Free harmonic oscillators, Jack polynomials, and Calogero-Sutherland systems

Citation
N. Gurappa et Pk. Panigrahi, Free harmonic oscillators, Jack polynomials, and Calogero-Sutherland systems, PHYS REV B, 62(3), 2000, pp. 1943-1949
Citations number
72
Categorie Soggetti
Apllied Physucs/Condensed Matter/Materiales Science
Journal title
PHYSICAL REVIEW B
ISSN journal
01631829 → ACNP
Volume
62
Issue
3
Year of publication
2000
Pages
1943 - 1949
Database
ISI
SICI code
0163-1829(20000715)62:3<1943:FHOJPA>2.0.ZU;2-C
Abstract
The algebraic structure and the relationships between the eigenspaces of th e Calogero-Sutherland model (CSM) and the Sutherland model (SM) on a circle are investigated through the Cherednik operators. We find an exact connect ion between the simultaneous nonsymmetric eigenfunctions of the A(N-1) Cher ednik operators, from which the eigenfunctions of the CSM and SM are constr ucted, and the monomials. This construction allows us to simultaneously dia gonalize both CSM and SM (after gauging away the Hamiltonians by suitable m easures) and also enables us to write down a harmonic oscillator algebra in volving the Cherednik operators, which yields the raising and lowering oper ators for both of these models. The connections of the CSM with free oscill ators and the SM with free particles on a circle are established in a novel way. We also point out the subtle differences between the excitations of t he CSM and the SM.