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New spin Calogero-Sutherland models related to B-N-type Dunkl operators

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Finkel Morgenstern, Federico and Gómez-Ullate Otaiza, David and González López, Artemio and Rodríguez González, Miguel Ángel (2001) New spin Calogero-Sutherland models related to B-N-type Dunkl operators. Nuclear physics B, 613 (3). pp. 472-496. ISSN 0550-3213

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Official URL: http://dx.doi.org/10.1016/S0550-3213(01)00378-9


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Abstract

We construct several new families of exactly and quasi-exactly solvable BCN-type Calogero-Sutherland models with internal degrees of freedom. Our approach is based on the introduction of a new family of Dunkl operators of B-N type which, together with the original B-N-type Dunkl operators, are shown to preserve certain polynomial subspaces of finite dimension. We prove that a wide class of quadratic combinations involving these three sets of Dunkl operators always yields a spin Calogero-Sutherland model, which is (quasi-)exactly solvable by construction. We show that all the spin Calogero-Sutherland models obtainable within this framework can be expressed in a unified way in terms of a Weierstrass rho function with suitable half-periods. This provides a natural spin counterpart of the well-known general formula for a scalar completely integrable potential of BCN type due to Olshanetsky and Perelomov. As an illustration of our method, we exactly compute several energy levels and their corresponding wavefunctions of an elliptic quasi-exactly solvable potential for two and three particles of spin 1/2.


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©2001 Elsevier Science B.V. All rights, reserved.
This work was partially supported by the DGES under grant PB98-0821. R. Zhdanov would like to acknowledge the financial support of the Spanish Ministry of Education and Culture during his stay at the Universidad Complutense de Madrid.

Uncontrolled Keywords:Many-body problems; Integrable systems; Fractional statistics; Knizhnik-zamolodchikov; One-dimension; Particles; Exchange; Algebras; Chain
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:30944
Deposited On:17 Jun 2015 14:14
Last Modified:10 Dec 2018 15:10

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