The lowest scattering state of one-dimensional Bose gas with attractive interactions

TL;DR

This paper analyzes the lowest scattering state of a one-dimensional attractive Bose gas in a hard wall trap, revealing how weak attraction influences density and correlation properties through exact solutions.

Contribution

It provides the first numerical solution of the Bethe ansatz for this system, detailing the full energy spectrum and wave functions for varying attractive interactions.

Findings

Decreased attraction leads to diverse density profiles.

Weak attraction induces specific correlation properties.

Exact wave functions reveal detailed quantum states.

Abstract

We investigate the lowest scattering state of one-dimensional Bose gas with attractive interactions trapped in a hard wall trap. By solving the Bethe ansatz equation numerically we determine the full energy spectrum and the exact wave function for different attractive interaction parameters. The resultant density distribution, momentum distribution, reduced one body density matrix and two body correlation show that the decreased attractive interaction induces rich density profiles and specific correlation properties in the weakly attractive Bose gas.