Variational Approach to the Dilute Bose Gas

TL;DR

This paper develops a variational method to accurately describe the thermodynamics and phase transitions of dilute Bose gases in two and three dimensions, improving upon traditional perturbative approaches.

Contribution

It introduces a ladder-approximation variational framework to analyze weakly-interacting Bose gases, capturing phase transition signatures missed by perturbation theory.

Findings

Improved mean-field description of 3D Bose-Einstein condensation

Detection of phase transition signatures in 2D Bose gases

Enhanced theoretical understanding of dilute Bose gas thermodynamics

Abstract

We study the weakly-interacting Bose gas in both two and three dimensions using a variational approach. In particular we construct the thermodynamic potential of the gas to within ladder approximation and find by minimization an accurate mean-field description of the dilute Bose gas. Using spin-polarized atomic hydrogen as a specific example, we obtain an improved description of the Bose-Einstein condensed phase in three dimensions and a signature of a phase transition in two dimensions. The latter cannot be found by straightforward application of perturbation theory around the ideal Bose gas.