Eur. Phys. J. B 24, 107-124 (2001)
https://doi.org/10.1007/s100510170028

Bose-Einstein transition in a dilute interacting gas

¹ University of Illinois at Urbana-Champaign, 1110 W. Green St., Urbana, IL 61801, USA
² CEA-Saclay, Service de Physique Théorique, 91191 Gif-sur-Yvette, Cedex, France
³ LKB and LPS, École Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
⁴ LPNHE, Case 200, Universités Paris 6/7, 4 Place Jussieu, 75005 Paris, France

Corresponding author: ^a holzmann@mail.physics.uiuc.edu

Received: 15 July 2001
Published online: 15 November 2001

Abstract

We study the effects of repulsive interactions on the critical density for the Bose-Einstein transition in a homogeneous dilute gas of bosons. First, we point out that the simple mean field approximation produces no change in the critical density, or critical temperature, and discuss the inadequacies of various contradictory results in the literature. Then, both within the frameworks of Ursell operators and of Green's functions, we derive self-consistent equations that include correlations in the system and predict the change of the critical density. We argue that the dominant contribution to this change can be obtained within classical field theory and show that the lowest order correction introduced by interactions is linear in the scattering length, a, with a positive coefficient. Finally, we calculate this coefficient within various approximations, and compare with various recent numerical estimates.