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Titlebook: Calogero—Moser— Sutherland Models; Jan Felipe Diejen,Luc Vinet Book 2000 Springer Science+Business Media New York 2000 Potential.chaos.dif

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书目名称Calogero—Moser— Sutherland Models
编辑Jan Felipe Diejen,Luc Vinet
视频video
丛书名称CRM Series in Mathematical Physics
图书封面Titlebook: Calogero—Moser— Sutherland Models;  Jan Felipe Diejen,Luc Vinet Book 2000 Springer Science+Business Media New York 2000 Potential.chaos.dif
描述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 syst
出版日期Book 2000
关键词Potential; chaos; differential equation; dynamical system; dynamical systems; eigenvalue; field theory; inv
版次1
doihttps://doi.org/10.1007/978-1-4612-1206-5
isbn_softcover978-1-4612-7043-0
isbn_ebook978-1-4612-1206-5Series ISSN 2627-7654 Series E-ISSN 2627-7662
issn_series 2627-7654
copyrightSpringer Science+Business Media New York 2000
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Calogero—Moser— Sutherland Models978-1-4612-1206-5Series ISSN 2627-7654 Series E-ISSN 2627-7662
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Neurobiology of Cognitive Learningormalization of Jack polynomials with prescribed symmetry (i.e., eigenfunctions that can be chosen to be symmetric or antisymmetric in certain variables) are given. In addition Macdonald polynomials of prescribed symmetry are considered, and it is shown that factorization can be achieved in certain cases.
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Neurobiology of Decision-Makingstruction of .-matrices in terms of any generalized inverse of ad(.). For generic . a generalized inverse (and indeed the Moore-Penrose inverse) is explicitly constructed. The .-matrices are in general momentum dependent and dynamical. We apply our construction to the elliptic Calogero-Moser-Sutherland models associated with gl..
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https://doi.org/10.1007/b111152ecial inverse problem for linear operators with elliptic coefficients. Hamiltonian theory of such systems is developed with the help of universal symplectic structure proposed by D. H. Phong and the author. Canonically conjugated variables for spin generalizations of the elliptic CM and RS systems are found.
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