The 1D Bose Gas with Weakly Repulsive Delta Interaction

TL;DR

This paper analyzes the asymptotic solutions of the Bethe ansatz equations for a 1D Bose gas with weak repulsive interactions, revealing a mapping to a strongly-coupled bosonic pairing model's highest energy state.

Contribution

It introduces a novel connection between weakly interacting 1D Bose gases and strongly-coupled bosonic pairing models through asymptotic analysis.

Findings

Ground state maps to highest energy state of a strongly-coupled pairing model

Asymptotic solutions elucidate the behavior in the weak interaction limit

Provides insights into the integrable structure of the model

Abstract

We consider the asymptotic solutions to the Bethe ansatz equations of the integrable model of interacting bosons in the weakly interacting limit. In this limit we establish that the ground state maps to the highest energy state of a strongly-coupled repulsive bosonic pairing model.