron counting) statistics are discussed
International Nuclear Information System (INIS)
Osborne, Tobias J.; Eisert, Jens; Verstraete, Frank
2010-01-01
We show how continuous matrix product states of quantum fields can be described in terms of the dissipative nonequilibrium dynamics of a lower-dimensional auxiliary boundary field by demonstrating that the spatial correlation functions of the bulk field correspond to the temporal statistics of the boundary field. This equivalence (1) illustrates an intimate connection between the theory of continuous quantum measurement and quantum field theory, (2) gives an explicit construction of the boundary field allowing the extension of real-space renormalization group methods to arbitrary dimensional quantum field theories without the introduction of a lattice parameter, and (3) yields a novel interpretation of recent cavity QED experiments in terms of quantum field theory, and hence paves the way toward observing genuine quantum phase transitions in such zero-dimensional driven quantum systems.
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 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.
Non-equilibrium Dynamics, Thermalization and Entropy Production
International Nuclear Information System (INIS)
Hinrichsen, Haye; Janotta, Peter; Gogolin, Christian
2011-01-01
This paper addresses fundamental aspects of statistical mechanics such as the motivation of a classical state space with spontaneous transitions, the meaning of non-equilibrium in the context of thermalization, and the justification of these concepts from the quantum-mechanical point of view. After an introductory part we focus on the problem of entropy production in non-equilibrium systems. In particular, the generally accepted formula for entropy production in the environment is analyzed from a critical perspective. It is shown that this formula is only valid in the limit of separated time scales of the system's and the environmental degrees of freedom. Finally, we present an alternative simple proof of the fluctuation theorem.
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems.
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.
Probing the statistical properties of Anderson localization with quantum emitters
DEFF Research Database (Denmark)
Smolka, Stephan; Nielsen, Henri Thyrrestrup; Sapienza, Luca
2011-01-01
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...... 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......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...
Statistical Thermodynamics and Microscale Thermophysics
Carey, Van P.
1999-08-01
Many exciting new developments in microscale engineering are based on the application of traditional principles of statistical thermodynamics. In this text Van Carey offers a modern view of thermodynamics, interweaving classical and statistical thermodynamic principles and applying them to current engineering systems. He begins with coverage of microscale energy storage mechanisms from a quantum mechanics perspective and then develops the fundamental elements of classical and statistical thermodynamics. Subsequent chapters discuss applications of equilibrium statistical thermodynamics to solid, liquid, and gas phase systems. The remainder of the book is devoted to nonequilibrium thermodynamics of transport phenomena and to nonequilibrium effects and noncontinuum behavior at the microscale. Although the text emphasizes mathematical development, Carey includes many examples and exercises to illustrate how the theoretical concepts are applied to systems of scientific and engineering interest. In the process he offers a fresh view of statistical thermodynamics for advanced undergraduate and graduate students, as well as practitioners, in mechanical, chemical, and materials engineering.
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.)
Electromagnetic phenomena in matter statistical and quantum approaches
Toptygin, Igor N
2015-01-01
Modern electrodynamics in different media is a wide branch of electrodynamics which combines the exact theory of electromagnetic fields in the presence of electric charges and currents with statistical description of these fields in gases, plasmas, liquids and solids; dielectrics, conductors and superconductors. It is widely used in physics and in other natural sciences (such as astrophysics and geophysics, biophysics, ecology and evolution of terrestrial climate), and in various technological applications (radio electronics, technology of artificial materials, laser-based technological proces
Parallelism in computations in quantum and statistical mechanics
International Nuclear Information System (INIS)
Clementi, E.; Corongiu, G.; Detrich, J.H.
1985-01-01
Often very fundamental biochemical and biophysical problems defy simulations because of limitations in today's computers. We present and discuss a distributed system composed of two IBM 4341 s and/or an IBM 4381 as front-end processors and ten FPS-164 attached array processors. This parallel system - called LCAP - has presently a peak performance of about 110 Mflops; extensions to higher performance are discussed. Presently, the system applications use a modified version of VM/SP as the operating system: description of the modifications is given. Three applications programs have been migrated from sequential to parallel: a molecular quantum mechanical, a Metropolis-Monte Carlo and a molecular dynamics program. Descriptions of the parallel codes are briefly outlined. Use of these parallel codes has already opened up new capabilities for our research. The very positive performance comparisons with today's supercomputers allow us to conclude that parallel computers and programming, of the type we have considered, represent a pragmatic answer to many computationally intensive problems. (orig.)
Modelling Thomson scattering for systems with non-equilibrium electron distributions
Directory of Open Access Journals (Sweden)
Chapman D.A.
2013-11-01
Full Text Available We investigate the effect of non-equilibrium electron distributions in the analysis of Thomson scattering for a range of conditions of interest to inertial confinement fusion experiments. Firstly, a generalised one-component model based on quantum statistical theory is given in the random phase approximation (RPA. The Chihara expression for electron-ion plasmas is then adapted to include the new non-equilibrium electron physics. The theoretical scattering spectra for both diffuse and dense plasmas in which non-equilibrium electron distributions are expected to arise are considered. We find that such distributions strongly influence the spectra and are hence an important consideration for accurately determining the plasma conditions.
Instabilities and nonequilibrium structures
International Nuclear Information System (INIS)
Tirapegui, E.; Villarroel, D.
1987-01-01
Physical systems can be studied both near to and far from equilibrium where instabilities appear. The behaviour in these two regions is reviewed in this book, from both the theoretical and application points of view. The influence of noise in these situations is an essential feature which cannot be ignored. It is therefore discussed using phenomenological and theoretical approaches for the numerous problems which still remain in the field. This volume should appeal to mathematicians and physicists interested in the areas of instability, bifurcation theory, dynamical systems, pattern formation, nonequilibrium structures and statistical mechanics. (Auth.)
International Nuclear Information System (INIS)
Frank, T.D.
2002-01-01
We study many particle systems in the context of mean field forces, concentration-dependent diffusion coefficients, generalized equilibrium distributions, and quantum statistics. Using kinetic transport theory and linear nonequilibrium thermodynamics we derive for these systems a generalized multivariate Fokker-Planck equation. It is shown that this Fokker-Planck equation describes relaxation processes, has stationary maximum entropy distributions, can have multiple stationary solutions and stationary solutions that differ from Boltzmann distributions
Quantum statistical mechanics selected works of N N Bogolubov
Bogolyubov, N N
2015-01-01
In this book we have solved the complicated problem of constructing upper bounds for many-time averages for the case of a fairly broad class of model systems with four-fermion interaction. The methods proposed in this book for solving this problem will undoubtedly find application not only for the model systems associated with the theory of superconductivity considered here. The theoretical methods developed in Chapters 1 and 2 are already applicable to a much broader class of model systems from statistical physics and the theory of elementary particles. Contents: On the Theory of Superfluidit
Non-dissipative effects in nonequilibrium systems
Maes, Christian
2018-01-01
This book introduces and discusses both the fundamental aspects and the measurability of applications of time-symmetric kinetic quantities, outlining the features that constitute the non-dissipative branch of non-equilibrium physics. These specific features of non-equilibrium dynamics have largely been ignored in standard statistical mechanics texts. This introductory-level book offers novel material that does not take the traditional line of extending standard thermodynamics to the irreversible domain. It shows that although stationary dissipation is essentially equivalent with steady non-equilibrium and ubiquitous in complex phenomena, non-equilibrium is not determined solely by the time-antisymmetric sector of energy-entropy considerations. While this should not be very surprising, this book provides timely, simple reminders of the role of time-symmetric and kinetic aspects in the construction of non-equilibrium statistical mechanics.
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)
A new quantum statistical evaluation method for time correlation functions
International Nuclear Information System (INIS)
Loss, D.; Schoeller, H.
1989-01-01
Considering a system of N identical interacting particles, which obey Fermi-Dirac or Bose-Einstein statistics, the authors derive new formulas for correlation functions of the type C(t) = i= 1 N A i (t) Σ j=1 N B j > (where B j is diagonal in the free-particle states) in the thermodynamic limit. Thereby they apply and extend a superoperator formalism, recently developed for the derivation of long-time tails in semiclassical systems. As an illustrative application, the Boltzmann equation value of the time-integrated correlation function C(t) is derived in a straight-forward manner. Due to exchange effects, the obtained t-matrix and the resulting scattering cross section, which occurs in the Boltzmann collision operator, are now functionals of the Fermi-Dirac or Bose-Einstein distribution
Non-equilibrium dynamics of one-dimensional Bose gases
International Nuclear Information System (INIS)
Langen, T.
2013-01-01
Understanding the non-equilibrium dynamics of isolated quantum many-body systems is an open problem on vastly different energy, length, and time scales. Examples range from the dynamics of the early universe and heavy-ion collisions to the subtle coherence and transport properties in condensed matter physics. However, realizations of such quantum many-body systems, which are both well isolated from the environment and accessible to experimental study are scarce. This thesis presents a series of experiments with ultracold one-dimensional Bose gases. These gases combine a nearly perfect isolation from the environment with many well-established methods to manipulate and probe their quantum states. This makes them an ideal model system to explore the physics of quantum many body systems out of equilibrium. In the experiments, a well-defined non-equilibrium state is created by splitting a single one-dimensional gas coherently into two parts. The relaxation of this state is probed using matter-wave interferometry. The Observations reveal the emergence of a prethermalized steady state which differs strongly from thermal equilibrium. Such thermal-like states had previously been predicted for a large variety of systems, but never been observed directly. Studying the relaxation process in further detail shows that the thermal correlations of the prethermalized state emerge locally in their final form and propagate through the system in a light-cone-like evolution. This provides first experimental evidence for the local relaxation conjecture, which links relaxation processes in quantum many-body systems to the propagation of correlations. Furthermore, engineering the initial state of the evolution demonstrates that the prethermalized state is described by a generalized Gibbs ensemble, an observation which substantiates the importance of this ensemble as an extension of standard statistical mechanics. Finally, an experiment is presented, where pairs of gases with an atom
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
Quantum probability, choice in large worlds, and the statistical structure of reality.
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.
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.)
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.)
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
Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions
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
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.
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.)
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)
A non-critical string approach to black holes, time and quantum dynamics
Ellis, John R.; Nanopoulos, Dimitri V.
1994-01-01
We review our approach to time and quantum dynamics based on non-critical string theory, developing its relationship to previous work on non-equilibrium quantum statistical mechanics and the microscopic arrow of time. We exhibit specific non-factorizing contributions to the {\
Non-equilibrium dog-flea model
Ackerson, Bruce J.
2017-11-01
We develop the open dog-flea model to serve as a check of proposed non-equilibrium theories of statistical mechanics. The model is developed in detail. Then it is applied to four recent models for non-equilibrium statistical mechanics. Comparison of the dog-flea solution with these different models allows checking claims and giving a concrete example of the theoretical models.
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)
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
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
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 BekensteinâHawking area law is obtained from microstates of black holes in loop quantum gravity, for arbitrary real positive values of the BarberoâImmirzi parameter (Î³. The arbitrariness of Î³ is encoded in the strength of the âbiasâ created in the horizon microstates through the coupling with the quantum geometric fields exterior to the horizon. An experimental determination of Î³ will fix this coupling, leaving out the macroscopic area of the black hole to be the only free quantity of the theory.
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
Energy Technology Data Exchange (ETDEWEB)
Okumura, M; Onishi, H; Yamada, S; Machida, M, E-mail: okumura@riken.j
2010-11-01
We study non-equilibrium properties of one-dimensional Hubbard model by the density-matrix renormalization-group method. First, we demonstrate stability of 'doublon', which characterized by double occupation on a site due to the integrability of the model. Next, we present a kind of anomalous transport caused by the doublons created under strong non-equilibrium conditions in an optical lattice system regarded as an ideal testbed to investigate fundamental properties of the Hubbard model. Finally, we give a result on development of the pair correlation function in a strong non-equilibrium condition. This can be understood as a development of coherence among many excited doublons.
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.
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.
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...
Quantum statistical effects in the mass transport of interstitial solutes in a crystalline solid
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.
Many-body problem in quantum mechanics and quantum statistical mechanics
International Nuclear Information System (INIS)
Lee, T.D.; Yang, C.N.
1983-01-01
This is a progress report on some work concerning the quantum mechanical calculation of the fugacity coefficients b/sub l/ (which correspond to the classical cluster integrals) of a Bose, a Fermi, and a Boltzmann gas at low temperatures. A binary collision expansion method is developed which allows for the systematic calculation of b/sub l/ as expansions in powers of a/λ, where a represents the parameters of the dimensions of length that characterize the low-energy two-body collision and λ is the thermal wavelength. To any power of (a/λ) the calculation of any specific b/sub l/ is reduced to a finite number of quadratures. The method, therefore, is the low-temperature counterpart of the high-temperature expansion of b/sub l/
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.)
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.
Path integral molecular dynamics for exact quantum statistics of multi-electronic-state systems.
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.
Quantum statistical model of nuclear multifragmentation in the canonical ensemble method
International Nuclear Information System (INIS)
Toneev, V.D.; Ploszajczak, M.; Parvant, A.S.; Toneev, V.D.; Parvant, A.S.
