On The Eigenstates Of The Elliptic Calogero Moser Model
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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."
Universality Of Calogero Moser Model
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Author : M. A. Olshanetsky
language : en
Publisher:
Release Date : 2004
Universality Of Calogero Moser Model written by M. A. Olshanetsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Elliptic functions categories.
Abstract: "In this review we explain interrelations between the Elliptic Calogero-Moser model, the integrable Elliptic Euler-Arnold top, monodromy preserving equations and the Knizhnik-Zamolodchikov-Bernard equation on a torus."
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.
Symmetry And Perturbation Theory Proceedings Of The International Conference On Spt2004
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Author : Giuseppe Gaeta
language : en
Publisher: World Scientific
Release Date : 2005-01-25
Symmetry And Perturbation Theory Proceedings Of The International Conference On Spt2004 written by Giuseppe Gaeta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-25 with Science categories.
This proceedings volume is a collection of papers presented at the International Conference on SPT2004 focusing on symmetry, perturbation theory, and integrability.The book provides an updated overview of the recent developments in the various different fields of nonlinear dynamics, covering both theory and applications. Special emphasis is given to algebraic and geometric integrability, solutions to the N-body problem of the “choreography” type, geometry and symmetry of dynamical systems, integrable evolution equations, various different perturbation theories, and bifurcation analysis.The contributors to this volume include some of the leading scientists in the field, among them: I Anderson, D Bambusi, S Benenti, S Bolotin, M Fels, W Y Hsiang, V Matveev, A V Mikhailov, P J Olver, G Pucacco, G Sartori, M A Teixeira, S Terracini, F Verhulst and I Yehorchenko.
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.
Jack Hall Littlewood And Macdonald Polynomials
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Author : Vadim B. Kuznetsov
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Jack Hall Littlewood And Macdonald Polynomials written by Vadim B. Kuznetsov 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 2006 with Mathematics categories.
The subject of symmetric functions began with the work of Jacobi, Schur, Weyl, Young and others on the Schur polynomials. In the 1950's and 60's, far-reaching generalizations of Schur polynomials were obtained by Hall and Littlewood (independently) and, in a different direction, by Jack. In the 1980's, Macdonald unified these developments by introducing a family of polynomials associated with arbitrary root systems. The last twenty years have witnessed considerable progress in this area, revealing new and profound connections with representation theory, algebraic geometry, combinatorics, special functions, classical analysis and mathematical physics. All these fields and more are represented in this volume, which contains the proceedings of a conference on Jack, Hall-Littlewood and Macdonald polynomials held at ICMS, Edinburgh, during September 23-26, 2003. of historical material, including brief biographies of Hall, Littlewood, Jack and Macdonald; the original papers of Littlewood and Jack; notes on Hall's work by Macdonald; and a recently discovered unpublished manuscript by Jack (annotated by Macdonald). The book will be invaluable to students and researchers who wish to learn about this beautiful and exciting subject.
Integrability Of Difference Calogero Moser Systems
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Author : Jan Felipe Van Diejen
language : en
Publisher:
Release Date : 1993
Integrability Of Difference Calogero Moser Systems written by Jan Felipe Van Diejen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Elliptic functions categories.
Abstract: "A general class of n-particle difference Calogero-Moser systems with elliptic potentials is introduced. Besides the step size and two periods, the Hamiltonian depends on nine coupling constants. We prove the quantum integrability of the model for n = 2 and present partial results for n [> or =] 3. In degenerate cases (rational, hyperbolic or trigonometric limit), the integrability follows for arbitrary particle number from previous work connected with the multivariable q-polynomials of Koornwinder and Macdonald. Liouville integrability of the corresponding classical systems follows as a corollary. Limit transitions lead to various well-known models such as the nonrelativistic Calogero-Moser systems associated with classical root systems and the relativistic Calogero-Moser system."
Integrable Quantum Field Theories And Their Application
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Author : Changrim Ahn
language : en
Publisher: World Scientific
Release Date : 2001
Integrable Quantum Field Theories And Their Application written by Changrim Ahn and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Applications of reflection amplitudes in Toda-type theories / C. Ahn, C. Kim and C. Rim -- Lax pairs and involutive Hamiltonians for CN and BCN Ruijsenaars-Schneider models / Kai Chen, B.-Y. Hou and W.-L. Yang -- Fateev's models and their applications / D. Controzzi and A.M. Tsvelik -- The ODE/IM correspondence / P. Dorey, C. Dunning and R. Tateo -- Integrable sigma models / P. Fendley -- Lorentz lattice gases and spin chains / M.J. Martins -- Quantum Calogero-Moser models for any root system / R. Sasaki -- Quasi-particles in conformal field theories for fractional quantum Hall systems / K. Schoutens and R.A.J. van Elburg -- Towards form factors in finite volume / F.A. Smirnov -- Static and dynamic properties of trapped Bose-Einstein condensates / T. Tsurumi, H. Morise and M. Wadati -- Integrability of the Calogero Model: Conserved quantities, the classical general solution and the quantum orthogonal basis / H. Ujino, A. Nishino and M. Wadati -- Conformal boundary conditions / J.-B. Zuber
Noncommutative Geometry And Representation Theory In Mathematical Physics
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Author : Jürgen Fuchs
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Noncommutative Geometry And Representation Theory In Mathematical Physics written by Jürgen Fuchs 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 2005 with Mathematics categories.
Mathematics provides a language in which to formulate the laws that govern nature. It is a language proven to be both powerful and effective. In the quest for a deeper understanding of the fundamental laws of physics, one is led to theories that are increasingly difficult to put to the test. In recent years, many novel questions have emerged in mathematical physics, particularly in quantum field theory. Indeed, several areas of mathematics have lately become increasingly influentialin physics and, in turn, have become influenced by developments in physics. Over the last two decades, interactions between mathematicians and physicists have increased enormously and have resulted in a fruitful cross-fertilization of the two communities. This volume contains the plenary talks fromthe international symposium on Noncommutative Geometry and Representation Theory in Mathematical Physics held at Karlstad University (Sweden) as a satellite conference to the Fourth European Congress of Mathematics. The scope of the volume is large and its content is relevant to various scientific communities interested in noncommutative geometry and representation theory. It offers a comprehensive view of the state of affairs for these two branches of mathematical physics. The book is suitablefor graduate students and researchers interested in mathematical physics.
Integrable Quantum Field Theories And Their Applications Procs Of The Apctp Winter School
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Author : Changrim Ahn
language : en
Publisher: World Scientific
Release Date : 2001-09-25
Integrable Quantum Field Theories And Their Applications Procs Of The Apctp Winter School written by Changrim Ahn and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-09-25 with Science categories.
This volume includes several lecture notes on the fundamentals and elementary techniques of integrable field theories and on their applications to low-dimensional physics systems contributed by leading scientists in the respective fields. The main topics covered are various aspects of the thermodynamic Bethe ansatz, form factors, Calogero (and related) models, sigma models, conformal boundary conditions, etc. The volume presents both pedagogical material and a current research trend in the field.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)