Bose-Einstein transition in a dilute interacting gas

Details Bose-Einstein transition in a dilute interacting gas Bose-Einstein transition in a dilute interacting gas

2001-07-06

arxiv.org/abs/cond-mat/0107129v2

Physics

Condensed Matter

Statistical Mechanics

25 pages, 6 figures, 2 ref. added, minor changes in introduction and conclusion, to appear in EJP B

Scientific paper

10.1007/s100510170028

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 the dynamic 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.

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