Quasiparticle kinetic theory for Calogero models

TL;DR

This paper develops a quasiparticle kinetic theory for Calogero models, showing that their complex interactions can be described by a free-streaming Boltzmann equation with quasiparticles linked to Lax matrix eigenvectors, validated by numerical simulations.

Contribution

It introduces a Bethe-Lax correspondence for classical Calogero models, simplifying their kinetic description and extending understanding of their quasiparticle dynamics.

Findings

Kinetic theory reduces to free-streaming Boltzmann equation

Excellent agreement with numerical simulations in various traps

Simple description of multi-soliton solutions in harmonic traps

Abstract

We show that the quasiparticle kinetic theory for quantum and classical Calogero models reduces to the free-streaming Boltzmann equation. We reconcile this simple emergent behaviour with the strongly interacting character of the model by developing a Bethe-Lax correspondence in the classical case. This demonstrates explicitly that the freely propagating degrees of freedom are not bare particles, but rather quasiparticles corresponding to eigenvectors of the Lax matrix. We apply the resulting kinetic theory to classical Calogero particles in external trapping potentials and find excellent agreement with numerical simulations in all cases, both for harmonic traps that preserve integrability and exhibit perfect revivals, and for anharmonic traps that break microscopic integrability. Our framework also yields a simple description of multi-soliton solutions in a harmonic trap, with solitons corresponding to sharp peaks in the quasiparticle density. Extensions to quantum systems of Calogero particles are discussed.