Supersymmetric Extensions of Calogero--Moser--Sutherland like Models: Construction and Some Solutions

Abstract

We introduce a new class of models for interacting particles. Our construction is based on Jacobians for the radial coordinates on certain superspaces. The resulting models contain two parameters determining the strengths of the interactions. This extends and generalizes the models of the Calogero--Moser--Sutherland type for interacting particles in ordinary spaces. The latter ones are included in our models as special cases. Using results which we obtained previously for spherical functions in superspaces, we obtain various properties and some explicit forms for the solutions. We present physical interpretations. Our models involve two kinds of interacting particles. One of the models can be viewed as describing interacting electrons in a lower and upper band of a one--dimensional semiconductor. Another model is quasi--two--dimensional. Two kinds of particles are confined to two different spatial directions, the interaction contains dipole--dipole or tensor forces.

21 pages, 4 figures

References in corpus (6)

• Deformed quantum Calogero-Moser problems and Lie superalgebras
• A multispecies Calogero model
• Superanalogs of the Calogero operators and Jack polynomials
• Generalized Calogero model in arbitrary dimensions
• Interacting families of Calogero-type particles and SU(1,1) algebra
• Supersymmetry and Models for Two Kinds of Interacting Particles

Cited by in corpus (9)

• Derivation of determinantal structures for random matrix ensembles in a new way
• Arbitrary rotation invariant random matrix ensembles and supersymmetry: orthogonal and unitary-symplectic case
• Integration of Grassmann variables over invariant functions on flat superspaces
• Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type
• Comparison of the superbosonization formula and the generalized Hubbard-Stratonovich transformation
• Some properties of angular integrals
• Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries
• Supermatrix models, loop equations, and duality
• From Jack to Double Jack Polynomials via the Supersymmetric Bridge