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

TL;DR

This paper introduces a new class of supersymmetric particle interaction models extending Calogero--Moser--Sutherland models, with explicit solutions and physical interpretations for systems with two particle types and variable interactions.

Contribution

It constructs a generalized supersymmetric model based on Jacobians in superspaces, extending classical models and providing explicit solutions and physical insights.

Findings

Models include two parameters controlling interaction strengths.

Explicit solutions are derived using superspace spherical functions.

Physical interpretations include semiconductor and quasi-two-dimensional systems.

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.