1999-01-01
A quantum statistical model of nuclear multifragmentation is proposed. The recurrence equation method used the canonical ensemble makes the model solvable and transparent to physical assumptions and allows to get results without involving the Monte Carlo technique. The model exhibits the first order phase transition. Quantum statistics effects are clearly seen on the microscopic level of occupation numbers but are almost washed out for global thermodynamic variables and the averaged observables studied. In the latter case, the recurrence relations for multiplicity distributions of both intermediate-mass and all fragments are derived and the specific changes in the shape of multiplicity distributions in the narrow region of the transition temperature is stressed. The temperature domain favorable to search for the HBT effect is noted. (authors)
Quantum statistical model of nuclear multifragmentation in the canonical ensemble method
Energy Technology Data Exchange (ETDEWEB)
Toneev, V.D.; Ploszajczak, M. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France); Parvant, A.S. [Institute of Applied Physics, Moldova Academy of Sciences, MD Moldova (Ukraine); Parvant, A.S. [Joint Institute for Nuclear Research, Bogoliubov Lab. of Theoretical Physics, Dubna (Russian Federation)
1999-07-01
A quantum statistical model of nuclear multifragmentation is proposed. The recurrence equation method used the canonical ensemble makes the model solvable and transparent to physical assumptions and allows to get results without involving the Monte Carlo technique. The model exhibits the first order phase transition. Quantum statistics effects are clearly seen on the microscopic level of occupation numbers but are almost washed out for global thermodynamic variables and the averaged observables studied. In the latter case, the recurrence relations for multiplicity distributions of both intermediate-mass and all fragments are derived and the specific changes in the shape of multiplicity distributions in the narrow region of the transition temperature is stressed. The temperature domain favorable to search for the HBT effect is noted. (authors)
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.
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.
Quantum Statistics: Is there an effective fermion repulsion or boson attraction?
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.
Rheology via nonequilibrium molecular dynamics
International Nuclear Information System (INIS)
Hoover, W.G.
1982-10-01
The equilibrium molecular dynamics formulated by Newton, Lagrange, and Hamilton has been modified in order to simulate rheologial molecular flows with fast computers. This modified Nonequilibrium Molecular Dynamics (NEMD) has been applied to fluid and solid deformations, under both homogeneous and shock conditions, as well as to the transport of heat. The irreversible heating associated with dissipation could be controlled by carrying out isothermal NEMD calculations. The new isothermal NEMD equations of motion are consistent with Gauss' 1829 Least-Constraint principle as well as certain microscopic equilibrium and nonequilibrium statistical formulations due to Gibbs and Boltzmann. Application of isothermal NEMD revealed high-frequency and high-strain-rate behavior for simple fluids which resembled the behavior of polymer solutions and melts at lower frequencies and strain rates. For solids NEMD produces plastic flows consistent with experimental observations at much lower strain rates. The new nonequilibrium methods also suggest novel formulations of thermodynamics in nonequilibrium systems and shed light on the failure of the Principle of Material Frame Indifference
Computer simulation of nonequilibrium processes
International Nuclear Information System (INIS)
Wallace, D.C.
1985-07-01
The underlying concepts of nonequilibrium statistical mechanics, and of irreversible thermodynamics, will be described. The question at hand is then, how are these concepts to be realize in computer simulations of many-particle systems. The answer will be given for dissipative deformation processes in solids, on three hierarchical levels: heterogeneous plastic flow, dislocation dynamics, an molecular dynamics. Aplication to the shock process will be discussed
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)
Higher-Order Statistical Correlations and Mutual Information Among Particles in a Quantum Well
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.
Asenov, Asen; Brown, A. R.; Slavcheva, G.; Davies, J. H.
2000-01-01
voltage only single solution of the nonlinear Poisson equation is sufficient to extract the current with satisfactory accuracy. A pilot version of a hydrodynamic 'atomistic' simulator has been developed in order to study the effect of the nonequilibrium, non local transport in decanano MOSFETs on the random dopant induced current fluctuations. For the first time we have also applied the density gradient approach in 3D to investigate the effect of the quantum confinement on the threshold voltage fluctuations. The developed 'atomistic' simulation techniques have been applied to study various fluctuation resistant MOSFET architectures including epitaxial and delta doped devices.
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...
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.
Quantum statistics and squeezing for a microwave-driven interacting magnon system.
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.
Non-Equilibrium Liouville and Wigner Equations: Moment Methods and Long-Time Approximations
Directory of Open Access Journals (Sweden)
Ramon F. Álvarez-Estrada
2014-03-01
Full Text Available We treat the non-equilibrium evolution of an open one-particle statistical system, subject to a potential and to an external “heat bath” (hb with negligible dissipation. For the classical equilibrium Boltzmann distribution, Wc,eq, a non-equilibrium three-term hierarchy for moments fulfills Hermiticity, which allows one to justify an approximate long-time thermalization. That gives partial dynamical support to Boltzmann’s Wc,eq, out of the set of classical stationary distributions, Wc;st, also investigated here, for which neither Hermiticity nor that thermalization hold, in general. For closed classical many-particle systems without hb (by using Wc,eq, the long-time approximate thermalization for three-term hierarchies is justified and yields an approximate Lyapunov function and an arrow of time. The largest part of the work treats an open quantum one-particle system through the non-equilibrium Wigner function, W. Weq for a repulsive finite square well is reported. W’s (< 0 in various cases are assumed to be quasi-definite functionals regarding their dependences on momentum (q. That yields orthogonal polynomials, HQ,n(q, for Weq (and for stationary Wst, non-equilibrium moments, Wn, of W and hierarchies. For the first excited state of the harmonic oscillator, its stationary Wst is a quasi-definite functional, and the orthogonal polynomials and three-term hierarchy are studied. In general, the non-equilibrium quantum hierarchies (associated with Weq for the Wn’s are not three-term ones. As an illustration, we outline a non-equilibrium four-term hierarchy and its solution in terms of generalized operator continued fractions. Such structures also allow one to formulate long-time approximations, but make it more difficult to justify thermalization. For large thermal and de Broglie wavelengths, the dominant Weq and a non-equilibrium equation for W are reported: the non-equilibrium hierarchy could plausibly be a three-term one and possibly not
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.
Quantum Statistics of the Toda Oscillator in the Wigner Function Formalism
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.
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.
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.
International Nuclear Information System (INIS)
Gaidash, A A; Egorov, V I; Gleim, A V
2014-01-01
Quantum cryptography in theory allows distributing secure keys between two users so that any performed eavesdropping attempt would be immediately discovered. However, in practice an eavesdropper can obtain key information from multi-photon states when attenuated laser radiation is used as a source. In order to overcome this possibility, it is generally suggested to implement special cryptographic protocols, like decoy states or SARG04. We present an alternative method based on monitoring photon number statistics after detection. This method can therefore be used with any existing protocol
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
Information Graph Flow: A Geometric Approximation of Quantum and Statistical Systems
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.
Thermodynamics of ideal quantum gas with fractional statistics in D dimensions.
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.
Kadanoff-Baym Approach to Thermalization of Quantum Fields
International Nuclear Information System (INIS)
Nishiyama, Akihiro; Hatta, Yoshitaka
2013-01-01
Numerical results of nonequilibrium field theory are shown for O(N) sealer model in 2+1 dimensions with longitudinal expansion. We adopt Next-to-Leading Order of 1/N expansion of self energy with background classical fields to cover all of time evolution of instability. We show differences between quantum dynamics and classical statistical approximation in strongly coupled regimes. As a result we show that we can achieve Boltzmann tail of the final distribution function only in quantum dynamics
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)
A modern course in statistical physics
Reichl, Linda E
2016-01-01
"A Modern Course in Statistical Physics" is a textbook that illustrates the foundations of equilibrium and non-equilibrium statistical physics, and the universal nature of thermodynamic processes, from the point of view of contemporary research problems. The book treats such diverse topics as the microscopic theory of critical phenomena, superfluid dynamics, quantum conductance, light scattering, transport processes, and dissipative structures, all in the framework of the foundations of statistical physics and thermodynamics. It shows the quantum origins of problems in classical statistical physics. One focus of the book is fluctuations that occur due to the discrete nature of matter, a topic of growing importance for nanometer scale physics and biophysics. Another focus concerns classical and quantum phase transitions, in both monatomic and mixed particle systems. This fourth edition extends the range of topics considered to include, for example, entropic forces, electrochemical processes in biological syste...
Introduction to the nonequilibrium functional renormalization group
International Nuclear Information System (INIS)
Berges, J.; Mesterházy, D.
2012-01-01
In these lectures we introduce the functional renormalization group out of equilibrium. While in thermal equilibrium typically a Euclidean formulation is adequate, nonequilibrium properties require real-time descriptions. For quantum systems specified by a given density matrix at initial time, a generating functional for real-time correlation functions can be written down using the Schwinger-Keldysh closed time path. This can be used to construct a nonequilibrium functional renormalization group along similar lines as for Euclidean field theories in thermal equilibrium. Important differences include the absence of a fluctuation-dissipation relation for general out-of-equilibrium situations. The nonequilibrium renormalization group takes on a particularly simple form at a fixed point, where the corresponding scale-invariant system becomes independent of the details of the initial density matrix. We discuss some basic examples, for which we derive a hierarchy of fixed point solutions with increasing complexity from vacuum and thermal equilibrium to nonequilibrium. The latter solutions are then associated to the phenomenon of turbulence in quantum field theory.
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.
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.
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.
Nonequilibrium molecular dynamics theory, algorithms and applications
Todd, Billy D
2017-01-01
Written by two specialists with over twenty-five years of experience in the field, this valuable text presents a wide range of topics within the growing field of nonequilibrium molecular dynamics (NEMD). It introduces theories which are fundamental to the field - namely, nonequilibrium statistical mechanics and nonequilibrium thermodynamics - and provides state-of-the-art algorithms and advice for designing reliable NEMD code, as well as examining applications for both atomic and molecular fluids. It discusses homogenous and inhomogenous flows and pays considerable attention to highly confined fluids, such as nanofluidics. In addition to statistical mechanics and thermodynamics, the book covers the themes of temperature and thermodynamic fluxes and their computation, the theory and algorithms for homogenous shear and elongational flows, response theory and its applications, heat and mass transport algorithms, applications in molecular rheology, highly confined fluids (nanofluidics), the phenomenon of slip and...
Quantum 1/f noise in non-degerate semiconductors and emission statistics of alpha particles
International Nuclear Information System (INIS)
Kousik, G.S.
1985-01-01
Charged particle scattering is accompanied by the emission of soft photons. Handel's theory of 1/f noise, based on the infrared divergent coupling of the system to the electromagnetic field or other elementary excitations, states that the current associated with a beam of scattered particles will exhibit 1/f noise. The fraction of the particles scattered with an energy loss epsilon to soft photon emission is proportional to 1/epsilon and herein lies the origin of the quantum theory of 1/f noise. The 1/f noise caused by mobility fluctuations in semiconductors is related to the scattering cross section fluctuation given by Handel's theory, through the relaxation time. Chapters Two through Five of this dissertation presents the results of the detailed calculation of mobility fluctuation 1/f noise and Hooge parameter in nondegenerate semiconductors. Numerical results are given for silicon and gallium arsenide. Data obtained from extensive measurements on counting techniques for alpha-particles radioactive decay from a source containing 94 Pu 239 , 95 Am 241 and 96 Cm 244 are presented in Chapters Six and Seven of this dissertation. These data show that the statistics are non-Poissonian for large counting times (of the order of 1000 minutes) contrary to the popular belief that alpha-decay is an example of Poissonian statistics. Measurements of the Allan variance indicated the presence of a slow Lorentzian flicker noise and 1/f noise and the magnitude of the noise for large counting times is considerably larger than that predicted by Poissonian statistics
Coons, Marc P.; Herbert, John M.
2018-06-01
Widely used continuum solvation models for electronic structure calculations, including popular polarizable continuum models (PCMs), usually assume that the continuum environment is isotropic and characterized by a scalar dielectric constant, ɛ. This assumption is invalid at a liquid/vapor interface or any other anisotropic solvation environment. To address such scenarios, we introduce a more general formalism based on solution of Poisson's equation for a spatially varying dielectric function, ɛ(r). Inspired by nonequilibrium versions of PCMs, we develop a similar formalism within the context of Poisson's equation that includes the out-of-equilibrium dielectric response that accompanies a sudden change in the electron density of the solute, such as that which occurs in a vertical ionization process. A multigrid solver for Poisson's equation is developed to accommodate the large spatial grids necessary to discretize the three-dimensional electron density. We apply this methodology to compute vertical ionization energies (VIEs) of various solutes at the air/water interface and compare them to VIEs computed in bulk water, finding only very small differences between the two environments. VIEs computed using approximately two solvation shells of explicit water molecules are in excellent agreement with experiment for F-(aq), Cl-(aq), neat liquid water, and the hydrated electron, although errors for Li+(aq) and Na+(aq) are somewhat larger. Nonequilibrium corrections modify VIEs by up to 1.2 eV, relative to models based only on the static dielectric constant, and are therefore essential to obtain agreement with experiment. Given that the experiments (liquid microjet photoelectron spectroscopy) may be more sensitive to solutes situated at the air/water interface as compared to those in bulk water, our calculations provide some confidence that these experiments can indeed be interpreted as measurements of VIEs in bulk water.
