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Condensate density and superfluid mass density of a dilute Bose gas near the condensation transition

Markus Holzmann·Gordon Baym
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Abstract

We derive, through analysis of the structure of diagrammatic perturbation theory, the scaling behavior of the condensate and superfluid mass density of a dilute Bose gas just below the condensation transition. Sufficiently below the critical temperature, $T_c$, the system is governed by the mean field (Bogoliubov) description of the particle excitations. Close to $T_c$, however, mean field breaks down and the system undergoes a second order phase transition, rather than the first order transition predicted in Bogoliubov theory. Both condensation and superfluidity occur at the same critical temperature, $T_c$ and have similar scaling functions below $T_c$, but different finite size scaling at $T_c$ to leading order in the system size. Through a simple self-consistent two loop calculation we derive the critical exponent for the condensate fraction, $2β\simeq 0.66$.

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Markus Holzmann, Gordon Baym. 2002-09-27. Condensate density and superfluid mass density of a dilute Bose gas near the condensation transition. https://doi.org/10.1103/physrevlett.90.040402

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