Solitons in Nonlinear Schr\"{o}dinger Model and the Collective Ground State of One-Dimensional Delta-Function Gas

TL;DR

This paper investigates the formation of bright solitons in a one-dimensional Bose gas with attractive delta-function interactions, revealing how collective ground states stabilize the system against instabilities.

Contribution

It demonstrates the emergence of bright soliton solutions in the nonlinear Schrödinger model derived from the Bose gas with attractive interactions, using large-N collective field theory.

Findings

Uniform ground state is unstable under attractive interactions.

Formation of bright solitons stabilizes the system.

Connection established between Bose gas and nonlinear Schrödinger solitons.

Abstract

We examine one-dimensional Bose gas interacting with delta-function potential using the large-$N$ collective field theory. We show that in the case of attractive potential the uniform ground state is unstable to small perturbations and the instability is cured by formation of a collective ground state, \lq\lq bright soliton'' configuration in corresponding nonlinear Schr\"odinger field theory.