Eur. Phys. J. B 10, 739-760 (1999)
https://doi.org/10.1007/s100510050905

Bose-Einstein condensation in interacting gases

¹ LKB (The Laboratoire Kastler Brossel is Unité Associée au CNRS (UA 18) et à l'Université Pierre et Marie Curie.) and LPS (The Laboratoire de Physique Statistique de l'ENS is Unité Associée au CNRS (UA 1306) et aux Universités Paris 6 et Paris 7.) , Département de Physique de l'ENS, 24 rue Lhomond, 75005 Paris, France
² Institute of Theoretical Physics, UCSB, Santa Barbara, CA 93106, USA

Corresponding author: ^a laloe@ens.fr

Received: 13 November 1998
Published online: 15 August 1999

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 change of the velocity profile just above the transition: the proportion of atoms with low velocities is higher 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.