Integrable Many Particle Systems

Author : Vladimir Inozemtsev
Publisher : World Scientific
Page : 267 pages
File Size : 49,6 Mb
Release : 2023-04-25
Category : Science
ISBN : 9781800613836

Get Book

Integrable Many-particle Systems by Vladimir Inozemtsev Pdf

It is commonly known that three or more particles interacting via a two-body potential is an intractable problem. However, similar systems confined to one dimension yield exactly solvable equations, which have seeded widely pursued studies of one-dimensional n-body problems. The interest in these investigations is justified by their rich and quantitative insights into real-world classical and quantum problems, birthing a field that is the subject of this book. Spanning four bulk chapters, this book is written with the hope that readers come to appreciate the beauty of the mathematical results concerning the models of many-particle systems, such as the interaction between light particles and infinitely massive particles, as well as interacting quasiparticles. As the book discusses several unsolved problems in the subject, it functions as an insightful resource for researchers working in this branch of mathematical physics.In Chapter 1, the author first introduces readers to interesting problems in mathematical physics, with the prime objective of finding integrals of motion for classical many-particle systems as well as the exact solutions of the corresponding equations of motions. For these studied systems, their quantum mechanical analogue is then developed in Chapter 2. In Chapter 3, the book focuses on a quintessential problem in the quantum theory of magnetism: namely, to find all integrable one-dimensional systems involving quasiparticles of interacting one-half spins. Readers will study the integrable periodic chains of interacting one-half spins and discover the integrals of motion for such systems, as well as the eigenvectors of their corresponding Hamiltonians. In the last chapter, readers will study about integrable systems of quantum particles, with spin and mutual interactions involving rational, trigonometric, or elliptic potentials.

Author : Vladimir I. Inozemtsev
Publisher : Unknown
Page : 0 pages
File Size : 49,8 Mb
Release : 2023
Category : Electronic books
ISBN : 1800613822

Get Book

Integrable Many-particle Systems by Vladimir I. Inozemtsev Pdf

Author : John W. Negele
Publisher : CRC Press
Page : 474 pages
File Size : 48,8 Mb
Release : 2018-03-05
Category : Science
ISBN : 9780429966477

Get Book

Quantum Many-particle Systems by John W. Negele Pdf

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.

Author : Alexander L. Fetter,John Dirk Walecka
Publisher : Courier Corporation
Page : 640 pages
File Size : 40,6 Mb
Release : 2012-03-08
Category : Science
ISBN : 9780486134758

Get Book

Quantum Theory of Many-Particle Systems by Alexander L. Fetter,John Dirk Walecka Pdf

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.

Author : Robert Mills
Publisher : CRC Press
Page : 150 pages
File Size : 47,5 Mb
Release : 1969
Category : Science
ISBN : 0677020406

Get Book

Propagators for Many-particle Systems by Robert Mills Pdf

Author : Daniel C. Cabra,Andreas Honecker,Pierre Pujol
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 44,6 Mb
Release : 2012-01-05
Category : Technology & Engineering
ISBN : 9783642104480

Get Book

Modern Theories of Many-Particle Systems in Condensed Matter Physics by Daniel C. Cabra,Andreas Honecker,Pierre Pujol Pdf

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.

Author : John W. Negele,Henri Orland
Publisher : Addison Wesley Publishing Company
Page : 490 pages
File Size : 42,9 Mb
Release : 1988-01-21
Category : Science
ISBN : UVA:X001402744

Get Book

Quantum Many-particle Systems by John W. Negele,Henri Orland Pdf

Author : Herbert Spohn
Publisher : World Scientific
Page : 255 pages
File Size : 54,6 Mb
Release : 2024-02-27
Category : Science
ISBN : 9789811283543

Get Book

Hydrodynamic Scales Of Integrable Many-body Systems by Herbert Spohn Pdf

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.

Author : I.P. Bazarov,P.N. Nikolaev
Publisher : American Institute of Physics
Page : 328 pages
File Size : 49,6 Mb
Release : 1989-06
Category : Science
ISBN : UCAL:B4422924

Get Book

Theory of Many-Particle Systems by I.P. Bazarov,P.N. Nikolaev Pdf

Contents: General. Materials: Single Crystals, Ceramics, Polymers, Composites, Polar Glass Ceramics. Measurements and Standards: Constants of Alpha Quartz, Acoustic Microscopy, IEEE Standard. Devices and Applications (16 papers). Appendices. Author Index.

