The Calogero-Sutherland Model and Generalized Classical Polynomials
نویسندگان
چکیده
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...
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The Schrödinger operators with exchange terms for certain Calogero-Sutherland quantum many body systems have eigenfunctions which factor into the symmetric ground state and a multivariable polynomial. The polynomial can be chosen to have a prescribed symmetry (i.e. be symmetric or antisymmetric) with respect to the interchange of some specified variables. For four particular Calogero-Sutherland...
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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 ...
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On the basis of the collective field method, we analyze the Calogero– Sutherland model (CSM) and the Selberg–Aomoto integral, which defines, in particular case, the partition function of the matrix models. Vertex operator realizations for some of the eigenstates (the Jack polynomials) of the CSM Hamiltonian are obtained. We derive Virasoro constraint for the generalized matrix models and indica...
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Motivated by the concept of ideal mutual statistics, we study a multispecies Calogero-Sutherland model in which the interaction parameters and masses satisfy some specific relations. The ground state is exactly solvable if those relations hold, both on a circle and on a line with a simple harmonic potential. In the latter case, the one-particle densities can be obtained using a generalization o...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1997
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s002200050161