Introduction To Classical Integrable Systems
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Introduction To Classical Integrable Systems
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Author : Olivier Babelon
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-17
Introduction To Classical Integrable Systems written by Olivier Babelon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-17 with Mathematics categories.
This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.
Introduction To Classical Integrable Systems
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Author : Olivier Babelon
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-17
Introduction To Classical Integrable Systems written by Olivier Babelon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-17 with Science categories.
A clear and pedagogical introduction to classical integrable systems and their applications. It synthesizes the different approaches to the subject, providing a set of interconnected methods for solving problems in mathematical physics. Each method is introduced and explained, before being applied to particular examples.
Introduction To Classical Integrable Systems
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Author : Olivier Babelon
language : en
Publisher:
Release Date : 2003
Introduction To Classical Integrable Systems written by Olivier Babelon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Dynamics categories.
Elements Of Classical And Quantum Integrable Systems
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Author : Gleb Arutyunov
language : en
Publisher: Springer
Release Date : 2020-08-15
Elements Of Classical And Quantum Integrable Systems written by Gleb Arutyunov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-15 with Science categories.
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
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Author : Fabio Franchini
language : en
Publisher: Springer
Release Date : 2017-05-25
An Introduction To Integrable Techniques For One Dimensional Quantum Systems written by Fabio Franchini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-25 with Science categories.
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.
Integrable Systems Of Classical Mechanics And Lie Algebras
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Author : A. M. Perelomov
language : en
Publisher: Springer
Release Date : 1990
Integrable Systems Of Classical Mechanics And Lie Algebras written by A. M. Perelomov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Electronic books categories.
This book offers a systematic presentation of a variety of methods and results concerning integrable systems of classical mechanics. The investigation of integrable systems was an important line of study in the last century, but up until recently only a small number of examples with two or more degrees of freedom were known. In the last fifteen years however, remarkable progress has been made in this field via the so-called isospectral deformation method which makes extensive use of group-theoretical concepts. The book focuses mainly on the development and applications of this new method, and also gives a fairly complete survey of the older classic results. Chapter 1 contains the necessary background material and outlines the isospectral deformation method in a Lie-algebraic form. Chapter 2 gives an account of numerous previously known integrable systems. Chapter 3 deals with many-body systems of generalized Calogero-Moser type, related to root systems of simple Lie algebras. Chapter 4 is devoted to the Toda lattice and its various modifications seen from the group-theoretic point of view. Chapter 5 investigates some additional topics related to many-body systems. The book will be valuable to students as well as researchers.
Quantum Integrable Systems
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Author : Asesh Roy Chowdhury
language : en
Publisher: CRC Press
Release Date : 2004-01-28
Quantum Integrable Systems written by Asesh Roy Chowdhury and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-28 with Science categories.
The study of integrable systems has opened new horizons in classical physics over the past few decades, particularly in the subatomic world. Yet despite the field now having reached a level of maturity, very few books provide an introduction to the field accessible to specialists and nonspecialists alike, and none offer a systematic survey of the m
Integrable And Superintegrable Systems
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Author : Boris A Kuperschmidt
language : en
Publisher: World Scientific
Release Date : 1990-10-25
Integrable And Superintegrable Systems written by Boris A Kuperschmidt and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-10-25 with Science categories.
Some of the most active practitioners in the field of integrable systems have been asked to describe what they think of as the problems and results which seem to be most interesting and important now and are likely to influence future directions. The papers in this collection, representing their authors' responses, offer a broad panorama of the subject as it enters the 1990's.
Yang Baxter Deformation Of 2d Non Linear Sigma Models
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Author : Kentaroh Yoshida
language : en
Publisher: Springer Nature
Release Date : 2021-06-03
Yang Baxter Deformation Of 2d Non Linear Sigma Models written by Kentaroh Yoshida and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-03 with Science categories.
In mathematical physics, one of the fascinating issues is the study of integrable systems. In particular, non-perturbative techniques that have been developed have triggered significant insight for real physics. There are basically two notions of integrability: classical integrability and quantum integrability. In this book, the focus is on the former, classical integrability. When the system has a finite number of degrees of freedom, it has been well captured by the Arnold–Liouville theorem. However, when the number of degrees of freedom is infinite, as in classical field theories, the integrable structure is enriched profoundly. In fact, the study of classically integrable field theories has a long history and various kinds of techniques, including the classical inverse scattering method, which have been developed so far. In previously published books, these techniques have been collected and well described and are easy to find in traditional, standard textbooks. One of the intriguing subjects in classically integrable systems is the investigation of deformations preserving integrability. Usually, it is not considered systematic to perform such a deformation, and one must study systems case by case and show the integrability of the deformed systems by constructing the associated Lax pair or action-angle variables. Recently, a new, systematic method to perform integrable deformations of 2D non-linear sigma models was developed. It was invented by C. Klimcik in 2002, and the integrability of the deformed sigma models was shown in 2008. The original work was done for 2D principal chiral models, but it has been generalized in various directions nowadays. In this book, the recent progress on this Yang–Baxter deformation is described in a pedagogical manner, including some simple examples. Applications of Yang–Baxter deformation to string theory are also described briefly.
Classical And Quantum Nonlinear Integrable Systems
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Author : A Kundu
language : en
Publisher: CRC Press
Release Date : 2019-04-23
Classical And Quantum Nonlinear Integrable Systems written by A Kundu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-23 with Science categories.
Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories