Introduction to the Statistical Physics of Integrable Many-body Systems

Introduction to the Statistical Physics of Integrable Many-body Systems
Title Introduction to the Statistical Physics of Integrable Many-body Systems PDF eBook
Author Ladislav Šamaj
Publisher Cambridge University Press
Pages 525
Release 2013-05-16
Genre Science
ISBN 1107067669

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Including topics not traditionally covered in literature, such as (1+1)-dimensional QFT and classical 2D Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied. Beginning with a treatise of nonrelativistic 1D continuum Fermi and Bose quantum gases of identical spinless particles, the book describes the quantum inverse scattering method and the analysis of the related Yang–Baxter equation and integrable quantum Heisenberg models. It also discusses systems within condensed matter physics, the complete solution of the sine-Gordon model and modern trends in the thermodynamic Bethe ansatz. Each chapter concludes with problems and solutions to help consolidate the reader's understanding of the theory and its applications. Basic knowledge of quantum mechanics and equilibrium statistical physics is assumed, making this book suitable for graduate students and researchers in statistical physics, quantum mechanics and mathematical and theoretical physics.

Elements of Classical and Quantum Integrable Systems

Elements of Classical and Quantum Integrable Systems
Title Elements of Classical and Quantum Integrable Systems PDF eBook
Author Gleb Arutyunov
Publisher Springer
Pages 420
Release 2019-07-23
Genre Science
ISBN 303024198X

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Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.

An Introduction to Integrable Techniques for One-Dimensional Quantum Systems

An Introduction to Integrable Techniques for One-Dimensional Quantum Systems
Title An Introduction to Integrable Techniques for One-Dimensional Quantum Systems PDF eBook
Author Fabio Franchini
Publisher Springer
Pages 186
Release 2017-05-25
Genre Science
ISBN 3319484877

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This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and the choice of topics, this book tries to touch all fundamental ideas behind integrability and is meant for students and researchers interested either in an introduction to later delve in the advance aspects of Bethe Ansatz or in an overview of the topic for broadening their culture.

Exactly Solved Models in Statistical Mechanics

Exactly Solved Models in Statistical Mechanics
Title Exactly Solved Models in Statistical Mechanics PDF eBook
Author Rodney J. Baxter
Publisher Elsevier
Pages 499
Release 2016-06-12
Genre Science
ISBN 1483265943

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Exactly Solved Models in Statistical Mechanics

Statistical Field Theory

Statistical Field Theory
Title Statistical Field Theory PDF eBook
Author G. Mussardo
Publisher Oxford University Press, USA
Pages 778
Release 2010
Genre Mathematics
ISBN 0199547580

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A thorough and pedagogical introduction to phase transitions and exactly solved models in statistical physics and quantum field theory.

Hydrodynamic Scales Of Integrable Many-body Systems

Hydrodynamic Scales Of Integrable Many-body Systems
Title Hydrodynamic Scales Of Integrable Many-body Systems PDF eBook
Author Herbert Spohn
Publisher World Scientific
Pages 255
Release 2024-02-27
Genre Science
ISBN 9811283540

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This book provides a broad introduction to integrable systems with many degrees of freedom. Within a much larger orbit, discussed are models such as the classical Toda lattice, Calogero fluid, and Ablowitz-Ladik discretized nonlinear Schrödinger equation. On the quantum mechanical side, featured are the Lieb-Liniger delta-Bose gas and the quantum Toda lattice. As a genuinely novel twist, the study deals with random initial data described by generalized Gibbs ensembles with parameters of slow spatial variation. This is the hydrodynamic scale, in spirit similar to the ballistic Euler scale of nonintegrable simple fluids. While integrable microscopic particle models are very diverse, the central theme of this book is to elucidate their structural similarity on hydrodynamic scales.

Modern Theories of Many-Particle Systems in Condensed Matter Physics

Modern Theories of Many-Particle Systems in Condensed Matter Physics
Title Modern Theories of Many-Particle Systems in Condensed Matter Physics PDF eBook
Author Daniel C. Cabra
Publisher Springer Science & Business Media
Pages 380
Release 2012-01-05
Genre Technology & Engineering
ISBN 3642104487

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Condensed matter systems where interactions are strong are inherently difficult to analyze theoretically. The situation is particularly interesting in low-dimensional systems, where quantum fluctuations play a crucial role. Here, the development of non-perturbative methods and the study of integrable field theory have facilitated the understanding of the behavior of many quasi one- and two-dimensional strongly correlated systems. In view of the same rapid development that has taken place for both experimental and numerical techniques, as well as the emergence of novel testing-grounds such as cold atoms or graphene, the current understanding of strongly correlated condensed matter systems differs quite considerably from standard textbook presentations. The present volume of lecture notes aims to fill this gap in the literature by providing a collection of authoritative tutorial reviews, covering such topics as quantum phase transitions of antiferromagnets and cuprate-based high-temperature superconductors, electronic liquid crystal phases, graphene physics, dynamical mean field theory applied to strongly correlated systems, transport through quantum dots, quantum information perspectives on many-body physics, frustrated magnetism, statistical mechanics of classical and quantum computational complexity, and integrable methods in statistical field theory. As both graduate-level text and authoritative reference on this topic, this book will benefit newcomers and more experienced researchers in this field alike.