Quantum Integrable Systems

Quantum Integrable Systems Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Quantum Integrable Systems book. This book definitely worth reading, it is an incredibly well-written.

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 : 50,6 Mb
Release : 2019-07-23
Category : Science
ISBN : 9783030241988

Get Book

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.

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 : 54,6 Mb
Release : 2004-01-28
Category : Science
ISBN : 9780203498019

Get Book

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

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 : 51,9 Mb
Release : 2017-05-25
Category : Science
ISBN : 9783319484877

Get Book

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.

From Quantum Cohomology to Integrable Systems

Martin A. Guest
From Quantum Cohomology to Integrable Systems Book PDF

Author : Martin A. Guest
Publisher : OUP Oxford
Page : 336 pages
File Size : 40,9 Mb
Release : 2008-03-13
Category : Mathematics
ISBN : 9780191606960

Get Book

From Quantum Cohomology to Integrable Systems by Martin A. Guest Pdf

Quantum cohomology has its origins in symplectic geometry and algebraic geometry, but is deeply related to differential equations and integrable systems. This text explains what is behind the extraordinary success of quantum cohomology, leading to its connections with many existing areas of mathematics as well as its appearance in new areas such as mirror symmetry. Certain kinds of differential equations (or D-modules) provide the key links between quantum cohomology and traditional mathematics; these links are the main focus of the book, and quantum cohomology and other integrable PDEs such as the KdV equation and the harmonic map equation are discussed within this unified framework. Aimed at graduate students in mathematics who want to learn about quantum cohomology in a broad context, and theoretical physicists who are interested in the mathematical setting, the text assumes basic familiarity with differential equations and cohomology.

Quantum Group And Quantum Integrable Systems - Nankai Lectures On Mathematical Physics

Mo-lin Ge
Quantum Group And Quantum Integrable Systems Nankai Lectures On Mathematical Physics Book PDF

Author : Mo-lin Ge
Publisher : World Scientific
Page : 242 pages
File Size : 54,5 Mb
Release : 1992-05-30
Category : Electronic
ISBN : 9789814555838

Get Book

Quantum Group And Quantum Integrable Systems - Nankai Lectures On Mathematical Physics by Mo-lin Ge Pdf

This volume contains the lectures given by the three speakers, M Jimbo, P P Kulish and E K Sklyanin, who are outstanding experts in their field. It is essential reading to those working in the fields of Quantum Groups, and Integrable Systems.

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 : 52,9 Mb
Release : 2008-09-15
Category : Science
ISBN : 9783540472742

Get Book

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.

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 : 40,8 Mb
Release : 2021-04-12
Category : Education
ISBN : 9781470455910

Get Book

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.

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 : 49,9 Mb
Release : 2003-04-17
Category : Mathematics
ISBN : 052182267X

Get Book

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

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.

Integrable Systems in Quantum Field Theory and Statistical Mechanics

M. Jimbo,T. Miwa,A. Tsuchiya
Integrable Systems in Quantum Field Theory and Statistical Mechanics Book PDF

Author : M. Jimbo,T. Miwa,A. Tsuchiya
Publisher : Elsevier
Page : 695 pages
File Size : 51,7 Mb
Release : 2014-05-19
Category : Science
ISBN : 9781483295251

Get Book

Integrable Systems in Quantum Field Theory and Statistical Mechanics by M. Jimbo,T. Miwa,A. Tsuchiya Pdf

Integrable Sys Quantum Field Theory

Integrable Systems, Quantum Groups, and Quantum Field Theories

Alberto Ibort,M.A. Rodríguez
Integrable Systems Quantum Groups and Quantum Field Theories Book PDF

Author : Alberto Ibort,M.A. Rodríguez
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401119801

Get Book

Integrable Systems, Quantum Groups, and Quantum Field Theories by Alberto Ibort,M.A. Rodríguez Pdf

In many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects.