Author : Kuzemsky Alexander Leonidovich
Publisher : World Scientific
Page : 1260 pages
File Size : 47,6 Mb
Release : 2017-02-24
Category : Science
ISBN : 9789813145658

Get Book

Statistical Mechanics And The Physics Of Many-particle Model Systems by Kuzemsky Alexander Leonidovich Pdf

The book is devoted to the study of the correlation effects in many-particle systems. It presents the advanced methods of quantum statistical mechanics (equilibrium and nonequilibrium), and shows their effectiveness and operational ability in applications to problems of quantum solid-state theory, quantum theory of magnetism and the kinetic theory. The book includes description of the fundamental concepts and techniques of analysis following the approach of N N Bogoliubov's school, including recent developments. It provides an overview that introduces the main notions of quantum many-particle physics with the emphasis on concepts and models. This book combines the features of textbook and research monograph. For many topics the aim is to start from the beginning and to guide the reader to the threshold of advanced researches. Many chapters include also additional information and discuss many complex research areas which are not often discussed in other places. The book is useful for established researchers to organize and present the advanced material disseminated in the literature. The book contains also an extensive bibliography. The book serves undergraduate, graduate and postgraduate students, as well as researchers who have had prior experience with the subject matter at a more elementary level or have used other many-particle techniques.

Author : Harry L. Morrison
Publisher : Unknown
Page : 372 pages
File Size : 42,6 Mb
Release : 1963
Category : Science
ISBN : UOM:39015017220743

Get Book

The Quantum Theory of Many-particle Systems by Harry L. Morrison Pdf

Author : Eberhard K. U. Gross,E. Runge,O. Heinonen
Publisher : CRC Press
Page : 442 pages
File Size : 48,8 Mb
Release : 1991-11
Category : Art
ISBN : MINN:31951D008016769

Get Book

Many-Particle Theory, by Eberhard K. U. Gross,E. Runge,O. Heinonen Pdf

The quantum theory of many-particle systems has applications in various branches of physics including condensed matter, atomic, molecular, nuclear and high-energy. An understanding of this theory is therefore important to most students of physics and Many-Particle Theory is an excellent introduction to the subject. Many-Particle Theory presents a detailed and logical account of the theory and techniques used. Basic subjects such as Green's functions and Feynman diagrams are discussed in detail, and many examples and applications are given, such as the Hartee-Fock approximation, superconductivity and the Kondo problem. Due to the detailed derivations and the fact that only a grasp of basic quantum mechanics is assumed, the book is an ideal textbook for graduate students and teachers of physics. The comprehensive bibliography contains many recent books and articles for further studies. Many-Particle Theory is a translation of the second German edition, which is an expanded version of the popular first edition. All three authors, E K U Gross, E Runge and O Heinonen, are well respected researchers in the field.

Author : Ladislav Šamaj,Zoltán Bajnok
Publisher : Cambridge University Press
Page : 525 pages
File Size : 46,5 Mb
Release : 2013-05-16
Category : Science
ISBN : 9781107067660

Get Book

Introduction to the Statistical Physics of Integrable Many-body Systems by Ladislav Šamaj,Zoltán Bajnok Pdf

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.

Author : Percy Deift,Peter Forrester
Publisher : Cambridge University Press
Page : 539 pages
File Size : 41,8 Mb
Release : 2014-12-15
Category : Language Arts & Disciplines
ISBN : 9781107079922

Get Book

Random Matrix Theory, Interacting Particle Systems and Integrable Systems by Percy Deift,Peter Forrester Pdf

This volume includes review articles and research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles.

Author : John P. Harnad,Pavel Winternitz
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 49,6 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821820933

Get Book

Integrable Systems: From Classical to Quantum by John P. Harnad,Pavel Winternitz Pdf

This volume presents the papers based upon lectures given at the 1999 Séminaire de Mathémathiques Supérieurs held in Montreal. It includes contributions from many of the most active researchers in the field. This subject has been in a remarkably active state of development throughout the past three decades, resulting in new motivation for study in r s3risingly different directions. Beyond the intrinsic interest in the study of integrable models of many-particle systems, spin chains, lattice and field theory models at both the classical and the quantum level, and completely solvable models in statistical mechanics, there have been new applications in relation to a number of other fields of current interest. These fields include theoretical physics and pure mathematics, for example the Seiberg-Witten approach to supersymmetric Yang-Mills theory, the spectral theory of random matrices, topological models of quantum gravity, conformal field theory, mirror symmetry, quantum cohomology, etc. This collection gives a nice cross-section of the current state of the work in the area of integrable systems which is presented by some of the leading active researchers in this field. The scope and quality of the articles in this volume make this a valuable resource for those interested in an up-to-date introduction and an overview of many of the main areas of study in the theory of integral systems.