Physics colloquium: Single-electron counting in quantum metrology and in statistical mechanics
Geneva University
2011-01-01
GENEVA UNIVERSITY Ecole de physique Département de physique nucléaire et corspusculaire 24, quai Ernest-Ansermet 1211 Genève 4 Tél.: (022) 379 62 73 Fax: (022) 379 69 92olé Lundi 17 octobre 2011 17h00 - Ecole de Physique, Auditoire Stueckelberg PHYSICS COLLOQUIUM « Single-electron counting in quantum metrology and in statistical mechanics » Prof. Jukka Pekola Low Temperature Laboratory, Aalto University Helsinki, Finland First I discuss the basics of single-electron tunneling and its potential applications in metrology. My main focus is in developing an accurate source of single-electron current for the realization of the unit ampere. I discuss the principle and the present status of the so-called single- electron turnstile. Investigation of errors in transporting electrons one by one has revealed a wealth of observations on fundamental phenomena in mesoscopic superconductivity, including individual Andreev...
Quantum-like microeconomics: Statistical model of distribution of investments and production
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.
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.
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.).
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)
Non-equilibrium thermodynamics and physical kinetics
Bikkin, Halid
2014-01-01
This graduate textbook covers contemporary directions of non-equilibrium statistical mechanics as well as classical methods of kinetics. With one of the main propositions being to avoid terms such as "obviously" and "it is easy to show", this treatise is an easy-to-read introduction into this traditional, yet vibrant field.
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.
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.
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
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.
Quantum statistical description of transport of the quasi-particles in optic fibers
International Nuclear Information System (INIS)
Rasulova, M.Yu.; Hassan, T.; Mohamed Ridza bin Wahiddin; Umarov, B.
2006-12-01
On the basis of BBGKY hierarchy of quantum kinetic equations the quasi-quantum analogue of the linearized wave equation for one, two quasi-particles in optic fiber is obtained. The method which enables to obtain the quasi-quantum analogue of wave equations for any number of quasi- particles in fiber is suggested. (author)
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
Non-Equilibrium Thermodynamics in Multiphase Flows
Mauri, Roberto
2013-01-01
Non-equilibrium thermodynamics is a general framework that allows the macroscopic description of irreversible processes. This book introduces non-equilibrium thermodynamics and its applications to the rheology of multiphase flows. The subject is relevant to graduate students in chemical and mechanical engineering, physics and material science. This book is divided into two parts. The first part presents the theory of non-equilibrium thermodynamics, reviewing its essential features and showing, when possible, some applications. The second part of this book deals with how the general theory can be applied to model multiphase flows and, in particular, how to determine their constitutive relations. Each chapter contains problems at the end, the solutions of which are given at the end of the book. No prior knowledge of statistical mechanics is required; the necessary prerequisites are elements of transport phenomena and on thermodynamics. “The style of the book is mathematical, but nonetheless it remains very re...
Time Dependent Hartree Fock Equation: Gateway to Nonequilibrium Plasmas
International Nuclear Information System (INIS)
Dufty, James W.
2007-01-01
This is the Final Technical Report for DE-FG02-2ER54677 award 'Time Dependent Hartree Fock Equation - Gateway to Nonequilibrium Plasmas'. Research has focused on the nonequilibrium dynamics of electrons in the presence of ions, both via basic quantum theory and via semi-classical molecular dynamics (MD) simulation. In addition, fundamental notions of dissipative dynamics have been explored for models of grains and dust, and for scalar fields (temperature) in turbulent edge plasmas. The specific topics addressed were Quantum Kinetic Theory for Metallic Clusters, Semi-classical MD Simulation of Plasmas , and Effects of Dissipative Dynamics.
Kusaba, Akira; Li, Guanchen; von Spakovsky, Michael R.; Kangawa, Yoshihiro; Kakimoto, Koichi
2017-01-01
Clearly understanding elementary growth processes that depend on surface reconstruction is essential to controlling vapor-phase epitaxy more precisely. In this study, ammonia chemical adsorption on GaN(0001) reconstructed surfaces under metalorganic vapor phase epitaxy (MOVPE) conditions (3Ga-H and Nad-H + Ga-H on a 2 × 2 unit cell) is investigated using steepest-entropy-ascent quantum thermodynamics (SEAQT). SEAQT is a thermodynamic-ensemble based, first-principles framework that can predict...
Hayslett, H T
1991-01-01
Statistics covers the basic principles of Statistics. The book starts by tackling the importance and the two kinds of statistics; the presentation of sample data; the definition, illustration and explanation of several measures of location; and the measures of variation. The text then discusses elementary probability, the normal distribution and the normal approximation to the binomial. Testing of statistical hypotheses and tests of hypotheses about the theoretical proportion of successes in a binomial population and about the theoretical mean of a normal population are explained. The text the
Fractional statistics and quantum scaling properties of the integrable Penson-Kolb-Hubbard chain
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
Full counting statistics in a serially coupled double quantum dot system with spin-orbit coupling
Wang, Qiang; Xue, Hai-Bin; Xie, Hai-Qing
2018-04-01
We study the full counting statistics of electron transport through a serially coupled double quantum dot (QD) system with spin-orbit coupling (SOC) weakly coupled to two electrodes. We demonstrate that the spin polarizations of the source and drain electrodes determine whether the shot noise maintains super-Poissonian distribution, and whether the sign transitions of the skewness from positive to negative values and of the kurtosis from negative to positive values take place. In particular, the interplay between the spin polarizations of the source and drain electrodes and the magnitude of the external magnetic field, can give rise to a gate-voltage-tunable strong negative differential conductance (NDC) and the shot noise in this NDC region is significantly enhanced. Importantly, for a given SOC parameter, the obvious variation of the high-order current cumulants as a function of the energy-level detuning in a certain range, especially the dip position of the Fano factor of the skewness can be used to qualitatively extract the information about the magnitude of the SOC.
Rate of tunneling nonequilibrium quasiparticles in superconducting qubits
International Nuclear Information System (INIS)
Ansari, Mohammad H
2015-01-01
In superconducting qubits the lifetime of quantum states cannot be prolonged arbitrarily by decreasing temperature. At low temperature quasiparticles tunneling between the electromagnetic environment and superconducting islands takes the condensate state out of equilibrium due to charge imbalance. We obtain the tunneling rate from a phenomenological model of non-equilibrium, where nonequilibrium quasiparticle tunnelling stimulates a temperature-dependent chemical potential shift in the superconductor. As a result we obtain a non-monotonic behavior for relaxation rate as a function of temperature. Depending on the fabrication parameters for some qubits, the lowest tunneling rate of nonequilibrium quasiparticles can take place only near the onset temperature below which nonequilibrium quasiparticles dominate over equilibrium one. Our theory also indicates that such tunnelings can influence the probability of transitions in qubits through a coupling to the zero-point energy of phase fluctuations. (paper)
Nonequilibrium thermodynamics of nucleation
Schweizer, M.; Sagis, L.M.C.
2014-01-01
We present a novel approach to nucleation processes based on the GENERIC framework (general equation for the nonequilibrium reversible-irreversible coupling). Solely based on the GENERIC structure of time-evolution equations and thermodynamic consistency arguments of exchange processes between a
Links to sources of cancer-related statistics, including the Surveillance, Epidemiology and End Results (SEER) Program, SEER-Medicare datasets, cancer survivor prevalence data, and the Cancer Trends Progress Report.
The non-equilibrium Green's function method for nanoscale device simulation
Pourfath, Mahdi
2014-01-01
For modeling the transport of carriers in nanoscale devices, a Green-function formalism is the most accurate approach. Due to the complexity of the formalism, one should have a deep understanding of the underlying principles and use smart approximations and numerical methods for solving the kinetic equations at a reasonable computational time. In this book the required concepts from quantum and statistical mechanics and numerical methods for calculating Green functions are presented. The Green function is studied in detail for systems both under equilibrium and under nonequilibrium conditions. Because the formalism enables rigorous modeling of different scattering mechanisms in terms of self-energies, but an exact evaluation of self-energies for realistic systems is not possible, their approximation and inclusion in the quantum kinetic equations of the Green functions are elaborated. All the elements of the kinetic equations, which are the device Hamiltonian, contact self-energies, and scattering self-energie...
Askerov, Bahram M
2010-01-01
This book deals with theoretical thermodynamics and the statistical physics of electron and particle gases. While treating the laws of thermodynamics from both classical and quantum theoretical viewpoints, it posits that the basis of the statistical theory of macroscopic properties of a system is the microcanonical distribution of isolated systems, from which all canonical distributions stem. To calculate the free energy, the Gibbs method is applied to ideal and non-ideal gases, and also to a crystalline solid. Considerable attention is paid to the Fermi-Dirac and Bose-Einstein quantum statistics and its application to different quantum gases, and electron gas in both metals and semiconductors is considered in a nonequilibrium state. A separate chapter treats the statistical theory of thermodynamic properties of an electron gas in a quantizing magnetic field.
Nonlinear dynamics of non-equilibrium holes in p-type modulation-doped GaInNAs/GaAs quantum wells
Directory of Open Access Journals (Sweden)
Amann Andreas
2011-01-01
Full Text Available Abstract Nonlinear charge transport parallel to the layers of p-modulation-doped GaInNAs/GaAs quantum wells (QWs is studied both theoretically and experimentally. Experimental results show that at low temperature, T = 13 K, the presence of an applied electric field of about 6 kV/cm leads to the heating of the high mobility holes in the GaInNAs QWs, and their real-space transfer (RST into the low-mobility GaAs barriers. This results in a negative differential mobility and self-generated oscillatory instabilities in the RST regime. We developed an analytical model based upon the coupled nonlinear dynamics of the real-space hole transfer and of the interface potential barrier controlled by space-charge in the doped GaAs layer. Our simulation results predict dc bias-dependent self-generated current oscillations with frequencies in the high microwave range.
International Nuclear Information System (INIS)
2005-01-01
For the years 2004 and 2005 the figures shown in the tables of Energy Review are partly preliminary. The annual statistics published in Energy Review are presented in more detail in a publication called Energy Statistics that comes out yearly. Energy Statistics also includes historical time-series over a longer period of time (see e.g. Energy Statistics, Statistics Finland, Helsinki 2004.) The applied energy units and conversion coefficients are shown in the back cover of the Review. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in GDP, energy consumption and electricity consumption, Carbon dioxide emissions from fossile fuels use, Coal consumption, Consumption of natural gas, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices in heat production, Fuel prices in electricity production, Price of electricity by type of consumer, Average monthly spot prices at the Nord pool power exchange, Total energy consumption by source and CO 2 -emissions, Supplies and total consumption of electricity GWh, Energy imports by country of origin in January-June 2003, Energy exports by recipient country in January-June 2003, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Price of natural gas by type of consumer, Price of electricity by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Energy taxes, precautionary stock fees and oil pollution fees
Statistical Exploration of Electronic Structure of Molecules from Quantum Monte-Carlo Simulations
Energy Technology Data Exchange (ETDEWEB)
Prabhat, Mr; Zubarev, Dmitry; Lester, Jr., William A.
2010-12-22
In this report, we present results from analysis of Quantum Monte Carlo (QMC) simulation data with the goal of determining internal structure of a 3N-dimensional phase space of an N-electron molecule. We are interested in mining the simulation data for patterns that might be indicative of the bond rearrangement as molecules change electronic states. We examined simulation output that tracks the positions of two coupled electrons in the singlet and triplet states of an H2 molecule. The electrons trace out a trajectory, which was analyzed with a number of statistical techniques. This project was intended to address the following scientific questions: (1) Do high-dimensional phase spaces characterizing electronic structure of molecules tend to cluster in any natural way? Do we see a change in clustering patterns as we explore different electronic states of the same molecule? (2) Since it is hard to understand the high-dimensional space of trajectories, can we project these trajectories to a lower dimensional subspace to gain a better understanding of patterns? (3) Do trajectories inherently lie in a lower-dimensional manifold? Can we recover that manifold? After extensive statistical analysis, we are now in a better position to respond to these questions. (1) We definitely see clustering patterns, and differences between the H2 and H2tri datasets. These are revealed by the pamk method in a fairly reliable manner and can potentially be used to distinguish bonded and non-bonded systems and get insight into the nature of bonding. (2) Projecting to a lower dimensional subspace ({approx}4-5) using PCA or Kernel PCA reveals interesting patterns in the distribution of scalar values, which can be related to the existing descriptors of electronic structure of molecules. Also, these results can be immediately used to develop robust tools for analysis of noisy data obtained during QMC simulations (3) All dimensionality reduction and estimation techniques that we tried seem to
International Nuclear Information System (INIS)
2001-01-01
For the year 2000, part of the figures shown in the tables of the Energy Review are preliminary or estimated. The annual statistics of the Energy Review appear in more detail from the publication Energiatilastot - Energy Statistics issued annually, which also includes historical time series over a longer period (see e.g. Energiatilastot 1999, Statistics Finland, Helsinki 2000, ISSN 0785-3165). The inside of the Review's back cover shows the energy units and the conversion coefficients used for them. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in the volume of GNP and energy consumption, Changes in the volume of GNP and electricity, Coal consumption, Natural gas consumption, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices for heat production, Fuel prices for electricity production, Carbon dioxide emissions from the use of fossil fuels, Total energy consumption by source and CO 2 -emissions, Electricity supply, Energy imports by country of origin in 2000, Energy exports by recipient country in 2000, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Average electricity price by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Energy taxes and precautionary stock fees on oil products
International Nuclear Information System (INIS)
2000-01-01
For the year 1999 and 2000, part of the figures shown in the tables of the Energy Review are preliminary or estimated. The annual statistics of the Energy Review appear in more detail from the publication Energiatilastot - Energy Statistics issued annually, which also includes historical time series over a longer period (see e.g., Energiatilastot 1998, Statistics Finland, Helsinki 1999, ISSN 0785-3165). The inside of the Review's back cover shows the energy units and the conversion coefficients used for them. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in the volume of GNP and energy consumption, Changes in the volume of GNP and electricity, Coal consumption, Natural gas consumption, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices for heat production, Fuel prices for electricity production, Carbon dioxide emissions, Total energy consumption by source and CO 2 -emissions, Electricity supply, Energy imports by country of origin in January-March 2000, Energy exports by recipient country in January-March 2000, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Average electricity price by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Energy taxes and precautionary stock fees on oil products
International Nuclear Information System (INIS)
1999-01-01
For the year 1998 and the year 1999, part of the figures shown in the tables of the Energy Review are preliminary or estimated. The annual statistics of the Energy Review appear in more detail from the publication Energiatilastot - Energy Statistics issued annually, which also includes historical time series over a longer period (see e.g. Energiatilastot 1998, Statistics Finland, Helsinki 1999, ISSN 0785-3165). The inside of the Review's back cover shows the energy units and the conversion coefficients used for them. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in the volume of GNP and energy consumption, Changes in the volume of GNP and electricity, Coal consumption, Natural gas consumption, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices for heat production, Fuel prices for electricity production, Carbon dioxide emissions, Total energy consumption by source and CO 2 -emissions, Electricity supply, Energy imports by country of origin in January-June 1999, Energy exports by recipient country in January-June 1999, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Average electricity price by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Energy taxes and precautionary stock fees on oil products
Thermalization and prethermalization in isolated quantum systems: a theoretical overview
Mori, Takashi; Ikeda, Tatsuhiko N.; Kaminishi, Eriko; Ueda, Masahito
2018-06-01
The approach to thermal equilibrium, or thermalization, in isolated quantum systems is among the most fundamental problems in statistical physics. Recent theoretical studies have revealed that thermalization in isolated quantum systems has several remarkable features, which emerge from quantum entanglement and are quite distinct from those in classical systems. Experimentally, well isolated and highly controllable ultracold quantum gases offer an ideal testbed to study the nonequilibrium dynamics in isolated quantum systems, promoting intensive recent theoretical endeavors on this fundamental subject. Besides thermalization, many isolated quantum systems show intriguing behavior in relaxation processes, especially prethermalization. Prethermalization occurs when there is a clear separation of relevant time scales and has several different physical origins depending on individual systems. In this review, we overview theoretical approaches to the problems of thermalization and prethermalization.
International Nuclear Information System (INIS)
2003-01-01
For the year 2002, part of the figures shown in the tables of the Energy Review are partly preliminary. The annual statistics of the Energy Review also includes historical time-series over a longer period (see e.g. Energiatilastot 2001, Statistics Finland, Helsinki 2002). The applied energy units and conversion coefficients are shown in the inside back cover of the Review. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in GDP, energy consumption and electricity consumption, Carbon dioxide emissions from fossile fuels use, Coal consumption, Consumption of natural gas, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices in heat production, Fuel prices in electricity production, Price of electricity by type of consumer, Average monthly spot prices at the Nord pool power exchange, Total energy consumption by source and CO 2 -emissions, Supply and total consumption of electricity GWh, Energy imports by country of origin in January-June 2003, Energy exports by recipient country in January-June 2003, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Price of natural gas by type of consumer, Price of electricity by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Excise taxes, precautionary stock fees on oil pollution fees on energy products
International Nuclear Information System (INIS)
2004-01-01
For the year 2003 and 2004, the figures shown in the tables of the Energy Review are partly preliminary. The annual statistics of the Energy Review also includes historical time-series over a longer period (see e.g. Energiatilastot, Statistics Finland, Helsinki 2003, ISSN 0785-3165). The applied energy units and conversion coefficients are shown in the inside back cover of the Review. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in GDP, energy consumption and electricity consumption, Carbon dioxide emissions from fossile fuels use, Coal consumption, Consumption of natural gas, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices in heat production, Fuel prices in electricity production, Price of electricity by type of consumer, Average monthly spot prices at the Nord pool power exchange, Total energy consumption by source and CO 2 -emissions, Supplies and total consumption of electricity GWh, Energy imports by country of origin in January-March 2004, Energy exports by recipient country in January-March 2004, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Price of natural gas by type of consumer, Price of electricity by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Excise taxes, precautionary stock fees on oil pollution fees
International Nuclear Information System (INIS)
2000-01-01
For the year 1999 and 2000, part of the figures shown in the tables of the Energy Review are preliminary or estimated. The annual statistics of the Energy also includes historical time series over a longer period (see e.g., Energiatilastot 1999, Statistics Finland, Helsinki 2000, ISSN 0785-3165). The inside of the Review's back cover shows the energy units and the conversion coefficients used for them. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in the volume of GNP and energy consumption, Changes in the volume of GNP and electricity, Coal consumption, Natural gas consumption, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices for heat production, Fuel prices for electricity production, Carbon dioxide emissions, Total energy consumption by source and CO 2 -emissions, Electricity supply, Energy imports by country of origin in January-June 2000, Energy exports by recipient country in January-June 2000, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Average electricity price by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Energy taxes and precautionary stock fees on oil products
Phase locking and quantum statistics in a parametrically driven nonlinear resonator
Hovsepyan, G. H.; Shahinyan, A. R.; Chew, Lock Yue; Kryuchkyan, G. Yu.
2016-01-01
We discuss phase-locking phenomena at low-level of quanta for parametrically driven nonlinear Kerr resonator (PDNR) in strong quantum regime. Oscillatory mode of PDNR is created in the process of a degenerate down-conversion of photons under interaction with a train of external Gaussian pulses. We calculate the Wigner functions of cavity mode showing two-fold symmetry in phase space and analyse formation of phase-locked states in the regular as well as the quantum chaotic regime.
Decoherence and thermalization of a pure quantum state in quantum field theory.
Giraud, Alexandre; Serreau, Julien
2010-06-11
We study the real-time evolution of a self-interacting O(N) scalar field initially prepared in a pure, coherent quantum state. We present a complete solution of the nonequilibrium quantum dynamics from a 1/N expansion of the two-particle-irreducible effective action at next-to-leading order, which includes scattering and memory effects. We demonstrate that, restricting one's attention (or ability to measure) to a subset of the infinite hierarchy of correlation functions, one observes an effective loss of purity or coherence and, on longer time scales, thermalization. We point out that the physics of decoherence is well described by classical statistical field theory.
Quantum-Classical Correspondence Principle for Work Distributions
Directory of Open Access Journals (Sweden)
Christopher Jarzynski
2015-09-01
Full Text Available For closed quantum systems driven away from equilibrium, work is often defined in terms of projective measurements of initial and final energies. This definition leads to statistical distributions of work that satisfy nonequilibrium work and fluctuation relations. While this two-point measurement definition of quantum work can be justified heuristically by appeal to the first law of thermodynamics, its relationship to the classical definition of work has not been carefully examined. In this paper, we employ semiclassical methods, combined with numerical simulations of a driven quartic oscillator, to study the correspondence between classical and quantal definitions of work in systems with 1 degree of freedom. We find that a semiclassical work distribution, built from classical trajectories that connect the initial and final energies, provides an excellent approximation to the quantum work distribution when the trajectories are assigned suitable phases and are allowed to interfere. Neglecting the interferences between trajectories reduces the distribution to that of the corresponding classical process. Hence, in the semiclassical limit, the quantum work distribution converges to the classical distribution, decorated by a quantum interference pattern. We also derive the form of the quantum work distribution at the boundary between classically allowed and forbidden regions, where this distribution tunnels into the forbidden region. Our results clarify how the correspondence principle applies in the context of quantum and classical work distributions and contribute to the understanding of work and nonequilibrium work relations in the quantum regime.
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)
Non-equilibrium dynamics from RPMD and CMD.
Welsch, Ralph; Song, Kai; Shi, Qiang; Althorpe, Stuart C; Miller, Thomas F
2016-11-28
We investigate the calculation of approximate non-equilibrium quantum time correlation functions (TCFs) using two popular path-integral-based molecular dynamics methods, ring-polymer molecular dynamics (RPMD) and centroid molecular dynamics (CMD). It is shown that for the cases of a sudden vertical excitation and an initial momentum impulse, both RPMD and CMD yield non-equilibrium TCFs for linear operators that are exact for high temperatures, in the t = 0 limit, and for harmonic potentials; the subset of these conditions that are preserved for non-equilibrium TCFs of non-linear operators is also discussed. Furthermore, it is shown that for these non-equilibrium initial conditions, both methods retain the connection to Matsubara dynamics that has previously been established for equilibrium initial conditions. Comparison of non-equilibrium TCFs from RPMD and CMD to Matsubara dynamics at short times reveals the orders in time to which the methods agree. Specifically, for the position-autocorrelation function associated with sudden vertical excitation, RPMD and CMD agree with Matsubara dynamics up to O(t 4 ) and O(t 1 ), respectively; for the position-autocorrelation function associated with an initial momentum impulse, RPMD and CMD agree with Matsubara dynamics up to O(t 5 ) and O(t 2 ), respectively. Numerical tests using model potentials for a wide range of non-equilibrium initial conditions show that RPMD and CMD yield non-equilibrium TCFs with an accuracy that is comparable to that for equilibrium TCFs. RPMD is also used to investigate excited-state proton transfer in a system-bath model, and it is compared to numerically exact calculations performed using a recently developed version of the Liouville space hierarchical equation of motion approach; again, similar accuracy is observed for non-equilibrium and equilibrium initial conditions.
Non-equilibrium thermionic electron emission for metals at high temperatures
Domenech-Garret, J. L.; Tierno, S. P.; Conde, L.
2015-08-01
Stationary thermionic electron emission currents from heated metals are compared against an analytical expression derived using a non-equilibrium quantum kappa energy distribution for the electrons. The latter depends on the temperature decreasing parameter κ ( T ) , which decreases with increasing temperature and can be estimated from raw experimental data and characterizes the departure of the electron energy spectrum from equilibrium Fermi-Dirac statistics. The calculations accurately predict the measured thermionic emission currents for both high and moderate temperature ranges. The Richardson-Dushman law governs electron emission for large values of kappa or equivalently, moderate metal temperatures. The high energy tail in the electron energy distribution function that develops at higher temperatures or lower kappa values increases the emission currents well over the predictions of the classical expression. This also permits the quantitative estimation of the departure of the metal electrons from the equilibrium Fermi-Dirac statistics.
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)
Efficiency bounds for nonequilibrium heat engines
International Nuclear Information System (INIS)
Mehta, Pankaj; Polkovnikov, Anatoli
2013-01-01
We analyze the efficiency of thermal engines (either quantum or classical) working with a single heat reservoir like an atmosphere. The engine first gets an energy intake, which can be done in an arbitrary nonequilibrium way e.g. combustion of fuel. Then the engine performs the work and returns to the initial state. We distinguish two general classes of engines where the working body first equilibrates within itself and then performs the work (ergodic engine) or when it performs the work before equilibrating (non-ergodic engine). We show that in both cases the second law of thermodynamics limits their efficiency. For ergodic engines we find a rigorous upper bound for the efficiency, which is strictly smaller than the equivalent Carnot efficiency. I.e. the Carnot efficiency can be never achieved in single reservoir heat engines. For non-ergodic engines the efficiency can be higher and can exceed the equilibrium Carnot bound. By extending the fundamental thermodynamic relation to nonequilibrium processes, we find a rigorous thermodynamic bound for the efficiency of both ergodic and non-ergodic engines and show that it is given by the relative entropy of the nonequilibrium and initial equilibrium distributions. These results suggest a new general strategy for designing more efficient engines. We illustrate our ideas by using simple examples. -- Highlights: ► Derived efficiency bounds for heat engines working with a single reservoir. ► Analyzed both ergodic and non-ergodic engines. ► Showed that non-ergodic engines can be more efficient. ► Extended fundamental thermodynamic relation to arbitrary nonequilibrium processes
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...
Borelli, M. E. S.; Kleinert, H.; Schakel, Adriaan M. J.
2000-03-01
The effect of quantum fluctuations on a nearly flat, nonrelativistic two-dimensional membrane with extrinsic curvature stiffness and tension is investigated. The renormalization group analysis is carried out in first-order perturbative theory. In contrast to thermal fluctuations, which soften the membrane at large scales and turn it into a crumpled surface, quantum fluctuations are found to stiffen the membrane, so that it exhibits a Hausdorff dimension equal to two. The large-scale behavior of the membrane is further studied at finite temperature, where a nontrivial fixed point is found, signaling a crumpling transition.