Classical and Quantum Nonlinear Integrable Systems

A Kundu
Classical and Quantum Nonlinear Integrable Systems Book PDF

Author : A Kundu
Publisher : CRC Press
Page : 310 pages
File Size : 49,5 Mb
Release : 2019-04-23
Category : Science
ISBN : 9781420034615

Get Book

Classical and Quantum Nonlinear Integrable Systems by A Kundu Pdf

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

New Trends in Quantum Integrable Systems

Boris Feigin,Michio Jimbo,Masato Okado
New Trends in Quantum Integrable Systems Book PDF

Author : Boris Feigin,Michio Jimbo,Masato Okado
Publisher : World Scientific
Page : 517 pages
File Size : 51,6 Mb
Release : 2010-10-29
Category : Mathematics
ISBN : 9789814324366

Get Book

New Trends in Quantum Integrable Systems by Boris Feigin,Michio Jimbo,Masato Okado Pdf

The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009. As a continuation of the RIMS Research Project "Method of Algebraic Analysis in Integrable Systems" in 2004, the workshop's aim was to cover exciting new developments that have emerged during the recent years. Collected here are research articles based on the talks presented at the workshop, including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models, integrable models in quantum field theory, conformal field theory, mathematical aspects of Bethe ansatz, special functions and integrable differential/difference equations, representation theory of infinite dimensional algebras, integrable models and combinatorics. Through these topics, the reader is exposed to the most recent developments in the field of quantum integrable systems and related areas of mathematical physics.

New Trends in Quantum Integrable Systems

Boris Feigin
New Trends in Quantum Integrable Systems Book PDF

Author : Boris Feigin
Publisher : World Scientific
Page : 128 pages
File Size : 55,8 Mb
Release : 2014-05-14
Category : Electronic
ISBN : 9789814462921

Get Book

New Trends in Quantum Integrable Systems by Boris Feigin Pdf

The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto Japan from 27 to 31 July 2009. As a continuation of the RIMS Research Project a Method of Algebraic Analysis in Integrable Systemsa in 2004 the workshop's aim was to cover exciting new developments that have emerged during the recent years.Collected here are research articles based on the talks presented at the workshop including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models integrable models in quantum field theory conformal field theory mathematical aspects of Bethe ansatz special functions and integrable differential/difference equations representation theory of infinite dimensional algebras integrable models and combinatorics.Through these topics the reader can learn about the most recent developments in the field of quantum integrable systems and related areas of mathematical physics."

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 : 54,9 Mb
Release : 2022-02-05
Category : Mathematics
ISBN : 9783030781484

Get Book

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.

What Is Integrability?

Vladimir E. Zakharov
What Is Integrability Book PDF

Author : Vladimir E. Zakharov
Publisher : Springer Science & Business Media
Page : 339 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642887031

Get Book

What Is Integrability? by Vladimir E. Zakharov Pdf

The idea of devoting a complete book to this topic was born at one of the Workshops on Nonlinear and Turbulent Processes in Physics taking place reg ularly in Kiev. With the exception of E. D. Siggia and N. Ercolani, all authors of this volume were participants at the third of these workshops. All of them were acquainted with each other and with each other's work. Yet it seemed to be somewhat of a discovery that all of them were and are trying to understand the same problem - the problem of integrability of dynamical systems, primarily Hamiltonian ones with an infinite number of degrees of freedom. No doubt that they (or to be more exact, we) were led to this by the logical process of scientific evolution which often leads to independent, almost simultaneous discoveries. Integrable, or, more accurately, exactly solvable equations are essential to theoretical and mathematical physics. One could say that they constitute the "mathematical nucleus" of theoretical physics whose goal is to describe real clas sical or quantum systems. For example, the kinetic gas theory may be considered to be a theory of a system which is trivially integrable: the system of classical noninteracting particles. One of the main tasks of quantum electrodynamics is the development of a theory of an integrable perturbed quantum system, namely, noninteracting electromagnetic and electron-positron fields.