Quantum Interacting Particle Systems
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Quantum Interacting Particle Systems
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Author : Luigi Accardi
language : en
Publisher: World Scientific
Release Date : 2002-07-19
Quantum Interacting Particle Systems written by Luigi Accardi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-19 with Mathematics categories.
The problem of extending ideas and results on the dynamics of infinite classical lattice systems to the quantum domain naturally arises in different branches of physics (nonequilibrium statistical mechanics, quantum optics, solid state, …) and new momentum from the development of quantum computer and quantum neural networks (which are in fact interacting arrays of binary systems) has been found.The stochastic limit of quantum theory allowed to deduce, as limits of the usual Hamiltonian systems, a new class of quantum stochastic flows which, when restricted to an appropriate Abelian subalgebra, produces precisely those interacting particle systems studied in classical statistical mechanics.Moreover, in many interesting cases, the underlying classical process “drives” the quantum one, at least as far as ergodicity or convergence to equilibrium are concerned. Thus many deep results concerning classical systems can be directly applied to carry information on the corresponding quantum system. The thermodynamic limit itself is obtained thanks to a technique (the four-semigroup method, new even in the classical case) which reduces the infinitesimal structure of a stochastic flow to that of four semigroups canonically associated to it (Chap. 1).Simple and effective methods to analyze qualitatively the ergodic behavior of quantum Markov semigroups are discussed in Chap. 2.Powerful estimates used to control the infinite volume limit, ergodic behavior and the spectral gap (Gaussian, exponential and hypercontractive bounds, classical and quantum logarithmic Sobolev inequalities, …) are discussed in Chap. 3.
Quantum Interacting Particle Systems
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Author : Luigi Accardi
language : en
Publisher: World Scientific
Release Date : 2002
Quantum Interacting Particle Systems written by Luigi Accardi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Science categories.
The dynamics of infinite classical lattice systems has been considered and has led to the study of the properties of ergodicity and convergence to equilibrium of a new class of Markov semigroups. Quantum analogues of these semigroups have also been considered. However, the problem of deriving these Markovian semigroups and, what is much more interesting, the associated stochastic flows, as limits of Hamiltonian systems, rather than postulating their form on a phenomenological basis, is essentially open both in the classical case and in the quantum case. This book presents a conjecture that, by coupling a quantum spin system in finite volume to a quantum field via a suitable interaction, applying the stochastic golden rule and taking the thermodynamic limit, one may obtain a class of quantum flows which, when restricted to an appropriate Abelian subalgebra, gives rise to the classical interacting particle systems studied in classical statistical mechanics.
Quantum Many Particle Systems
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Author : John W. Negele
language : en
Publisher: CRC Press
Release Date : 2018-03-05
Quantum Many Particle Systems written by John W. Negele and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-05 with Science categories.
This book explains the fundamental concepts and theoretical techniques used to understand the properties of quantum systems having large numbers of degrees of freedom. A number of complimentary approaches are developed, including perturbation theory; nonperturbative approximations based on functional integrals; general arguments based on order parameters, symmetry, and Fermi liquid theory; and stochastic methods.
Quantum Theory Of Many Particle Systems
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Author : Alexander L. Fetter
language : en
Publisher: Courier Corporation
Release Date : 2012-03-08
Quantum Theory Of Many Particle Systems written by Alexander L. Fetter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-08 with Science categories.
Self-contained treatment of nonrelativistic many-particle systems discusses both formalism and applications in terms of ground-state (zero-temperature) formalism, finite-temperature formalism, canonical transformations, and applications to physical systems. 1971 edition.
Scattering Theory Of Classical And Quantum N Particle Systems
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Author : Jan Derezinski
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-06-05
Scattering Theory Of Classical And Quantum N Particle Systems written by Jan Derezinski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-05 with Mathematics categories.
This monograph addresses researchers and students. It is a modern presentation of time-dependent methods for studying problems of scattering theory in the classical and quantum mechanics of N-particle systems. Particular attention is paid to long-range potentials. For a large class of interactions the existence of the asymptotic velocity and the asymptotic completeness of the wave operators is shown. The book is self-contained and explains in detail concepts that deepen the understanding. As a special feature of the book, the beautiful analogy between classical and quantum scattering theory (e.g., for N-body Hamiltonians) is presented with deep insight into the physical and mathematical problems.
Feynman Kac Formulae
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Author : Pierre Del Moral
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-03-30
Feynman Kac Formulae written by Pierre Del Moral and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-30 with Mathematics categories.
This text takes readers in a clear and progressive format from simple to recent and advanced topics in pure and applied probability such as contraction and annealed properties of non-linear semi-groups, functional entropy inequalities, empirical process convergence, increasing propagations of chaos, central limit, and Berry Esseen type theorems as well as large deviation principles for strong topologies on path-distribution spaces. Topics also include a body of powerful branching and interacting particle methods.
Active Particles Volume 3
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Author : Nicola Bellomo
language : en
Publisher: Springer Nature
Release Date : 2022-03-28
Active Particles Volume 3 written by Nicola Bellomo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-28 with Mathematics categories.
This edited volume collects six surveys that present state-of-the-art results on modeling, qualitative analysis, and simulation of active matter, focusing on specific applications in the natural sciences. Following the previously published Active Particles volumes, these chapters are written by leading experts in the field and reflect the diversity of subject matter in theory and applications within an interdisciplinary framework. Topics covered include: Variability and heterogeneity in natural swarms Multiscale aspects of the dynamics of human crowds Mathematical modeling of cell collective motion triggered by self-generated gradients Clustering dynamics on graphs Random Batch Methods for classical and quantum interacting particle systems The consensus-based global optimization algorithm and its recent variants Mathematicians and other members of the scientific community interested in active matter and its many applications will find this volume to be a timely, authoritative, and valuable resource.
Stochastic Interacting Systems Contact Voter And Exclusion Processes
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Author : Thomas M. Liggett
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-08-13
Stochastic Interacting Systems Contact Voter And Exclusion Processes written by Thomas M. Liggett and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-13 with Education categories.
Interactive particle systems is a branch of probability theory with close connections to mathematical physics and mathematical biology. This book takes three of the most important models in the area, and traces advances in our understanding of them since 1985. It explains and develops many of the most useful techniques in the field.
Random Walks Brownian Motion And Interacting Particle Systems
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Author : H. Kesten
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-06-01
Random Walks Brownian Motion And Interacting Particle Systems written by H. Kesten and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-06-01 with Mathematics categories.
This collection of articles is dedicated to Frank Spitzer on the occasion of his 65th birthday. The articles, written by a group of his friends, colleagues, former students and coauthors, are intended to demonstrate the major influence Frank has had on probability theory for the last 30 years and most likely will have for many years to come. Frank has always liked new phenomena, clean formulations and elegant proofs. He has created or opened up several research areas and it is not surprising that many people are still working out the consequences of his inventions. By way of introduction we have reprinted some of Frank's seminal articles so that the reader can easily see for himself the point of origin for much of the research presented here. These articles of Frank's deal with properties of Brownian motion, fluctuation theory and potential theory for random walks, and, of course, interacting particle systems. The last area was started by Frank as part of the general resurgence of treating problems of statistical mechanics with rigorous probabilistic tools.