The 1D interacting Bose gas in a hard wall box

TL;DR

This paper analyzes the ground state properties and boundary effects of the 1D delta-interacting Bose gas confined in a hard wall box, using Bethe Ansatz solutions to explore finite-size, boundary, and correlation effects.

Contribution

It provides exact solutions for the ground state energy, surface energy, and boundary effects in the 1D Bose gas with hard wall boundaries, including weak and strong coupling regimes.

Findings

Hard wall boundaries significantly influence ground state energy and correlations.

Surface energy and finite-size effects are quantitatively characterized.

Local two-body correlations are enhanced by boundary conditions.

Abstract

We consider the integrable one-dimensional delta-function interacting Bose gas in a hard wall box which is exactly solved via the coordinate Bethe Ansatz. The ground state energy, including the surface energy, is derived from the Lieb-Liniger type integral equations. The leading and correction terms are obtained in the weak coupling and strong coupling regimes from both the discrete Bethe equations and the integral equations. This allows the investigation of both finite-size and boundary effects in the integrable model. We also study the Luttinger liquid behaviour by calculating Luttinger parameters and correlations. The hard wall boundary conditions are seen to have a strong effect on the ground state energy and phase correlations in the weak coupling regime. Enhancement of the local two-body correlations is shown by application of the Hellmann-Feynman theorem.