Conserving Gapless Mean-Field Theory for Bose-Einstein Condensates

Abstract

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.

Minor errors removed

References in corpus (5)

• Conserving and Gapless Approximations for an Inhomogeneous Bose Gas at Finite Temperatures
• Transition temperature of a dilute homogeneous imperfect Bose gas
• Critical Temperature of Bose-Einstein Condensation of Hard Sphere Gases
• The transition temperature of the dilute interacting Bose gas for $N$ internal degrees of freedom
• Transition Temperature of the homogeneous, weakly interacting Bose gas

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