Integrable Systems

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Elements of Classical and Quantum Integrable Systems

Gleb Arutyunov
Elements of Classical and Quantum Integrable Systems Book PDF

Author : Gleb Arutyunov
Publisher : Springer
Page : 414 pages
File Size : 43,9 Mb
Release : 2019-07-23
Category : Science
ISBN : 9783030241988

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Elements of Classical and Quantum Integrable Systems by Gleb Arutyunov Pdf

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.

Integrable Systems

N.J. Hitchin,G. B. Segal,R.S. Ward
Integrable Systems Book PDF

Author : N.J. Hitchin,G. B. Segal,R.S. Ward
Publisher : Oxford University Press, USA
Page : 148 pages
File Size : 44,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9780199676774

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Integrable Systems by N.J. Hitchin,G. B. Segal,R.S. Ward Pdf

Designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors, this book has its origins in a lecture series given by the internationally renowned authors. Written in an accessible, informal style, it fills a gap in the existing literature.

Lectures on Integrable Systems

Jens Hoppe
Lectures on Integrable Systems Book PDF

Author : Jens Hoppe
Publisher : Springer Science & Business Media
Page : 109 pages
File Size : 52,5 Mb
Release : 2008-09-15
Category : Science
ISBN : 9783540472742

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Lectures on Integrable Systems by Jens Hoppe Pdf

Mainly drawing on explicit examples, the author introduces the reader to themost recent techniques to study finite and infinite dynamical systems. Without any knowledge of differential geometry or lie groups theory the student can follow in a series of case studies the most recent developments. r-matrices for Calogero-Moser systems and Toda lattices are derived. Lax pairs for nontrivial infinite dimensionalsystems are constructed as limits of classical matrix algebras. The reader will find explanations of the approach to integrable field theories, to spectral transform methods and to solitons. New methods are proposed, thus helping students not only to understand established techniques but also to interest them in modern research on dynamical systems.

Introduction to Classical Integrable Systems

Olivier Babelon,Denis Bernard,Michel Talon
Introduction to Classical Integrable Systems Book PDF

Author : Olivier Babelon,Denis Bernard,Michel Talon
Publisher : Cambridge University Press
Page : 622 pages
File Size : 48,8 Mb
Release : 2003-04-17
Category : Mathematics
ISBN : 052182267X

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Introduction to Classical Integrable Systems by Olivier Babelon,Denis Bernard,Michel Talon Pdf

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Quantum Integrable Systems

Asesh Roy Chowdhury,Aninlya Ghose Choudhury
Quantum Integrable Systems Book PDF

Author : Asesh Roy Chowdhury,Aninlya Ghose Choudhury
Publisher : CRC Press
Page : 425 pages
File Size : 42,6 Mb
Release : 2004-01-28
Category : Science
ISBN : 9780203498019

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Quantum Integrable Systems by Asesh Roy Chowdhury,Aninlya Ghose Choudhury Pdf

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

Global Aspects of Classical Integrable Systems

Richard H. Cushman,Larry M. Bates
Global Aspects of Classical Integrable Systems Book PDF

Author : Richard H. Cushman,Larry M. Bates
Publisher : Birkhäuser
Page : 477 pages
File Size : 49,7 Mb
Release : 2015-06-01
Category : Science
ISBN : 9783034809184

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Global Aspects of Classical Integrable Systems by Richard H. Cushman,Larry M. Bates Pdf

This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2-dimensional harmonic oscillator, the geodesic flow on the 3-sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis.

Symmetries, Integrable Systems and Representations

Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy
Symmetries Integrable Systems and Representations Book PDF

Author : Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy
Publisher : Springer Science & Business Media
Page : 633 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447148630

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Symmetries, Integrable Systems and Representations by Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy Pdf

This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

Integrability, Quantization, and Geometry: I. Integrable Systems

Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman
Integrability Quantization and Geometry I Integrable Systems Book PDF

Author : Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman
Publisher : American Mathematical Soc.
Page : 516 pages
File Size : 44,5 Mb
Release : 2021-04-12
Category : Education
ISBN : 9781470455910

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Integrability, Quantization, and Geometry: I. Integrable Systems by Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman Pdf

This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.

Representation Theory, Mathematical Physics, and Integrable Systems

Anton Alekseev,Edward Frenkel,Marc Rosso,Ben Webster,Milen Yakimov
Representation Theory Mathematical Physics and Integrable Systems Book PDF

Author : Anton Alekseev,Edward Frenkel,Marc Rosso,Ben Webster,Milen Yakimov
Publisher : Springer Nature
Page : 652 pages
File Size : 51,6 Mb
Release : 2022-02-05
Category : Mathematics
ISBN : 9783030781484

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Representation Theory, Mathematical Physics, and Integrable Systems by Anton Alekseev,Edward Frenkel,Marc Rosso,Ben Webster,Milen Yakimov Pdf

Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.

An Introduction to Integrable Techniques for One-Dimensional Quantum Systems

Fabio Franchini
An Introduction to Integrable Techniques for One Dimensional Quantum Systems Book PDF

Author : Fabio Franchini
Publisher : Springer
Page : 180 pages
File Size : 53,7 Mb
Release : 2017-05-25
Category : Science
ISBN : 9783319484877

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An Introduction to Integrable Techniques for One-Dimensional Quantum Systems by Fabio Franchini Pdf

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.

