Elements Of Classical And Quantum 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 : 47,9 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.

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 : 40,5 Mb
Release : 2019-04-23
Category : Science
ISBN : 9781420034615

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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

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 : 55,8 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

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 : 55,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401119801

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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.

Integrable Systems And Quantum Groups

Mauro Carfora,Maurizio Martellini,Annalisa Marzuoli
Integrable Systems And Quantum Groups Book PDF

Author : Mauro Carfora,Maurizio Martellini,Annalisa Marzuoli
Publisher : World Scientific
Page : 194 pages
File Size : 46,9 Mb
Release : 1992-04-30
Category : Electronic
ISBN : 9789814554763

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Integrable Systems And Quantum Groups by Mauro Carfora,Maurizio Martellini,Annalisa Marzuoli Pdf

This volume contains lectures on recent advances in the theory of integrable systems and quantum groups. It introduces the reader to attractive areas of current research.

Classical and Quantum Nonlinear Integrable Systems

A Kundu
Classical and Quantum Nonlinear Integrable Systems Book PDF

Author : A Kundu
Publisher : CRC Press
Page : 166 pages
File Size : 43,8 Mb
Release : 2019-04-23
Category : Science
ISBN : 9780429525049

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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

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 : 43,7 Mb
Release : 1992-05-30
Category : Electronic
ISBN : 9789814555838

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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.

Quantum versus Classical Mechanics and Integrability Problems

Maciej Błaszak
Quantum versus Classical Mechanics and Integrability Problems Book PDF

Author : Maciej Błaszak
Publisher : Springer
Page : 460 pages
File Size : 49,8 Mb
Release : 2020-08-14
Category : Science
ISBN : 3030183815

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Quantum versus Classical Mechanics and Integrability Problems by Maciej Błaszak Pdf

This accessible monograph introduces physicists to the general relation between classical and quantum mechanics based on the mathematical idea of deformation quantization and describes an original approach to the theory of quantum integrable systems developed by the author.The first goal of the book is to develop of a common, coordinate free formulation of classical and quantum Hamiltonian mechanics, framed in common mathematical language.In particular, a coordinate free model of quantum Hamiltonian systems in Riemannian spaces is formulated, based on the mathematical idea of deformation quantization, as a complete physical theory with an appropriate mathematical accuracy.The second goal is to develop of a theory which allows for a deeper understanding of classical and quantum integrability. For this reason the modern separability theory on both classical and quantum level is presented. In particular, the book presents a modern geometric separability theory, based on bi-Poissonian and bi-presymplectic representations of finite dimensional Liouville integrable systems and their admissible separable quantizations.The book contains also a generalized theory of classical Stäckel transforms and the discussion of the concept of quantum trajectories.In order to make the text consistent and self-contained, the book starts with a compact overview of mathematical tools necessary for understanding the remaining part of the book. However, because the book is dedicated mainly to physicists, despite its mathematical nature, it refrains from highlighting definitions, theorems or lemmas.Nevertheless, all statements presented are either proved or the reader is referred to the literature where the proof is available.

Integrable Systems

John P. Harnad,Gert Sabidussi,Pavel Winternitz
Integrable Systems Book PDF

Author : John P. Harnad,Gert Sabidussi,Pavel Winternitz
Publisher : American Mathematical Soc.
Page : 284 pages
File Size : 42,9 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 082187022X

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Integrable Systems by John P. Harnad,Gert Sabidussi,Pavel Winternitz Pdf

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.

Quantum Versus Classical Mechanics and Integrability Problems

Maciej BÅ‚aszak
Quantum Versus Classical Mechanics and Integrability Problems Book PDF

Author : Maciej BÅ‚aszak
Publisher : Unknown
Page : 460 pages
File Size : 49,7 Mb
Release : 2019
Category : Mechanics
ISBN : 3030183807

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Quantum Versus Classical Mechanics and Integrability Problems by Maciej BÅ‚aszak Pdf

