Download or read book Integrable Many particle Systems written by Vladimir Inozemtsev and published by World Scientific. This book was released on 2023-04-25 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Integrable Many particle Systems written by Vladimir I. Inozemtsev and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantum Many particle Systems written by John W. Negele and published by CRC Press. This book was released on 2018-03-05 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modern Theories of Many Particle Systems in Condensed Matter Physics written by Daniel C. Cabra and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantum Theory of Many Particle Systems written by Alexander L. Fetter and published by Courier Corporation. This book was released on 2012-03-08 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Propagators for Many particle Systems written by Robert Mills and published by CRC Press. This book was released on 1969 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hydrodynamic Scales Of Integrable Many body Systems written by Herbert Spohn and published by World Scientific. This book was released on 2024-02-27 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to the Statistical Physics of Integrable Many body Systems written by Ladislav Šamaj and published by Cambridge University Press. This book was released on 2013-05-16 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantum Many particle Systems written by John W. Negele and published by Addison Wesley Publishing Company. This book was released on 1988-01-21 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Quantum Theory of Many particle Systems written by Harry L. Morrison and published by . This book was released on 1963 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Random Matrix Theory Interacting Particle Systems and Integrable Systems written by Percy Deift and published by Cambridge University Press. This book was released on 2014-12-15 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes review articles and research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles.
Download or read book The Flow Equation Approach to Many Particle Systems written by Stefan Kehrein and published by Springer. This book was released on 2007-01-09 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained introduction addresses the novel flow equation approach for many particle systems and provides an up-to-date review of the subject. The text first discusses the general ideas and concepts of the flow equation method, and then in a second part illustrates them with various applications in condensed matter theory. The third and last part of the book contains an outlook with current perspectives for future research.
Download or read book Integrable systems written by John P. Harnad and published by . This book was released on 2000 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the papers based upon lectures given at the 1999 Séminaire de Mathémathiques Supérieurs held in Montréal. 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 surprisingly 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 s.
Download or read book Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds written by A.K. Prykarpatsky and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).
Download or read book From Particle Systems to Partial Differential Equations II written by Patrícia Gonçalves and published by Springer. This book was released on 2015-04-04 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on mathematical problems concerning different applications in physics, engineering, chemistry and biology. It covers topics ranging from interacting particle systems to partial differential equations (PDEs), statistical mechanics and dynamical systems. The purpose of the second meeting on Particle Systems and PDEs was to bring together renowned researchers working actively in the respective fields, to discuss their topics of expertise and to present recent scientific results in both areas. Further, the meeting was intended to present the subject of interacting particle systems, its roots in and impacts on the field of physics and its relation with PDEs to a vast and varied public, including young researchers. The book also includes the notes from two mini-courses presented at the conference, allowing readers who are less familiar with these areas of mathematics to more easily approach them. The contributions will be of interest to mathematicians, theoretical physicists and other researchers interested in interacting particle systems, partial differential equations, statistical mechanics, stochastic processes, kinetic theory, dynamical systems and mathematical modeling aspects.
Download or read book Functional Integral Representations for Quantum Many particle Systems written by Cindy Marie Blois and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integrable Systems From Classical to Quantum written by John P. Harnad and published by American Mathematical Soc.. This book was released on 2000 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