A consistent description of kinetics and hydrodynamics of quantum Bose-systems
Directory of Open Access Journals (Sweden)
P.A.Hlushak
2004-01-01
Full Text Available A consistent approach to the description of kinetics and hydrodynamics of many-Boson systems is proposed. The generalized transport equations for strongly and weakly nonequilibrium Bose systems are obtained. Here we use the method of nonequilibrium statistical operator by D.N. Zubarev. New equations for the time distribution function of the quantum Bose system with a separate contribution from both the kinetic and potential energies of particle interactions are obtained. The generalized transport coefficients are determined accounting for the consistent description of kinetic and hydrodynamic processes.
International Nuclear Information System (INIS)
Trovato, M.; Reggiani, L.
2011-01-01
By introducing a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is asserted as fundamental principle of quantum statistical mechanics. Accordingly, we develop a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theoretical formalism is formulated in both thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of (ℎ/2π) 2 . In particular, by using an arbitrary number of moments, we prove that (1) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives, both of the numerical density n and of the effective temperature T; (2) the results available from the literature in the framework of both a quantum Boltzmann gas and a degenerate quantum Fermi gas are recovered as a particular case; (3) the statistics for the quantum Fermi and Bose gases at different levels of degeneracy are explicitly incorporated; (4) a set of relevant applications admitting exact analytical equations are explicitly given and discussed; (5) the quantum maximum entropy principle keeps full validity in the classical limit, when (ℎ/2π)→0.
3. International Conference on Quantum Electrodynamics and Statistical Physics. Book of abstracts
International Nuclear Information System (INIS)
2011-01-01
The conference deals with the up-to-data problems of quantum field theory and elementary particle theory, QED processes at high energy, cosmology, theory of irreversible processes, nonlinear dynamics and chaos, phase transition and diffusion processes in condensed matter and gases.
On quantum statistics for ensembles with a finite number of particles
International Nuclear Information System (INIS)
Trifonov, Evgenii D
2011-01-01
The well-known Bose-Einstein and Fermi-Dirac quantum distributions can be considered as stationary solutions of kinetic equations for the mean occupation numbers in an ideal gas of an arbitrary finite number of identical particles. (methodological notes)
Nonequilibrium effects in Isoscaling
International Nuclear Information System (INIS)
Dorso, C. O.; Lopez, J. A.
2007-01-01
In this work we study within a simple model different properties of the system that allow us to understand the properties of the isoscaling observable. We first show that isoscaling is a general property of fragmenting systems. We show this by using a simple generalized percolation model. We show that the usual isoscaling property can be obtained in the case of bond percolation in bichromatic lattices with any regular topology. In this case the probabilities of each color (isospin) are independent. We then explore the effect of introducing 'non-equilibrium' effects
Non-equilibrium thermodynamics
De Groot, Sybren Ruurds
1984-01-01
The study of thermodynamics is especially timely today, as its concepts are being applied to problems in biology, biochemistry, electrochemistry, and engineering. This book treats irreversible processes and phenomena - non-equilibrium thermodynamics.S. R. de Groot and P. Mazur, Professors of Theoretical Physics, present a comprehensive and insightful survey of the foundations of the field, providing the only complete discussion of the fluctuating linear theory of irreversible thermodynamics. The application covers a wide range of topics: the theory of diffusion and heat conduction, fluid dyn
The nonequilibrium molecular dynamics
International Nuclear Information System (INIS)
Hoover, W.G.
1992-03-01
MOLECULAR DYNAMICS has been generalized in order to simulate a variety of NONEQUILIBRIUM systems. This generalization has been achieved by adopting microscopic mechanical definitions of macroscopic thermodynamic and hydrodynamic variables, such as temperature and stress. Some of the problems already treated include rapid plastic deformation, intense heat conduction, strong shockwaves simulation, and far-from-equilibrium phase transformations. Continuing advances in technique and in the modeling of interatomic forces, coupled with qualitative improvements in computer hardware, are enabling such simulations to approximate real-world microscale and nanoscale experiments
Nonequilibrium thermodynamics and fluctuation relations for small systems
International Nuclear Information System (INIS)
Cao Liang; Ke Pu; Qiao Li-Yan; Zheng Zhi-Gang
2014-01-01
In this review, we give a retrospect of the recent progress in nonequilibrium statistical mechanics and thermodynamics in small dynamical systems. For systems with only a few number of particles, fluctuations and nonlinearity become significant and contribute to the nonequilibrium behaviors of the systems, hence the statistical properties and thermodynamics should be carefully studied. We review recent developments of this topic by starting from the Gallavotti—Cohen fluctuation theorem, and then to the Evans—Searles transient fluctuation theorem, Jarzynski free-energy equality, and the Crooks fluctuation relation. We also investigate the nonequilibrium free energy theorem for trajectories involving changes of the heat bath temperature and propose a generalized free-energy relation. It should be noticed that the non-Markovian property of the heat bath may lead to the violation of the free-energy relation. (topical review - statistical physics and complex systems)
Bose, Deepak
2012-01-01
The design of entry vehicles requires predictions of aerothermal environment during the hypersonic phase of their flight trajectories. These predictions are made using computational fluid dynamics (CFD) codes that often rely on physics and chemistry models of nonequilibrium processes. The primary processes of interest are gas phase chemistry, internal energy relaxation, electronic excitation, nonequilibrium emission and absorption of radiation, and gas-surface interaction leading to surface recession and catalytic recombination. NASAs Hypersonics Project is advancing the state-of-the-art in modeling of nonequilibrium phenomena by making detailed spectroscopic measurements in shock tube and arcjets, using ab-initio quantum mechanical techniques develop fundamental chemistry and spectroscopic databases, making fundamental measurements of finite-rate gas surface interactions, implementing of detailed mechanisms in the state-of-the-art CFD codes, The development of new models is based on validation with relevant experiments. We will present the latest developments and a roadmap for the technical areas mentioned above
Exact infinite-time statistics of the Loschmidt echo for a quantum quench.
Campos Venuti, Lorenzo; Jacobson, N Tobias; Santra, Siddhartha; Zanardi, Paolo
2011-07-01
The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this Letter we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench. In the thermodynamic limit the logarithm of the Loschmidt echo becomes normally distributed, whereas for small quenches in the opposite, quasicritical regime, the distribution function acquires a universal double-peaked form indicating poor equilibration. These findings, obtained by a central limit theorem-type result, extend to completely general models in the small-quench regime.
International Nuclear Information System (INIS)
Horing, Norman J Morgenstern; Glasser, M Lawrence; Dong Bing
2006-01-01
We carry out a theoretical analysis of quantum well electron dynamics in a parallel magnetic field of arbitrary strength, for a narrow quantum well. An explicit analytical closed-form solution is obtained for the retarded Green's function for Landau-quantized electrons in skipping states of motion between the narrow well walls, effectively involving in-plane translational motion, and hybridized with the zero-field lowest subband energy eigenstate. The dispersion relation for electron eigenstates is examined, and we find a plethora of such discrete Landau-quantized modes coupled to the subband state. In the weak field limit, we determine low magnetic field corrections to the lowest subband state energy associated with close-packing (phase averaging) of the Landau levels in the skipping states. At higher fields the discrete energy levels of the well lie between adjacent Landau levels, but they are not equally spaced, albeit undamped. Furthermore, we also examine the associated thermodynamic Green's function for Landau-quantized electrons in a thin quantum well in a parallel magnetic field and construct the (grand) thermodynamic potential (logarithm of the grand partition function) determining the statistical thermodynamics of the system
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)
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.
Quantum conductance in silicon quantum wires
Bagraev, N T; Klyachkin, L E; Malyarenko, A M; Gehlhoff, W; Ivanov, V K; Shelykh, I A
2002-01-01
The results of investigations of electron and hole quantum conductance staircase in silicon quantum wires are presented. The characteristics of self-ordering quantum wells of n- and p-types, which from on the silicon (100) surface in the nonequilibrium boron diffusion process, are analyzed. The results of investigations of the quantum conductance as the function of temperature, carrier concentration and modulation degree of silicon quantum wires are given. It is found out, that the quantum conductance of the one-dimensional channels is observed, for the first time, at an elevated temperature (T >= 77 K)
On Nonextensive Statistics, Chaos and Fractal Strings
Castro, C
2004-01-01
Motivated by the growing evidence of universality and chaos in QFT and string theory, we study the Tsallis non-extensive statistics ( with a non-additive $ q$-entropy ) of an ensemble of fractal strings and branes of different dimensionalities. Non-equilibrium systems with complex dynamics in stationary states may exhibit large fluctuations of intensive quantities which are described in terms of generalized statistics. Tsallis statistics is a particular representative of such class. The non-extensive entropy and probability distribution of a canonical ensemble of fractal strings and branes is studied in terms of their dimensional spectrum which leads to a natural upper cutoff in energy and establishes a direct correlation among dimensions, energy and temperature. The absolute zero temperature ( Kelvin ) corresponds to zero dimensions (energy ) and an infinite temperature corresponds to infinite dimensions. In the concluding remarks some applications of fractal statistics, quasi-particles, knot theory, quantum...
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.
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.
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.
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)
Al-Khalili, Jim
2003-01-01
In this lively look at quantum science, a physicist takes you on an entertaining and enlightening journey through the basics of subatomic physics. Along the way, he examines the paradox of quantum mechanics--beautifully mathematical in theory but confoundingly unpredictable in the real world. Marvel at the Dual Slit experiment as a tiny atom passes through two separate openings at the same time. Ponder the peculiar communication of quantum particles, which can remain in touch no matter how far apart. Join the genius jewel thief as he carries out a quantum measurement on a diamond without ever touching the object in question. Baffle yourself with the bizzareness of quantum tunneling, the equivalent of traveling partway up a hill, only to disappear then reappear traveling down the opposite side. With its clean, colorful layout and conversational tone, this text will hook you into the conundrum that is quantum mechanics.
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
Bahauddin, Shah Mohammad; Mehedi Faruk, Mir
2016-09-01
From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases, trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in d = 3 and d = 2. But more importantly we found that, the virial coefficients of Bose and Fermi gases become identical (except the second virial coefficient, where the sign is different) when the gases are trapped under harmonic potential in d = 1. This result suggests the equivalence between Bose and Fermi gases established in d = 1 (J. Stat. Phys. DOI 10.1007/s10955-015-1344-4). Also, it is found that the virial coefficients of two-dimensional free Bose (Fermi) gas are equal to the virial coefficients of one-dimensional harmonically trapped Bose (Fermi) gas.
International Nuclear Information System (INIS)
Bahauddin, Shah Mohammad; Faruk, Mir Mehedi
2016-01-01
From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases, trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in d = 3 and d = 2. But more importantly we found that, the virial coefficients of Bose and Fermi gases become identical (except the second virial coefficient, where the sign is different) when the gases are trapped under harmonic potential in d = 1. This result suggests the equivalence between Bose and Fermi gases established in d = 1 (J. Stat. Phys. DOI 10.1007/s10955-015-1344-4). Also, it is found that the virial coefficients of two-dimensional free Bose (Fermi) gas are equal to the virial coefficients of one-dimensional harmonically trapped Bose (Fermi) gas. (paper)
Spin-Wave Wave Function for Quantum Spin Models : Condensed Matter and Statistical Physics
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...
Linewidth statistics of single InGaAs quantum dot photolumincescence lines
DEFF Research Database (Denmark)
Leosson, Kristjan; Jensen, Jacob Riis; Hvam, Jørn Märcher
2000-01-01
We have used photoluminescence spectroscopy with high spatial and spectral resolution to measure the linewidths of single emission lines from In0.5Ga0.5As/GaAs self-assembled quantum dots. At 10 K, we find a broad, asymmetric distribution of linewidths with a maximum at 50 mu eV. The distribution......-dot luminescence lines depends only weakly on temperature up to 50 K, showing a broadening of 0.4 mu eV/K. Above 50 K, a thermally activated behavior of the linewidth is observed. This temperature dependence is consistent with the discrete energy level structure of the dots....
Blinking in quantum dots: The origin of the grey state and power law statistics
Ye, Mao; Searson, Peter C.
2011-09-01
Quantum dot (QD) blinking is characterized by switching between an “on” state and an “off” state, and a power-law distribution of on and off times with exponents from 1.0 to 2.0. The origin of blinking behavior in QDs, however, has remained a mystery. Here we describe an energy-band model for QDs that captures the full range of blinking behavior reported in the literature and provides new insight into features such as the gray state, the power-law distribution of on and off times, and the power-law exponents.
Quantum statistics of ideal parafermi gases III: The Slater quasi-determinant
International Nuclear Information System (INIS)
Rachidi, M.; Zerouaoui, J.; Saidi, E.H.
