Bose-Einstein condensation of interacting gases

TL;DR

This paper investigates the Bose-Einstein transition in interacting gases using Ursell operators, revealing new physical effects like altered velocity profiles and an increased critical temperature, aligning with recent Monte-Carlo results.

Contribution

It introduces a formalism based on Ursell operators for analyzing Bose-Einstein condensation in interacting gases, providing more detailed insights than mean-field theories.

Findings

Velocity profile changes above the transition

Increase in critical temperature due to interactions

Agreement with Monte-Carlo simulations for hard spheres

Abstract

We study the occurrence of a Bose-Einstein transition in a dilute gas with repulsive interactions, starting from temperatures above the transition temperature. The formalism, based on the use of Ursell operators, allows us to evaluate the one-particle density operator with more flexibility than in mean-field theories, since it does not necessarily coincide with that of an ideal gas with adjustable parameters (chemical potential, etc.). In a first step, a simple approximation is used (Ursell-Dyson approximation), which allow us to recover results which are similar to those of the usual mean-field theories. In a second step, a more precise treatment of the correlations and velocity dependence of the populations in the system is elaborated. This introduces new physical effects, such as a marked change of the velocity profile just above the transition: low velocities are more populated than in an ideal gas. A consequence of this distortion is an increase of the critical temperature (at constant density) of the Bose gas, in agreement with those of recent path integral Monte-Carlo calculations for hard spheres.