Conserving Gapless Mean-Field Theory for Bose-Einstein Condensates

Details Conserving Gapless Mean-Field Theory for Bose-Einstein Condensates Conserving Gapless Mean-Field Theory for Bose-Einstein Condensates

2004-11-11

arxiv.org/abs/cond-mat/0411296v2

J. Phys. Soc. Jpn. 74, 1891 (2005)

Physics

Condensed Matter

Superconductivity

Minor errors removed

Scientific paper

10.1143/JPSJ.74.1891

We formulate a conserving gapless mean-field theory for Bose-Einstein condensates on the basis of a Luttinger-Ward thermodynamic functional. It is applied to a weakly interacting uniform gas with density $n$ and s-wave scattering length $a$ to clarify its fundamental thermodynamic properties. It is found that the condensation here occurs as a first-order transition. The shift of the transition temperature $\Delta T_c$ from the ideal-gas result $T_{0}$ is positive and given to the leading order by $\Delta T_c = 2.33a n^{1/3}T_0$, in agreement with a couple of previous estimates. The theory is expected to form a new theoretical basis for trapped Bose-Einstein condensates at finite temperatures.

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