1995-09-01
The wave function ψ (1,2,...,N) of a gas of N identical two-dimensional exotic particles of spin 1/M (mod 1), M = 2,3,4,... is constructed. It is shown that ψ (1,2,...,N) obeys a generalized Pauli exclusion principle according to which no more than (M - 1) identical particles of spin 1/M (mod 1) can live in the same quantum state. The Fermi nilpotency and the Bose condensation are recovered as special cases. Examples are given. (author). 9 refs
Path integrals in quantum mechanics, statistics, polymer physics, and financial markets
Kleinert, Hagen
2009-01-01
This is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's time-sliced formula to include singular attractive 1/r- and 1/r2-potentials. The second is a new nonholonomic mapping principle carrying p
Quantum statistics of ideal parafermi gases III: The Slater quasi-determinant
Energy Technology Data Exchange (ETDEWEB)
Rachidi, M; Zerouaoui, J [Faculte de Sciences, Rabat (Morocco). Section de Physique de Hautes Energies (LMPHE); Saidi, E H [International Centre for Theoretical Physics, Trieste (Italy)
1995-09-01
The wave function {psi} (1,2,...,N) of a gas of N identical two-dimensional exotic particles of spin 1/M (mod 1), M = 2,3,4,... is constructed. It is shown that {psi} (1,2,...,N) obeys a generalized Pauli exclusion principle according to which no more than (M - 1) identical particles of spin 1/M (mod 1) can live in the same quantum state. The Fermi nilpotency and the Bose condensation are recovered as special cases. Examples are given. (author). 9 refs.
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
Directory of Open Access Journals (Sweden)
Katalin Martinás
2007-02-01
Full Text Available A microeconomic, agent based framework to dynamic economics is formulated in a materialist approach. An axiomatic foundation of a non-equilibrium microeconomics is outlined. Economic activity is modelled as transformation and transport of commodities (materials owned by the agents. Rate of transformations (production intensity, and the rate of transport (trade are defined by the agents. Economic decision rules are derived from the observed economic behaviour. The non-linear equations are solved numerically for a model economy. Numerical solutions for simple model economies suggest that the some of the results of general equilibrium economics are consequences only of the equilibrium hypothesis. We show that perfect competition of selfish agents does not guarantee the stability of economic equilibrium, but cooperativity is needed, too.
Excess Entropy Production in Quantum System: Quantum Master Equation Approach
Nakajima, Satoshi; Tokura, Yasuhiro
2017-12-01
For open systems described by the quantum master equation (QME), we investigate the excess entropy production under quasistatic operations between nonequilibrium steady states. The average entropy production is composed of the time integral of the instantaneous steady entropy production rate and the excess entropy production. We propose to define average entropy production rate using the average energy and particle currents, which are calculated by using the full counting statistics with QME. The excess entropy production is given by a line integral in the control parameter space and its integrand is called the Berry-Sinitsyn-Nemenman (BSN) vector. In the weakly nonequilibrium regime, we show that BSN vector is described by ln \\breve{ρ }_0 and ρ _0 where ρ _0 is the instantaneous steady state of the QME and \\breve{ρ }_0 is that of the QME which is given by reversing the sign of the Lamb shift term. If the system Hamiltonian is non-degenerate or the Lamb shift term is negligible, the excess entropy production approximately reduces to the difference between the von Neumann entropies of the system. Additionally, we point out that the expression of the entropy production obtained in the classical Markov jump process is different from our result and show that these are approximately equivalent only in the weakly nonequilibrium regime.
Nonlinear and Nonequilibrium Spin Injection in Magnetic Tunneling Junctions
Guo, Hong
2007-03-01
Quantitative analysis of charge and spin quantum transport in spintronic devices requires an atomistic first principles approach that can handle nonlinear and nonequilibrium transport conditions. We have developed an approach for this purpose based on real space density functional theory (DFT) carried out within the Keldysh nonequilibrium Green's function formalism (NEGF). We report theoretical analysis of nonlinear and nonequilibrium spin injection and quantum transport in Fe/MgO/Fe trilayer structures as a function of external bias voltage. Devices with well relaxed atomic structures and with FeO oxidization layers are investigated as a function of external bias voltage. We also report calculations of nonequilibrium spin injection into molecular layers and graphene. Comparisons to experimental data will be presented. Work in collaborations with: Derek Waldron, Vladimir Timochevski (McGill University); Ke Xia (Institute of Physics, Chinese Academy of Science, Beijing, China); Eric Zhu, Jian Wang (University of Hong Kong); Paul Haney, and Allan MacDonald (University of Texas at Austin).
Nonequilibrium localization and the interplay between disorder and interactions
International Nuclear Information System (INIS)
Mascarenhas, Eduardo; Bragança, Helena; Aguiar, M C O; França Santos, M; Drumond, R
2016-01-01
We study the nonequilibrium interplay between disorder and interactions in a closed quantum system. We base our analysis on the notion of dynamical state-space localization, calculated via the Loschmidt echo. Although real-space and state-space localization are independent concepts in general, we show that both perspectives may be directly connected through a specific choice of initial states, namely, maximally localized states (ML-states). We show numerically that in the noninteracting case the average echo is found to be monotonically increasing with increasing disorder; these results are in agreement with an analytical evaluation in the single particle case in which the echo is found to be inversely proportional to the localization length. We also show that for interacting systems, the length scale under which equilibration may occur is upper bounded and such bound is smaller the greater the average echo of ML-states. When disorder and interactions, both being localization mechanisms, are simultaneously at play the echo features a non-monotonic behaviour indicating a non-trivial interplay of the two processes. This interplay induces delocalization of the dynamics which is accompanied by delocalization in real-space. This non-monotonic behaviour is also present in the effective integrability which we show by evaluating the gap statistics. (paper)
Nonequilibrium localization and the interplay between disorder and interactions.
Mascarenhas, Eduardo; Bragança, Helena; Drumond, R; Aguiar, M C O; França Santos, M
2016-05-18
We study the nonequilibrium interplay between disorder and interactions in a closed quantum system. We base our analysis on the notion of dynamical state-space localization, calculated via the Loschmidt echo. Although real-space and state-space localization are independent concepts in general, we show that both perspectives may be directly connected through a specific choice of initial states, namely, maximally localized states (ML-states). We show numerically that in the noninteracting case the average echo is found to be monotonically increasing with increasing disorder; these results are in agreement with an analytical evaluation in the single particle case in which the echo is found to be inversely proportional to the localization length. We also show that for interacting systems, the length scale under which equilibration may occur is upper bounded and such bound is smaller the greater the average echo of ML-states. When disorder and interactions, both being localization mechanisms, are simultaneously at play the echo features a non-monotonic behaviour indicating a non-trivial interplay of the two processes. This interplay induces delocalization of the dynamics which is accompanied by delocalization in real-space. This non-monotonic behaviour is also present in the effective integrability which we show by evaluating the gap statistics.
Non-equilibrium reactive flux: A unified framework for slow and fast reaction kinetics.
Bose, Amartya; Makri, Nancy
2017-10-21
The flux formulation of reaction rate theory is recast in terms of the expectation value of the reactive flux with an initial condition that corresponds to a non-equilibrium, factorized reactant density. In the common case of slow reactive processes, the non-equilibrium expression reaches the plateau regime only slightly slower than the equilibrium flux form. When the reactants are described by a single quantum state, as in the case of electron transfer reactions, the factorized reactant density describes the true initial condition of the reactive process. In such cases, the time integral of the non-equilibrium flux expression yields the reactant population as a function of time, allowing characterization of the dynamics in cases where there is no clear separation of time scales and thus a plateau regime cannot be identified. The non-equilibrium flux offers a unified approach to the kinetics of slow and fast chemical reactions and is ideally suited to mixed quantum-classical methods.
Bonitz, Michael
2016-01-01
This book presents quantum kinetic theory in a comprehensive way. The focus is on density operator methods and on non-equilibrium Green functions. The theory allows to rigorously treat nonequilibrium dynamics in quantum many-body systems. Of particular interest are ultrafast processes in plasmas, condensed matter and trapped atoms that are stimulated by rapidly developing experiments with short pulse lasers and free electron lasers. To describe these experiments theoretically, the most powerful approach is given by non-Markovian quantum kinetic equations that are discussed in detail, including computational aspects.
Quantum statistical vibrational entropy and enthalpy of formation of helium-vacancy complex in BCC W
Energy Technology Data Exchange (ETDEWEB)
Wen, Haohua [Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, 519082, Zhuhai (China); Woo, C.H., E-mail: chung.woo@polyu.edu.hk [ME Department, The Hong Kong Polytechnic University, Hong Kong SAR (China)
2016-12-15
High-temperature advance-reactor design and operation require knowledge of in-reactor materials properties far from the thermal ground state. Temperature-dependence due to the effects of lattice vibrations is important to the understanding and formulation of atomic processes involved in irradiation-damage accumulation. In this paper, we concentrate on the formation of He-V complex. The free-energy change in this regard is derived via thermodynamic integration from the phase-space trajectories generated from MD simulations based on the quantum fluctuation-dissipation relation. The change of frequency distribution of vibration modes during the complex formation is properly accounted for, and the corresponding entropy change avoids the classical ln(T) divergence that violates the third law. The vibrational enthalpy and entropy of formation calculated this way have significant effects on the He kinetics during irradiation.
International Nuclear Information System (INIS)
Testard, D.; Centre National de la Recherche Scientifique, 13 - Marseille
1977-09-01
For a finite non zero temperature state in Statistical Mechanics it is proved that the factor obtained in the corresponding representation of the quasilocal algebra has the property of Araki. The same result also holds for the 'wedge-algebras' of a hermitian scalar Wightman field
Ward identity for non-equilibrium Fermi systems
Czech Academy of Sciences Publication Activity Database
Velický, B.; Kalvová, Anděla; Špička, Václav
2008-01-01
Roč. 77, č. 4 (2008), 041201/1-041201/4 ISSN 1098-0121 R&D Projects: GA ČR GC202/07/J051 Institutional research plan: CEZ:AV0Z10100520; CEZ:AV0Z10100521 Keywords : non-equilibrium * Green’s functions * quantum transport equations * Ward identity Subject RIV: BE - Theoretical Physics Impact factor: 3.322, year: 2008
Simple models of equilibrium and nonequilibrium phenomena
International Nuclear Information System (INIS)
Lebowitz, J.L.
1987-01-01
This volume consists of two chapters of particular interest to researchers in the field of statistical mechanics. The first chapter is based on the premise that the best way to understand the qualitative properties that characterize many-body (i.e. macroscopic) systems is to study 'a number of the more significant model systems which, at least in principle are susceptible of complete analysis'. The second chapter deals exclusively with nonequilibrium phenomena. It reviews the theory of fluctuations in open systems to which they have made important contributions. Simple but interesting model examples are emphasised
Universality in Nonequilibrium Lattice Systems Theoretical Foundations
Ódor, Géza
2008-01-01
Universal scaling behavior is an attractive feature in statistical physics because a wide range of models can be classified purely in terms of their collective behavior due to a diverging correlation length. This book provides a comprehensive overview of dynamical universality classes occurring in nonequilibrium systems defined on regular lattices. The factors determining these diverse universality classes have yet to be fully understood, but the book attempts to summarize our present knowledge, taking them into account systematically.The book helps the reader to navigate in the zoo of basic m
Non-equilibrium QCD of high-energy multi-gluon dynamics
International Nuclear Information System (INIS)
Geiger, K.
1996-01-01
A non-equilibrium QCD description of multiparticle dynamics in space-time is of both fundamental and phenomenological interest. Here the authors discusses an attempt to derive from first principles, a real-time formalism to study the dynamical interplay of quantum and statistical-kinetic properties of non-equilibrium multi-parton systems produced in high-energy QCD processes. The ultimate goal (from which one is still far away) is to have a practically applicable description of the space-time evolution of a general initial system of gluons and quarks, characterized by some large energy or momentum scale, that expands, diffuses and dissipates according to the self- and mutual-interactions, and eventually converts dynamically into final state hadrons. For example, the evolution of parton showers in the mechanism of parton-hadron conversion in high-energy hadronic collisions, or, the description of formation, evolution and freezeout of a quark-gluon plasma, in ultra-relativistic heavy-ion collisions
Nonequilibrium dynamical mean-field theory
Energy Technology Data Exchange (ETDEWEB)
Eckstein, Martin
2009-12-21
The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)
Nonequilibrium dynamical mean-field theory
International Nuclear Information System (INIS)
Eckstein, Martin
2009-01-01
The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)
Quantum mechanics of the fractional-statistics gas: Random-phase approximation
International Nuclear Information System (INIS)
Dai, Q.; Levy, J.L.; Fetter, A.L.; Hanna, C.B.; Laughlin, R.B.
1992-01-01
A description of the fractional-statistics gas based on the complete summation of Hartree, Fock, ladder and bubble diagrams is presented. The superfluid properties identified previously in the random-phase-approximation (RPA) calculation of Fetter, Hanna, and Laughlin [Phys. Rev. B 39, 9679 (1989)] are substantially confirmed. The discrepancy between the RPA sound speed and the Hartree-Fock bulk modulus is found to be eliminated. The unusual Hall-effect behavior is found to vanish for the Bose gas test case but not for the fractional-statistics gas, implying that it is physically correct. Excellent agreement is obtained with the collective-mode dispersion obtained numerically by Xie, He, and Das Sarma [Phys. Rev. Lett. 65, 649 (1990)
Boosting up quantum key distribution by learning statistics of practical single-photon sources
International Nuclear Information System (INIS)
Adachi, Yoritoshi; Yamamoto, Takashi; Koashi, Masato; Imoto, Nobuyuki
2009-01-01
We propose a simple quantum-key-distribution (QKD) scheme for practical single-photon sources (SPSs), which works even with a moderate suppression of the second-order correlation g (2) of the source. The scheme utilizes a passive preparation of a decoy state by monitoring a fraction of the signal via an additional beam splitter and a detector at the sender's side to monitor photon-number splitting attacks. We show that the achievable distance increases with the precision with which the sub-Poissonian tendency is confirmed in higher photon-number distribution of the source, rather than with actual suppression of the multiphoton emission events. We present an example of the secure key generation rate in the case of a poor SPS with g (2) =0.19, in which no secure key is produced with the conventional QKD scheme, and show that learning the photon-number distribution up to several numbers is sufficient for achieving almost the same distance as that of an ideal SPS.
