One-Dimensional Bose Gases with N-Body Attractive Interactions

TL;DR

This paper investigates the properties of a one-dimensional Bose gas with N-body attractive interactions, analyzing soliton solutions, stability conditions, and effects of external trapping, revealing unique degeneracies and critical interaction strengths.

Contribution

It introduces explicit solutions for N-body attractive interactions in 1D Bose gases and explores their stability and degeneracy, extending understanding beyond two-body interactions.

Findings

Existence of localized soliton solutions only at critical interaction strength for N=3

Ground state degeneracy parameterized by chemical potential

Stabilization of solitons via external harmonic trap

Abstract

We study the ground state properties of a one-dimensional Bose gas with N-body attractive contact interactions. By using the explicit form of the bright soliton solution of a generalized nonlinear Schroedinger equation, we compute the chemical potential and the ground state energy. For N=3, a localized soliton wave-function exists only for a critical value of the interaction strength: in this case the ground state has an infinite degeneracy that can be parameterized by the chemical potential. The stabilization of the bright soliton solution by an external harmonic trap is also discussed, and a comparison with the effect of N-body attractive contact interactions in higher dimensions is presented.