Solitons in the Calogero model for distinguishable particles

TL;DR

This paper investigates soliton solutions in a large N two-family Calogero model using a collective-field approach, revealing localized paired structures and their relation to vortex profiles in certain limits.

Contribution

It introduces static-soliton configurations in the two-family Calogero model and analyzes their behavior, including the Bogomol'nyi limit and the connection to one-family vortex solutions.

Findings

Solitons from different families are localized at the same point.

Paired hole and lump structures depend on coupling strengths.

In the limit of one family dominating, solutions resemble one-family Calogero vortex profiles.

Abstract

We consider a large $- N, $ two-family Calogero model in the Hamiltonian, collective-field approach. The Bogomol'nyi limit appears and the corresponding solutions are given by the static-soliton configurations. Solitons from different families are localized at the same place. They behave like a paired hole and lump on the top of the uniform vacuum condensates, depending on the values of the coupling strengths. When the number of particles in the first family is much larger than that of the second family, the hole solution goes to the vortex profile already found in the one-family Calogero model.