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)
Anisotropic nonequilibrium hydrodynamic attractor
Strickland, Michael; Noronha, Jorge; Denicol, Gabriel S.
2018-02-01
We determine the dynamical attractors associated with anisotropic hydrodynamics (aHydro) and the DNMR equations for a 0 +1 d conformal system using kinetic theory in the relaxation time approximation. We compare our results to the nonequilibrium attractor obtained from the exact solution of the 0 +1 d conformal Boltzmann equation, the Navier-Stokes theory, and the second-order Mueller-Israel-Stewart theory. We demonstrate that the aHydro attractor equation resums an infinite number of terms in the inverse Reynolds number. The resulting resummed aHydro attractor possesses a positive longitudinal-to-transverse pressure ratio and is virtually indistinguishable from the exact attractor. This suggests that an optimized hydrodynamic treatment of kinetic theory involves a resummation not only in gradients (Knudsen number) but also in the inverse Reynolds number. We also demonstrate that the DNMR result provides a better approximation of the exact kinetic theory attractor than the Mueller-Israel-Stewart theory. Finally, we introduce a new method for obtaining approximate aHydro equations which relies solely on an expansion in the inverse Reynolds number. We then carry this expansion out to the third order, and compare these third-order results to the exact kinetic theory solution.
Landau superfluids as nonequilibrium stationary states
International Nuclear Information System (INIS)
Wreszinski, Walter F.
2015-01-01
We define a superfluid state to be a nonequilibrium stationary state (NESS), which, at zero temperature, satisfies certain metastability conditions, which physically express that there should be a sufficiently small energy-momentum transfer between the particles of the fluid and the surroundings (e.g., pipe). It is shown that two models, the Girardeau model and the Huang-Yang-Luttinger (HYL) model, describe superfluids in this sense and, moreover, that, in the case of the HYL model, the metastability condition is directly related to Nozières’ conjecture that, due to the repulsive interaction, the condensate does not suffer fragmentation into two (or more) parts, thereby assuring its quantum coherence. The models are rigorous examples of NESS in which the system is not finite, but rather a many-body system
Evanseck, Jeffrey Donald
The completed research covers a broad range of theoretical applications in organic chemistry. It is divided into three chapters which covers the chemistry of singlet carbenes (Chapter 1), substituent effects in pericyclic rearrangements (Chapter 2), and the effects of solvent on the reactivity of organic reactions (Chapter 3). The selectivity between 1,2- and 1,4-intramolecular additions to restricted diene systems has been investigated. A decrease in activation energy for the intramolecular cycloaddition is noted for systems which approach the idealized geometry found with intermolecular addition of carbenes to olefins. Direct substitution at the carbene site dramatically effects the predicted activation barriers for 1,2-hydrogen shifts. An excellent correlation between the activation energy and a substituents sigma_sp {rm R}{rm o} parameters has been demonstrated. The long standing problem of orbital alignment influences on the selectivity of 1,2-hydrogen arrangements shows significant geometric distortions, yet has little influence on the rates of singlet alkylcarbene rearrangements. The exo-selectivities observed for 1,2-shifts in rigid systems are explained by torsional and steric interactions which develop in the transition structures. Substituent effects on pericyclic reactions have been computed for several conrotatory and disrotatory electrocyclizations. The six-electron disrotatory electrocyclization of 1-substituted hexatrienes displays a strong electronic component in determining stereoselectivity, despite incredible steric interference. The eight-electron conrotatory electrocyclization transition structure of 1-substituted octatetraene has an unusual helical transition structure which does not differentiate between substituent position. The effects of solvents on the acidity differences between E and Z esters has supplemented earlier ab initio quantum mechanical results on the enhanced acidity of Meldrum's acid. Monte Carlo simulations predict a
Assaraf, Roland
2014-12-01
We show that the recently proposed correlated sampling without reweighting procedure extends the locality (asymptotic independence of the system size) of a physical property to the statistical fluctuations of its estimator. This makes the approach potentially vastly more efficient for computing space-localized properties in large systems compared with standard correlated methods. A proof is given for a large collection of noninteracting fragments. Calculations on hydrogen chains suggest that this behavior holds not only for systems displaying short-range correlations, but also for systems with long-range correlations.
International Nuclear Information System (INIS)
Kjoensberg, H.; Leinaas, J.M.
1999-01-01
We present Monte Carlo studies of charge expectation values and charge fluctuations for quasi-particles in the quantum Hall system. We have studied the Laughlin wave functions for quasi-hole and quasi-electron, and also Jain's definition of the quasi-electron wave function. The considered systems consist of from 50 to 200 electrons, and the filling fraction is 1/3. For all quasi-particles our calculations reproduce well the expected values of charge; ((-1)/(3)) times the electron charge for the quasi-hole, and 1/3 for the quasi-electron. Regarding fluctuations in the charge, our results for the quasi-hole and Jain quasi-electron are consistent with the expected value zero in the bulk of the system, but for the Laughlin quasi-electron we find small, but significant, deviations from zero throughout the whole electron droplet. We also present Berry phase calculations of charge and statistics parameter for the Jain quasi-electron, calculations which supplement earlier studies for the Laughlin quasi-particles. We find that the statistics parameter, calculated as a function of distance, is more well behaved for the Jain quasi-electron than it is for the Laughlin quasi-electron. However, the sign of the parameter is opposite of what is expected from qualitative arguments
Non-equilibrium thermodynamics of radiation-induced processes in solids
International Nuclear Information System (INIS)
Yurov, V.M.; Eshchanov, A.N.; Kuketaev, A.T.; Sidorenya, Yu.S.
2005-01-01
In the paper an item about a defect system response in solids on external action (temperature, pressure, light, etc.) from the point of view of non-equilibrium statistical thermodynamics is considered
On nonequilibrium many-body systems 2: ultra fast relaxation phenomena in semiconductors
International Nuclear Information System (INIS)
Algarte, A.C.S.; Vasconcellos, A.R.; Luzzi, R.
1986-01-01
The application of the nonequilibrium statistical operator (NSO) method to the study of the irreversible thermodynamics and optical responses of semiconductors probed by ultrafast laser spectroscopy is described. (Author) [pt
Non-Equilibrium Heavy Flavored Hadron Yields from Chemical Equilibrium Strangeness-Rich QGP
Kuznetsova, Inga; Rafelski, Johann
2008-01-01
The yields of heavy flavored hadrons emitted from strangeness-rich QGP are evaluated within chemical non-equilibrium statistical hadronization model, conserving strangeness, charm, and entropy yields at hadronization.
Elements of non-equilibrium (ℎ, k)-dynamics at zero and finite temperatures
International Nuclear Information System (INIS)
Golubeva, O.N.; Sukhanov, A.D.
2011-01-01
We suggest a method which allows developing some elements of non-equilibrium (ℎ, k)-dynamics without use of Schroedinger equation. It is based on the generalization pf Fokker-Planck and Hamilton-Jacobi equations. Sequential considering of stochastic influence of vacuum is realized in the quantum heat bath model. We show that at the presence of quantum-thermal diffusion non-equilibrium wave functions describe the process of nearing to generalized state of thermal equilibrium at zero and finite temperatures. They can be used as a ground for universal description of transport phenomena
Statistical properties of highly excited quantum eigenstates of a strongly chaotic system
International Nuclear Information System (INIS)
Aurich, R.; Steiner, F.
1992-06-01
Statistical properties of highly excited quantal eigenstates are studied for the free motion (geodesic flow) on a compact surface of constant negative curvature (hyperbolic octagon) which represents a strongly chaotic system (K-system). The eigenstates are expanded in a circular-wave basis, and it turns out that the expansion coefficients behave as Gaussian pseudo-random numbers. It is shown that this property leads to a Gaussian amplitude distribution P(ψ) in the semiclassical limit, i.e. the wavefunctions behave as Gaussian random functions. This behaviour, which should hold for chaotic systems in general, is nicely confirmed for eigenstates lying 10000 states above the ground state thus probing the semiclassical limit. In addition, the autocorrelation function and the path-correlation function are calculated and compared with a crude semiclassical Bessel-function approximation. Agreement with the semiclassical prediction is only found, if a local averaging is performed over roughly 1000 de Broglie wavelengths. On smaller scales, the eigenstates show much more structure than predicted by the first semiclassical approximation. (orig.)
Non-equilibrium phase transitions
Henkel, Malte; Lübeck, Sven
2009-01-01
This book describes two main classes of non-equilibrium phase-transitions: (a) static and dynamics of transitions into an absorbing state, and (b) dynamical scaling in far-from-equilibrium relaxation behaviour and ageing. The first volume begins with an introductory chapter which recalls the main concepts of phase-transitions, set for the convenience of the reader in an equilibrium context. The extension to non-equilibrium systems is made by using directed percolation as the main paradigm of absorbing phase transitions and in view of the richness of the known results an entire chapter is devoted to it, including a discussion of recent experimental results. Scaling theories and a large set of both numerical and analytical methods for the study of non-equilibrium phase transitions are thoroughly discussed. The techniques used for directed percolation are then extended to other universality classes and many important results on model parameters are provided for easy reference.
Step-wise pulling protocols for non-equilibrium dynamics
Ngo, Van Anh
The fundamental laws of thermodynamics and statistical mechanics, and the deeper understandings of quantum mechanics have been rebuilt in recent years. It is partly because of the increasing power of computing resources nowadays, that allow shedding direct insights into the connections among the thermodynamics laws, statistical nature of our world, and the concepts of quantum mechanics, which have not yet been understood. But mostly, the most important reason, also the ultimate goal, is to understand the mechanisms, statistics and dynamics of biological systems, whose prevailing non-equilibrium processes violate the fundamental laws of thermodynamics, deviate from statistical mechanics, and finally complicate quantum effects. I believe that investigations of the fundamental laws of non-equilibrium dynamics will be a frontier research for at least several more decades. One of the fundamental laws was first discovered in 1997 by Jarzynski, so-called Jarzynski's Equality. Since then, different proofs, alternative descriptions of Jarzynski's Equality, and its further developments and applications have been quickly accumulated. My understandings, developments and applications of an alternative theory on Jarzynski's Equality form the bulk of this dissertation. The core of my theory is based on stepwise pulling protocols, which provide deeper insight into how fluctuations of reaction coordinates contribute to free-energy changes along a reaction pathway. We find that the most optimal pathways, having the largest contribution to free-energy changes, follow the principle of detailed balance. This is a glimpse of why the principle of detailed balance appears so powerful for sampling the most probable statistics of events. In a further development on Jarzynski's Equality, I have been trying to use it in the formalism of diagonal entropy to propose a way to extract useful thermodynamic quantities such temperature, work and free-energy profiles from far
Complex quantum network geometries: Evolution and phase transitions
Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao
2015-08-01
Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.
Black hole evaporation in a heat bath as a nonequilibrium process and its final fate
International Nuclear Information System (INIS)
Saida, Hiromi
2007-01-01
We consider a black hole in a heat bath, and the whole system which consists of the black hole and the heat bath is isolated from outside environments. When the black hole evaporates, the Hawking radiation causes an energy flow from the black hole to the heat bath. Therefore, since no energy flow arises in an equilibrium state, the thermodynamic state of the whole system is not in equilibrium. That is, in a region around the black hole, the matter field of Hawking radiation and that of heat bath should be in a nonequilibrium state due to the energy flow. Using a simple model which reflects the nonequilibrium nature of energy flow, we find the nonequilibrium effect on a black hole evaporation as follows: if the nonequilibrium region around a black hole is not so large, the evaporation time scale of a black hole in a heat bath becomes longer than that in an empty space (a situation without heat bath), because of the incoming energy flow from the heat bath to the black hole. However, if the nonequilibrium region around a black hole is sufficiently large, the evaporation time scale in a heat bath becomes shorter than that in an empty space, because a nonequilibrium effect of the temperature difference between the black hole and heat bath appears as a strong energy extraction from the black hole by the heat bath. Further, a specific nonequilibrium phenomenon is found: a quasi-equilibrium evaporation stage under the nonequilibrium effect proceeds abruptly to a quantum evaporation stage at a semi-classical level (at black hole radius R g > Planck length) within a very short time scale with a strong burst of energy. (Contrarily, when the nonequilibrium effect is not taken into account, a quasi-equilibrium stage proceeds smoothly to a quantum stage at R g < Planck length without so strong an energy burst.) That is, the nonequilibrium effect of energy flow tends to make a black hole evaporation process more dynamical and to accelerate that process. Finally, on the final fate
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
Haghshenasfard, Zahra; Cottam, M. G.
