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