Calogero Models for Distinguishable Particles

TL;DR

This paper introduces a new class of one-dimensional Calogero models with label-dependent coupling constants, solving the ground state and constructing some excited states, inspired by topological quantum models and mutual statistics.

Contribution

It proposes a novel Calogero model with particle-specific couplings and provides solutions for ground and excited states, extending previous models.

Findings

Successfully solved the ground state of the new model

Constructed classes of excited states

Demonstrated the model's relation to topological quantum systems

Abstract

Motivated by topological bidimensional quantum models for distinguishable particles, and by Haldane's definition of mutual statistics for different species of particles, we propose a new class of one-dimensional $1/r_{ij}^2$ Calogero model with coupling constants $g_{ij}$ depending on the labels of the particles. We solve the groundstate problem, and show how to build some classes of excited states.