Bethe Ansatz study of one-dimensional Bose and Fermi gases with periodic and hard wall boundary conditions

TL;DR

This paper extends the Bethe Ansatz solution to one-dimensional Bose and Fermi gases with hard wall boundaries, analyzing ground state properties and energy expansions in various interaction regimes.

Contribution

It introduces a Bethe Ansatz framework for systems with hard wall boundaries and provides detailed ground state analysis for fermionic systems with internal degrees of freedom.

Findings

Ground state energy expansions in weak and strong coupling regimes

Extension of Bethe Ansatz to hard wall boundary conditions

Analysis of fermionic systems with internal degrees of freedom

Abstract

We extend the exact periodic Bethe Ansatz solution for one-dimensional bosons and fermions with delta-interaction and arbitrary internal degrees of freedom to the case of hard wall boundary conditions. We give an analysis of the ground state properties of fermionic systems with two internal degrees of freedom, including expansions of the ground state energy in the weak and strong coupling limits in the repulsive and attractive regimes.