Bose-Einstein transition in a dilute interacting gas

Abstract. We study the eects of repulsive interactions on the critical density for the Bose-Einstein tran-sition in a homogeneous dilute gas of bosons. First, we point out that the simple mean eld approximation produces no change in the critical density, or critical temperature, and discuss the inadequacies of vari-ous 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 eld theory and show that the lowest order correction introduced by interactions is linear in the scattering length, a, with a positive coecient. Finally, we calculate this coecient within various approximations, and compare with various recent numerical estimates. PACS. 05.30.Jp Boson systems { 05.30.-d Quantum statistical mechanics { 03.75.Fi Phase coherent atomic ensembles; quantum condensation phenomena