Calogero Moser Sutherland Models
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Calogero Moser Sutherland Models
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Author : Jan F. van Diejen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Calogero Moser Sutherland Models written by Jan F. van Diejen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
In the 1970s F. Calogero and D. Sutherland discovered that for certain potentials in one-dimensional systems, but for any number of particles, the Schrödinger eigenvalue problem is exactly solvable. Until then, there was only one known nontrivial example of an exactly solvable quantum multi-particle problem. J. Moser subsequently showed that the classical counterparts to these models is also amenable to an exact analytical approach. The last decade has witnessed a true explosion of activities involving Calogero-Moser-Sutherland models, and these now play a role in research areas ranging from theoretical physics (such as soliton theory, quantum field theory, string theory, solvable models of statistical mechanics, condensed matter physics, and quantum chaos) to pure mathematics (such as representation theory, harmonic analysis, theory of special functions, combinatorics of symmetric functions, dynamical systems, random matrix theory, and complex geometry). The aim of this volume is to provide an overview of the many branches into which research on CMS systems has diversified in recent years. The contributions are by leading researchers from various disciplines in whose work CMS systems appear, either as the topic of investigation itself or as a tool for further applications.
Superintegrability In Classical And Quantum Systems
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Author : P. Tempesta, P. Winternitz, J. Harnad, W. Miller, Jr., G. Pogosyan, and M. Rodriguez
language : en
Publisher: American Mathematical Soc.
Release Date :
Superintegrability In Classical And Quantum Systems written by P. Tempesta, P. Winternitz, J. Harnad, W. Miller, Jr., G. Pogosyan, and M. Rodriguez 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 Differential equations, Partial 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).
On The Eigenstates Of The Elliptic Calogero Moser Model
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Author : Kouichi Takemura
language : en
Publisher:
Release Date : 2000
On The Eigenstates Of The Elliptic Calogero Moser Model written by Kouichi Takemura and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Elliptic functions categories.
Abstract: "It is known that the trigonometric Calogero-Sutherland model is obtained by the trigonometric limit (r -> [square root of -1][infinity]) of the elliptic Calogero-Moser model, where (1,r) is a basic period of the elliptic function. We show that for all square-integrable eigenstates and eigenvalues of the Hamiltonian of the Calogero-Sutherland model, if exp(2[pi][square root of -1]r) is small enough then there exist square-integrable eigenstates and eigenvalues of the Hamiltonian of the elliptic Calogero-Moser model which converge to the ones of the Calogero-Sutherland model for the 2-particle and the coupling constant l is positive integer cases and the 3-particle and l=1 case. In other words, we justify the regular perturbation with respect to the parameter exp(2[pi][square root of -1]r). With some assumptions, we show analogous results for N-particle and l is positive integer cases."
Group 24
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Author : J.P Gazeau
language : en
Publisher: CRC Press
Release Date : 2003-11-30
Group 24 written by J.P Gazeau and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-30 with Mathematics categories.
One of the most enduring elements in theoretical physics has been group theory. GROUP 24: Physical and Mathematical Aspects of Symmetries provides an important selection of informative articles describing recent advances in the field. The applications of group theory presented in this book deal not only with the traditional fields of physics, but also include such disciplines as chemistry and biology. Awarded the Wigner Medal and the Weyl Prize, respectively, H.J. Lipkin and E. Frenkel begin the volume with their contributions. Plenary session contributions are represented by 18 longer articles, followed by nearly 200 shorter articles. The book also presents coherent states, wavelets, and applications and quantum group theory and integrable systems in two separate sections. As a record of an international meeting devoted to the physical and mathematical aspects of group theory, GROUP 24: Physical and Mathematical Aspects of Symmetries constitutes an essential reference for all researchers interested in various current developments related to the important concept of symmetry.
Elements Of Classical And Quantum Integrable Systems
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Author : Gleb Arutyunov
language : en
Publisher: Springer
Release Date : 2019-07-23
Elements Of Classical And Quantum Integrable Systems written by Gleb Arutyunov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-23 with Science categories.
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.
Pt Symmetry
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Author : Carl M Bender
language : en
Publisher: World Scientific Publishing
Release Date : 2018-11-22
Pt Symmetry written by Carl M Bender and has been published by World Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-22 with Science categories.
Originated by the author in 1998, the field of PT (parity-time) symmetry has become an extremely active and exciting area of research. PT-symmetric quantum and classical systems have theoretical, experimental, and commercial applications, and have been the subject of many journal articles, PhD theses, conferences, and symposia. Carl Bender's work has influenced major advances in physics and generations of students. This book is an accessible entry point to PT symmetry, ideal for students and scientists looking to begin their own research projects in this field.
Orthogonal Polynomials And Special Functions
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Author : Erik Koelink
language : en
Publisher: Springer
Release Date : 2003-07-03
Orthogonal Polynomials And Special Functions written by Erik Koelink and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-03 with Mathematics categories.
The set of lectures from the Summer School held in Leuven in 2002 provide an up-to-date account of recent developments in orthogonal polynomials and special functions, in particular for algorithms for computer algebra packages, 3nj-symbols in representation theory of Lie groups, enumeration, multivariable special functions and Dunkl operators, asymptotics via the Riemann-Hilbert method, exponential asymptotics and the Stokes phenomenon. Thenbsp;volume aims at graduate students and post-docs working in the field of orthogonal polynomials and special functions, and in related fields interacting with orthogonal polynomials, such as combinatorics, computer algebra, asymptotics, representation theory, harmonic analysis, differential equations, physics. The lectures are self-contained requiring onlynbsp;a basic knowledge of analysis and algebra, and each includes many exercises.
Integrability Quantization And Geometry I Integrable Systems
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Author : Sergey Novikov
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-04-12
Integrability Quantization And Geometry I Integrable Systems written by Sergey Novikov 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 2021-04-12 with Education categories.
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.
Analytic Extension Formulas And Their Applications
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Author : S. Saitoh
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Analytic Extension Formulas And Their Applications written by S. Saitoh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Analytic Extension is a mysteriously beautiful property of analytic functions. With this point of view in mind the related survey papers were gathered from various fields in analysis such as integral transforms, reproducing kernels, operator inequalities, Cauchy transform, partial differential equations, inverse problems, Riemann surfaces, Euler-Maclaurin summation formulas, several complex variables, scattering theory, sampling theory, and analytic number theory, to name a few. Audience: Researchers and graduate students in complex analysis, partial differential equations, analytic number theory, operator theory and inverse problems.
Journal Of Nonlinear Mathematical Physics
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Author :
language : en
Publisher: atlantis press
Release Date :
Journal Of Nonlinear Mathematical Physics written by and has been published by atlantis press this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.