Integrable Models

Author : Gleb Arutyunov
Publisher : Springer
ISBN 13 : 303024198X
Total Pages : 414 pages
Book Rating : 4.88/5 ( download)

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Download or read book Elements of Classical and Quantum Integrable Systems written by Gleb Arutyunov and published by Springer. This book was released on 2019-07-23 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Olivier Babelon
Publisher : Cambridge University Press
ISBN 13 : 9780521822671
Total Pages : 622 pages
Book Rating : 4.7X/5 ( download)

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Download or read book Introduction to Classical Integrable Systems written by Olivier Babelon and published by Cambridge University Press. This book was released on 2003-04-17 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Ashok Das
Publisher : World Scientific
ISBN 13 : 9814507385
Total Pages : 358 pages
Book Rating : 4.87/5 ( download)

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Download or read book Integrable Models written by Ashok Das and published by World Scientific. This book was released on 1989-04-01 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Fabio Franchini
Publisher : Springer
ISBN 13 : 3319484877
Total Pages : 180 pages
Book Rating : 4.77/5 ( download)

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Download or read book An Introduction to Integrable Techniques for One-Dimensional Quantum Systems written by Fabio Franchini and published by Springer. This book was released on 2017-05-25 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Ashok Das
Publisher : World Scientific
ISBN 13 : 9789971509118
Total Pages : 362 pages
Book Rating : 4.13/5 ( download)

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Download or read book Integrable Models written by Ashok Das and published by World Scientific. This book was released on 1989 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: http://www.worldscientific.com/worldscibooks/10.1142/0858

Author : N.J. Hitchin
Publisher : Oxford University Press, USA
ISBN 13 : 0199676771
Total Pages : 148 pages
Book Rating : 4.74/5 ( download)

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Download or read book Integrable Systems written by N.J. Hitchin and published by Oxford University Press, USA. This book was released on 2013-03-14 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : F A Smirnov
Publisher : World Scientific
ISBN 13 : 9814506907
Total Pages : 224 pages
Book Rating : 4.08/5 ( download)

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Download or read book Form Factors In Completely Integrable Models Of Quantum Field Theory written by F A Smirnov and published by World Scientific. This book was released on 1992-08-07 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph summarizes recent achievements in the calculation of matrix elements of local operators (form factors) for completely integrable models. Particularly, it deals with sine-Gordon, chiral Gross-Neven and O(3) nonlinear s models. General requirements on form factors are formulated and explicit formulas for form factors of most fundamental local operators are presented for the above mentioned models.

Author : Richard H. Cushman
Publisher : Birkhäuser
ISBN 13 : 3034809182
Total Pages : 493 pages
Book Rating : 4.84/5 ( download)

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Download or read book Global Aspects of Classical Integrable Systems written by Richard H. Cushman and published by Birkhäuser. This book was released on 2015-06-01 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Sergey Novikov
Publisher : American Mathematical Soc.
ISBN 13 : 1470455919
Total Pages : 516 pages
Book Rating : 4.10/5 ( download)

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Download or read book Integrability, Quantization, and Geometry: I. Integrable Systems written by Sergey Novikov and published by American Mathematical Soc.. This book was released on 2021-04-12 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jens Hoppe
Publisher : Springer Science & Business Media
ISBN 13 : 3540472746
Total Pages : 109 pages
Book Rating : 4.42/5 ( download)

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Download or read book Lectures on Integrable Systems written by Jens Hoppe and published by Springer Science & Business Media. This book was released on 2008-09-15 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.