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
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.
PACS: 05.30.Jp – Boson systems / 05.30.-d – Quantum statistical mechanics / 03.75.Fi – Phase coherent atomic ensembles; quantum condensation phenomena
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999