منابع مشابه
The Calogero-sutherland Model and Generalized Classical Polynomials
Multivariable generalizations of the classical Hermite, Laguerre and Jacobi polynomials occur as the polynomial part of the eigenfunctions of certain Schrödinger operators for Calogero-Sutherland-type quantum systems. For the generalized Hermite and Laguerre polynomials the multidimensional analogues of many classical results regarding generating functions, differentiation and integration formu...
متن کاملExact Yangian Symmetry in the classical Euler-Calogero-Moser Model
We compute the r-matrix for the elliptic Euler-Calogero-Moser model. In the trigonometric limit we show that the model possesses an exact Yangian symmetry. PAR LPTHE 94-03 L.P.T.H.E. Université Paris VI (CNRS UA 280), Box 126, Tour 16, 1er étage, 4 place Jussieu, F-75252 PARIS CEDEX 05
متن کاملLiouville Integrability of Classical Calogero-Moser Models
Liouville integrability of classical Calogero-Moser models is proved for models based on any root systems, including the non-crystallographic ones. It applies to all types of elliptic potentials, i.e. untwisted and twisted together with their degenerations (hyperbolic, trigonometric and rational), except for the rational potential models confined by a harmonic force. In this note we demonstrate...
متن کاملQuantum & Classical Eigenfunctions in Calogero & Sutherland Systems
An interesting observation was reported by Corrigan-Sasaki that all the frequencies of small oscillations around equilibrium are “quantised” for Calogero and Sutherland (C-S) systems, typical integrable multi-particle dynamics. We present an analytic proof by applying recent results of Loris-Sasaki. Explicit forms of ‘classical’ and quantum eigenfunctions are presented for C-S systems based on ...
متن کاملUniversality of Calogero-Moser Model
In this review we explain interrelations between the Elliptic Calogero-Moser model, integrable Elliptic Euler-Arnold top, monodromy preserving equations and the KnizhnikZamolodchikov-Bernard equation on a torus. Dedicated to 70-th birthday of Francesco Calogero
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ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 2012
ISSN: 1402-9251,1776-0852
DOI: 10.1142/s1402925112500350