Waves and Solitons in the Continuum Limit of the Calogero-Sutherland Model

TL;DR

This paper explores wave and soliton solutions in a particle system with inverse-square interactions, revealing their quantum and classical properties and identifying fundamental excitations.

Contribution

It provides explicit large-amplitude wave and soliton solutions in the continuum limit of the Calogero-Sutherland model, linking classical and quantum descriptions.

Findings

Explicit large-amplitude density waves and solitons derived.

Waves can be viewed as coherent states of solitons or phonons.

Solitons and phonons identified as fundamental excitations.

Abstract

We examine a collection of particles interacting with inverse-square two-body potentials in the thermodynamic limit. We find explicit large-amplitude density waves and soliton solutions for the motion of the system. Waves can be constructed as coherent states of either solitons or phonons. Therefore, either solitons or phonons can be considered as the fundamental excitations. The generic wave is shown to correspond to a two-band state in the quantum description of the system, while the limiting cases of solitons and phonons correspond to particle and hole excitations.