Differential Geometry and Integrable Systems

Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita
Differential Geometry and Integrable Systems Book PDF

Author : Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita
Publisher : American Mathematical Soc.
Page : 349 pages
File Size : 52,6 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821829387

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Differential Geometry and Integrable Systems by Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita Pdf

Ideas and techniques from the theory of integrable systems are playing an increasingly important role in geometry. Thanks to the development of tools from Lie theory, algebraic geometry, symplectic geometry, and topology, classical problems are investigated more systematically. New problems are also arising in mathematical physics. A major international conference was held at the University of Tokyo in July 2000. It brought together scientists in all of the areas influenced by integrable systems. This book is the first of three collections of expository and research articles. This volume focuses on differential geometry. It is remarkable that many classical objects in surface theory and submanifold theory are described as integrable systems. Having such a description generally reveals previously unnoticed symmetries and can lead to surprisingly explicit solutions.Surfaces of constant curvature in Euclidean space, harmonic maps from surfaces to symmetric spaces, and analogous structures on higher-dimensional manifolds are some of the examples that have broadened the horizons of differential geometry, bringing a rich supply of concrete examples into the theory of integrable systems. Many of the articles in this volume are written by prominent researchers and will serve as introductions to the topics. It is intended for graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics. The second volume from this conference, also available from the 'AMS', is ""Integrable Systems, Topology, and Physics, Volume 309"" in the ""Contemporary Mathematics"" series. The forthcoming third volume will be published by the Mathematical Society of Japan and will be available outside of Japan from the 'AMS' in the ""Advanced Studies in Pure Mathematics"" series.

Complex Analysis, Riemann Surfaces and Integrable Systems

Sergey M. Natanzon
Complex Analysis Riemann Surfaces and Integrable Systems Book PDF

Author : Sergey M. Natanzon
Publisher : Springer Nature
Page : 148 pages
File Size : 46,9 Mb
Release : 2020-01-03
Category : Mathematics
ISBN : 9783030346409

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Complex Analysis, Riemann Surfaces and Integrable Systems by Sergey M. Natanzon Pdf

This book is devoted to classical and modern achievements in complex analysis. In order to benefit most from it, a first-year university background is sufficient; all other statements and proofs are provided. We begin with a brief but fairly complete course on the theory of holomorphic, meromorphic, and harmonic functions. We then present a uniformization theory, and discuss a representation of the moduli space of Riemann surfaces of a fixed topological type as a factor space of a contracted space by a discrete group. Next, we consider compact Riemann surfaces and prove the classical theorems of Riemann-Roch, Abel, Weierstrass, etc. We also construct theta functions that are very important for a range of applications. After that, we turn to modern applications of this theory. First, we build the (important for mathematics and mathematical physics) Kadomtsev-Petviashvili hierarchy and use validated results to arrive at important solutions to these differential equations. We subsequently use the theory of harmonic functions and the theory of differential hierarchies to explicitly construct a conformal mapping that translates an arbitrary contractible domain into a standard disk – a classical problem that has important applications in hydrodynamics, gas dynamics, etc. The book is based on numerous lecture courses given by the author at the Independent University of Moscow and at the Mathematics Department of the Higher School of Economics.

Integrable Systems of Classical Mechanics and Lie Algebras Volume I

PERELOMOV
Integrable Systems of Classical Mechanics and Lie Algebras Volume I Book PDF

Author : PERELOMOV
Publisher : Birkhäuser
Page : 312 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034892575

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Integrable Systems of Classical Mechanics and Lie Algebras Volume I by PERELOMOV Pdf

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.

Integrable Systems

Ahmed Lesfari
Integrable Systems Book PDF

Author : Ahmed Lesfari
Publisher : John Wiley & Sons
Page : 340 pages
File Size : 42,9 Mb
Release : 2022-06-22
Category : Mathematics
ISBN : 9781119988571

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Integrable Systems by Ahmed Lesfari Pdf

This book illustrates the powerful interplay between topological, algebraic and complex analytical methods, within the field of integrable systems, by addressing several theoretical and practical aspects. Contemporary integrability results, discovered in the last few decades, are used within different areas of mathematics and physics. Integrable Systems incorporates numerous concrete examples and exercises, and covers a wealth of essential material, using a concise yet instructive approach. This book is intended for a broad audience, ranging from mathematicians and physicists to students pursuing graduate, Masters or further degrees in mathematics and mathematical physics. It also serves as an excellent guide to more advanced and detailed reading in this fundamental area of both classical and contemporary mathematics.

Integrable Systems

Jean Louis Verdier,Pierre Cartier,Yvette Kosmann-Schwarzbach
Integrable Systems Book PDF

Author : Jean Louis Verdier,Pierre Cartier,Yvette Kosmann-Schwarzbach
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 41,8 Mb
Release : 1993
Category : Mathematics
ISBN : 0817636536

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Integrable Systems by Jean Louis Verdier,Pierre Cartier,Yvette Kosmann-Schwarzbach Pdf

This book contains fifteen articles by eminent specialists in the theory of completely integrable systems, bringing together the diverse approaches to classical and quantum integrable systems and covering the principal current research developments.