Integrable Systems From Classical To Quantum
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Superintegrability In Classical And Quantum Systems
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Author : Piergiulio Tempesta
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Superintegrability In Classical And Quantum Systems written by Piergiulio Tempesta and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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 title is based on the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathematiques in Montreal (Quebec).
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
Integrable Systems
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Author : John P. Harnad
language : en
Publisher: American Mathematical Soc.
Release Date :
Integrable Systems written by John P. Harnad and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
A dozen papers provide a cross-section of current research into integrable systems. Contributors from Europe, North America, and the Asia explore such aspects as the geometry of generalized Hitchin systems, the quantum inverse scattering problem and correlation functions of integrable models, characteristic systems on Poisson Lie groups and their quantization, special functions associated with Calogero-Moser type quantum systems, and the universality of the distribution functions of random matrix theory. There is no index. Annotation copyrighted by Book News, Inc., Portland, OR
Yang Baxter Equation In Integrable Systems
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Author : Michio Jimbo
language : en
Publisher: World Scientific
Release Date : 1990
Yang Baxter Equation In Integrable Systems written by Michio Jimbo 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 with Science categories.
This volume will be the first reference book devoted specially to the Yang-Baxter equation. The subject relates to broad areas including solvable models in statistical mechanics, factorized S matrices, quantum inverse scattering method, quantum groups, knot theory and conformal field theory. The articles assembled here cover major works from the pioneering papers to classical Yang-Baxter equation, its quantization, variety of solutions, constructions and recent generalizations to higher genus solutions.
Calogero Moser Systems And Representation Theory
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Author : Pavel I. Etingof
language : en
Publisher: European Mathematical Society
Release Date : 2007
Calogero Moser Systems And Representation Theory written by Pavel I. Etingof and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Calogero-Moser systems, which were originally discovered by specialists in integrable systems, are currently at the crossroads of many areas of mathematics and within the scope of interests of many mathematicians. More specifically, these systems and their generalizations turned out to have intrinsic connections with such fields as algebraic geometry (Hilbert schemes of surfaces), representation theory (double affine Hecke algebras, Lie groups, quantum groups), deformation theory (symplectic reflection algebras), homological algebra (Koszul algebras), Poisson geometry, etc. The goal of the present lecture notes is to give an introduction to the theory of Calogero-Moser systems, highlighting their interplay with these fields. Since these lectures are designed for non-experts, the author gives short introductions to each of the subjects involved and provides a number of exercises.
Factorization And Integrable Systems
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Author : Israel Gohberg
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Factorization And Integrable Systems written by Israel Gohberg and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In September 2000 a Summer School on "Factorization and Integrable Systems" was held at the University of Algarve in Portugal. The main aim of the school was to review the modern factorization theory and its application to classical and quantum integrable systems. The program consisted of a number of short courses given by leading experts in the field. The lecture notes of the courses have been specially prepared for publication in this volume. The book consists of four contributions. I. Gohberg, M.A. Kaashoek and I.M. Spitkovsky present an extensive review of the factorization theory of matrix functions relative to a curve, with emphasis on the developments of the last 20-25 years. The group-theoretical approach to classical integrable systems is reviewed by M.A. Semenov-Tian-Shansky. P.P. Kulish surveyed the quantum inverse scattering method using the isotropic Heisenberg spin chain as the main example.
Integrable And Superintegrable Systems
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Author : Boris A. Kupershmidt
language : en
Publisher: World Scientific
Release Date : 1990
Integrable And Superintegrable Systems written by Boris A. Kupershmidt 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 with Mathematics 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.
Quantum Versus Classical Mechanics And Integrability Problems
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Author : Maciej Błaszak
language : en
Publisher: Springer
Release Date : 2019-06-11
Quantum Versus Classical Mechanics And Integrability Problems written by Maciej Błaszak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-11 with Science categories.
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.
Proceedings Of The Workshop Nonlinear Physics Theory And Experiment Ii
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Author : Mark J. Ablowitz
language : en
Publisher: World Scientific
Release Date : 2003
Proceedings Of The Workshop Nonlinear Physics Theory And Experiment Ii written by Mark J. Ablowitz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Science categories.
The theory of solitons involves a broad variety of mathematical methods and appears in many areas of physics, technology, biology, and pure and applied mathematics. In this book, emphasis is placed on both theory (considering mathematical approaches for classical and quantum nonlinear systems ? both continuous and discrete) and experiment (with special discussions on high bit rate optical communications and pulse dynamics in optical materials).
Nonlinear Physics Theory And Experiment Ii Proceedings Of The Workshop
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Author : Barbara Prinari
language : en
Publisher: World Scientific
Release Date : 2003-04-08
Nonlinear Physics Theory And Experiment Ii Proceedings Of The Workshop written by Barbara Prinari and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-08 with Science categories.
The theory of solitons involves a broad variety of mathematical methods and appears in many areas of physics, technology, biology, and pure and applied mathematics. In this book, emphasis is placed on both theory (considering mathematical approaches for classical and quantum nonlinear systems — both continuous and discrete) and experiment (with special discussions on high bit rate optical communications and pulse dynamics in optical materials).