This accessible monograph introduces physicists to the general relation between classical and quantum mechanics based on the mathematical idea of deformation quantization and describes an original approach to the theory of quantum integrable systems developed by the author. The first goal of the book is to develop of a common, coordinate free formulation of classical and quantum Hamiltonian mechanics, framed in common mathematical language. In particular, a coordinate free model of quantum Hamiltonian systems in Riemannian spaces is formulated, based on the mathematical idea of deformation quantization, as a complete physical theory with an appropriate mathematical accuracy. The second goal is to develop of a theory which allows for a deeper understanding of classical and quantum integrability. For this reason the modern separability theory on both classical and quantum level is presented. In particular, the book presents a modern geometric separability theory, based on bi-Poissonian and bi-presymplectic representations of finite dimensional Liouville integrable systems and their admissible separable quantizations. The book contains also a generalized theory of classical Stäckel transforms and the discussion of the concept of quantum trajectories. In order to make the text consistent and self-contained, the book starts with a compact overview of mathematical tools necessary for understanding the remaining part of the book. However, because the book is dedicated mainly to physicists, despite its mathematical nature, it refrains from highlighting definitions, theorems or lemmas. Nevertheless, all statements presented are either proved or the reader is referred to the literature where the proof is available.

Superintegrability in Classical and Quantum Systems

Piergiulio Tempesta
Superintegrability in Classical and Quantum Systems Book PDF

Author : Piergiulio Tempesta
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 54,9 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821833292

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Superintegrability in Classical and Quantum Systems by Piergiulio Tempesta Pdf

The volume is suitable for graduate students and research mathematicians interested in integrable systems.

Elements of Classical and Quantum Physics

Michele Cini
Elements of Classical and Quantum Physics Book PDF

Author : Michele Cini
Publisher : Springer
Page : 390 pages
File Size : 43,8 Mb
Release : 2018-02-09
Category : Science
ISBN : 9783319713304

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Elements of Classical and Quantum Physics by Michele Cini Pdf

This book presents the basic elements of theoretical physics in a highly accessible, captivating way for university students in the third year of a degree in physics. It covers analytical mechanics, thermodynamics and statistical physics, special and general relativity and non-relativistic quantum theory, fully developing the necessary mathematical methods beyond standard calculus. The central theme is scientific curiosity and the main focus is on the experimental meaning of all quantities and equations. Several recent verifications of General Relativity are presented, with emphasis on the physical effects – why they were predicted to exist and what signals they were seen to produce. Similarly, the basic reasons why superconductors have zero resistance and are perfect diamagnets are pinpointed. Quantum Eraser Experiments and Delayed Choice Experiments are described. Many statements of Quantum Theory are a challenge to common sense and some crucial predictions have often been considered hard to believe and have been tested experimentally. The book examines the EPR paradox, Bell states and teleportation. To show the beauty and richness of the subject, various topics from different areas of Physics are covered. These include: discrete quantum models and lattices (periodic and not), Casimir effect, Anyons, Fano Resonances, the Hanbury Brown and Twiss effect, the Aharonov-Bohm effect, the Meitner-Auger effect, Squeezed Light, the Rabi model, neutrino oscillations, aspects of Quantum Transport, Quantum Pumping, and Berry phases, black holes and cosmological problems.

Superintegrability in Classical and Quantum Systems

Piergiulio Tempesta
Superintegrability in Classical and Quantum Systems Book PDF

Author : Piergiulio Tempesta
Publisher : Unknown
Page : 347 pages
File Size : 46,8 Mb
Release : 2004
Category : Differential equations, Partial
ISBN : 1470439514

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Superintegrability in Classical and Quantum Systems by Piergiulio Tempesta Pdf

Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This proceedings volume grew out of the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathématiques in Montréal (Quebec). The meeting brought together scientists working in the area of finite-dimensional integrable systems to discuss new developments in this active field of interest. Properties possessed by these systems are manifold. In classical mechanics, they.

Integrable Systems

Ahmed Lesfari
Integrable Systems Book PDF

Author : Ahmed Lesfari
Publisher : John Wiley & Sons
Page : 340 pages
File Size : 41,7 Mb
Release : 2022-07-13
Category : Mathematics
ISBN : 9781786308276

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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.

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 : 50,9 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.