2018-01-01
Theoretical studies are reported for the quantum-statistical properties of microwave-driven multi-mode magnon systems as represented by ferromagnetic nanowires with a stripe geometry. Effects of both the exchange and the dipole-dipole interactions, as well as a Zeeman term for an external applied field, are included in the magnetic Hamiltonian. The model also contains the time-dependent nonlinear effects due to parallel pumping with an electromagnetic field. Using a coherent magnon state representation in terms of creation and annihilation operators, we investigate the effects of parallel pumping on the temporal evolution of various nonclassical properties of the system. A focus is on the interbranch mixing produced by the pumping field when there are three or more modes. In particular, the occupation magnon number and the multi-mode cross correlations between magnon modes are studied. Manipulation of the collapse and revival phenomena of the average magnon occupation number and the control of the cross correlation between the magnon modes are demonstrated through tuning of the parallel pumping field amplitude and appropriate choices for the coherent magnon states. The cross correlations are a direct consequence of the interbranch pumping effects and do not appear in the corresponding one- or two-mode magnon systems.
14th International Conference on Nonequilibrium Carrier Dynamics in Semiconductors
Saraniti, M; Nonequilibrium Carrier Dynamics in Semiconductors
2006-01-01
International experts gather every two years at this established conference to discuss recent developments in theory and experiment in non-equilibrium transport phenomena. These developments have been the driving force behind the spectacular advances in semiconductor physics and devices over the last few decades. Originally known as "Hot Carriers in Semiconductors," the 14th conference in the series covered a wide spectrum of traditional topics dealing with non-equilibrium phenomena, ranging from quantum transport to optical phenomena in mesoscopic and nano-scale structures. Particular attention was given this time to emerging areas of this rapidly evolving field, with many sessions covering terahertz devices, high field transport in nitride semiconductors, spintronics, molecular electronics, and bioelectronics applications.
Souto, R Seoane; Martín-Rodero, A; Yeyati, A Levy
2016-12-23
We analyze the quantum quench dynamics in the formation of a phase-biased superconducting nanojunction. We find that in the absence of an external relaxation mechanism and for very general conditions the system gets trapped in a metastable state, corresponding to a nonequilibrium population of the Andreev bound states. The use of the time-dependent full counting statistics analysis allows us to extract information on the asymptotic population of even and odd many-body states, demonstrating that a universal behavior, dependent only on the Andreev state energy, is reached in the quantum point contact limit. These results shed light on recent experimental observations on quasiparticle trapping in superconducting atomic contacts.
Non-equilibrium supramolecular polymerization.
Sorrenti, Alessandro; Leira-Iglesias, Jorge; Markvoort, Albert J; de Greef, Tom F A; Hermans, Thomas M
2017-09-18
Supramolecular polymerization has been traditionally focused on the thermodynamic equilibrium state, where one-dimensional assemblies reside at the global minimum of the Gibbs free energy. The pathway and rate to reach the equilibrium state are irrelevant, and the resulting assemblies remain unchanged over time. In the past decade, the focus has shifted to kinetically trapped (non-dissipative non-equilibrium) structures that heavily depend on the method of preparation (i.e., pathway complexity), and where the assembly rates are of key importance. Kinetic models have greatly improved our understanding of competing pathways, and shown how to steer supramolecular polymerization in the desired direction (i.e., pathway selection). The most recent innovation in the field relies on energy or mass input that is dissipated to keep the system away from the thermodynamic equilibrium (or from other non-dissipative states). This tutorial review aims to provide the reader with a set of tools to identify different types of self-assembled states that have been explored so far. In particular, we aim to clarify the often unclear use of the term "non-equilibrium self-assembly" by subdividing systems into dissipative, and non-dissipative non-equilibrium states. Examples are given for each of the states, with a focus on non-dissipative non-equilibrium states found in one-dimensional supramolecular polymerization.
Emergence of a fluctuation relation for heat in nonequilibrium Landauer processes
Taranto, Philip; Modi, Kavan; Pollock, Felix A.
2018-05-01
In a generalized framework for the Landauer erasure protocol, we study bounds on the heat dissipated in typical nonequilibrium quantum processes. In contrast to thermodynamic processes, quantum fluctuations are not suppressed in the nonequilibrium regime and cannot be ignored, making such processes difficult to understand and treat. Here we derive an emergent fluctuation relation that virtually guarantees the average heat produced to be dissipated into the reservoir either when the system or reservoir is large (or both) or when the temperature is high. The implication of our result is that for nonequilibrium processes, heat fluctuations away from its average value are suppressed independently of the underlying dynamics exponentially quickly in the dimension of the larger subsystem and linearly in the inverse temperature. We achieve these results by generalizing a concentration of measure relation for subsystem states to the case where the global state is mixed.
Phase transitions, nonequilibrium dynamics, and critical behavior of strongly interacting systems
International Nuclear Information System (INIS)
Mottola, E.; Bhattacharya, T.; Cooper, F.
1998-01-01
This is the final report of a three-year, Laboratory Directed Research and Development project at Los Alamos National Laboratory. In this effort, large-scale simulations of strongly interacting systems were performed and a variety of approaches to the nonequilibrium dynamics of phase transitions and critical behavior were investigated. Focus areas included (1) the finite-temperature quantum chromodynamics phase transition and nonequilibrium dynamics of a new phase of matter (the quark-gluon plasma) above the critical temperature, (2) nonequilibrium dynamics of a quantum fields using mean field theory, and (3) stochastic classical field theoretic models with applications to spinodal decomposition and structural phase transitions in a variety of systems, such as spin chains and shape memory alloys
Phase transitions, nonequilibrium dynamics, and critical behavior of strongly interacting systems
Energy Technology Data Exchange (ETDEWEB)
Mottola, E.; Bhattacharya, T.; Cooper, F. [and others
1998-12-31
This is the final report of a three-year, Laboratory Directed Research and Development project at Los Alamos National Laboratory. In this effort, large-scale simulations of strongly interacting systems were performed and a variety of approaches to the nonequilibrium dynamics of phase transitions and critical behavior were investigated. Focus areas included (1) the finite-temperature quantum chromodynamics phase transition and nonequilibrium dynamics of a new phase of matter (the quark-gluon plasma) above the critical temperature, (2) nonequilibrium dynamics of a quantum fields using mean field theory, and (3) stochastic classical field theoretic models with applications to spinodal decomposition and structural phase transitions in a variety of systems, such as spin chains and shape memory alloys.
Quantum Transport Through Tunable Molecular Diodes
Obodo, Tobechukwu Joshua; Murat, Altynbek; Schwingenschlö gl, Udo
2017-01-01
Employing self-interaction corrected density functional theory combined with the non-equilibrium Green's function method, we study the quantum transport through molecules with different numbers of phenyl (donor) and pyrimidinyl (acceptor) rings
Microscopic approaches to quantum nonequilibriumthermodynamics and information
2018-02-09
perspective on quantum thermalization for Science [8]. Wrote a joint experiment- theory paper on studying connections between quantum and classical chaos in...on the random matrix theory (eigenstate thermalization) and macroscopic phenomena (both equilibrium and non-equilibrium). Understanding thermodynamics...information. Specific questions to be addressed: connections of microscopic description of quantum chaotic systems based on the random matrix theory
Nonequilibrium work relation in a macroscopic system
International Nuclear Information System (INIS)
Sughiyama, Yuki; Ohzeki, Masayuki
2013-01-01
We reconsider a well-known relationship between the fluctuation theorem and the second law of thermodynamics by evaluating stochastic evolution of the density field (probability measure valued process). In order to establish a bridge between microscopic and macroscopic behaviors, we must take the thermodynamic limit of a stochastic dynamical system following the standard procedure in statistical mechanics. The thermodynamic path characterizing a dynamical behavior in the macroscopic scale can be formulated as an infimum of the action functional for the stochastic evolution of the density field. In our formulation, the second law of thermodynamics can be derived only by symmetry of the action functional without recourse to the Jarzynski equality. Our formulation leads to a nontrivial nonequilibrium work relation for metastable (quasi-stationary) states, which are peculiar in the macroscopic system. We propose a prescription for computing the free energy for metastable states based on the resultant work relation. (paper)
Putz, Mihai V
2009-11-10
The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.
Directory of Open Access Journals (Sweden)
Mihai V. Putz
2009-11-01
Full Text Available The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving many-electronic systems.
Ordered phase and non-equilibrium fluctuation in stock market
Maskawa, Jun-ichi
2002-08-01
We analyze the statistics of daily price change of stock market in the framework of a statistical physics model for the collective fluctuation of stock portfolio. In this model the time series of price changes are coded into the sequences of up and down spins, and the Hamiltonian of the system is expressed by spin-spin interactions as in spin glass models of disordered magnetic systems. Through the analysis of Dow-Jones industrial portfolio consisting of 30 stock issues by this model, we find a non-equilibrium fluctuation mode on the point slightly below the boundary between ordered and disordered phases. The remaining 29 modes are still in disordered phase and well described by Gibbs distribution. The variance of the fluctuation is outlined by the theoretical curve and peculiarly large in the non-equilibrium mode compared with those in the other modes remaining in ordinary phase.
Quantum Markov processes and applications in many-body systems
International Nuclear Information System (INIS)
Temme, P. K.
2010-01-01
This thesis is concerned with the investigation of quantum as well as classical Markov processes and their application in the field of strongly correlated many-body systems. A Markov process is a special kind of stochastic process, which is determined by an evolution that is independent of its history and only depends on the current state of the system. The application of Markov processes has a long history in the field of statistical mechanics and classical many-body theory. Not only are Markov processes used to describe the dynamics of stochastic systems, but they predominantly also serve as a practical method that allows for the computation of fundamental properties of complex many-body systems by means of probabilistic algorithms. The aim of this thesis is to investigate the properties of quantum Markov processes, i.e. Markov processes taking place in a quantum mechanical state space, and to gain a better insight into complex many-body systems by means thereof. Moreover, we formulate a novel quantum algorithm which allows for the computation of the thermal and ground states of quantum many-body systems. After a brief introduction to quantum Markov processes we turn to an investigation of their convergence properties. We find bounds on the convergence rate of the quantum process by generalizing geometric bounds found for classical processes. We generalize a distance measure that serves as the basis for our investigations, the chi-square divergence, to non-commuting probability spaces. This divergence allows for a convenient generalization of the detailed balance condition to quantum processes. We then devise the quantum algorithm that can be seen as the natural generalization of the ubiquitous Metropolis algorithm to simulate quantum many-body Hamiltonians. By this we intend to provide further evidence, that a quantum computer can serve as a fully-fledged quantum simulator, which is not only capable of describing the dynamical evolution of quantum systems, but
Nonequilibrium and irreversibility
Gallavotti, Giovanni
2014-01-01
This book concentrates on the properties of the stationary states in chaotic systems of particles or fluids, leaving aside the theory of the way they can be reached. The stationary states of particles or of fluids (understood as probability distributions on microscopic configurations or on the fields describing continua) have received important new ideas and data from numerical simulations and reviews are needed. The starting point is to find out which time invariant distributions come into play in physics. A special feature of this book is the historical approach. To identify the problems the author analyzes the papers of the founding fathers Boltzmann, Clausius and Maxwell including translations of the relevant (parts of ) historical documents. He also establishes a close link between treatment of irreversible phenomena in statistical mechanics and the theory of chaotic systems at and beyond the onset of turbulence as developed by Sinai, Ruelle, Bowen (SRB) and others: the author gives arguments intending t...
Drummond, P. D.; Chaturvedi, S.; Dechoum, K.; Comey, J.
2001-02-01
We investigate the theory of quantum fluctuations in non-equilibrium systems having large critical fluctuations. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction, and also to envisage future tests of quantum theory in regions of macroscopic quantum fluctuations. A long-term objective of this research is to identify suitable physical systems in which macroscopic 'Schrödinger cat'-like behaviour may be observed. We investigate two systems in particular of much current experimental interest, namely the degenerate parametric oscillator near threshold, and the evaporatively cooled (BEC). We compare the results obtained in the positive-P representation, as a fully quantum mechanical calculation, with the truncated Wigner phase space equation, also known as semi-classical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. In the region where the largest quantum fluctuations and Schrödinger cat-like behaviour might be expected, we find that the quantum predictions correspond very closely to the semi-classical theory. Nature abhors observing a Schrödinger cat. -Pacs: 03.65.Bz
On nonequilibrium many-body systems III: nonlinear transport theory
International Nuclear Information System (INIS)
Luzzi, R.; Vasconcellos, A.R.; Algarte, A.C.S.
1986-01-01
A nonlinear transport theory for many-body systems arbitrarily away from equilibrium, based on the nonequilibrium statistical operator (NSO) method, is presented. Nonlinear transport equations for a basis set of dynamical quantities are derived using two equivalent treatments that may be considered far reaching generalizations of the Hilbert-Chapman-Enskog method and Mori's generalized Langevin equations method. The first case is considered in some detail and the general characteristics of the theory are discussed. (Author) [pt
Cumulants in perturbation expansions for non-equilibrium field theory
International Nuclear Information System (INIS)
Fauser, R.
1995-11-01
The formulation of perturbation expansions for a quantum field theory of strongly interacting systems in a general non-equilibrium state is discussed. Non-vanishing initial correlations are included in the formulation of the perturbation expansion in terms of cumulants. The cumulants are shown to be the suitable candidate for summing up the perturbation expansion. Also a linked-cluster theorem for the perturbation series with cumulants is presented. Finally a generating functional of the perturbation series with initial correlations is studied. We apply the methods to a simple model of a fermion-boson system. (orig.)