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M. Wilkens, F. Illuminati, and M. Kraemer
Transition temperature of the weakly interacting Bose gas: perturbative solution of the crossover equations in the canonical ensemble
J. Phys. B 33 (2000) L779-L786


    We compute the shift of the critical temperature Tc with respect to the ideal case for a weakly interacting uniform Bose gas. We work in the framework of the canonical ensemble, extending the criterion of condensation provided by the canonical particle counting statistics for the zero-momentum state of the uniform ideal gas. The perturbative solution of the crossover equation to lowest order in powers of the scattering length yields (Tc-T0)/T0 = -0.93an1/3, where T0 is the transition temperature of the corresponding ideal Bose gas, a is the scattering length, and n is the particle number density. This result is at variance with the standard grand canonical prediction of a null shift of the critical temperature in the lowest perturbative order. The non-equivalence of statistical ensembles for the ideal Bose gas is thus confirmed (at the lowest perturbative level) also in the presence of interactions.

[ cond-mat/0001422 ]

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