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Published on: December 4, 2017
Interacting Bose gas: mean field and fluctuations revisited
1Laboratoire de Physique, ENS Lyon and CNRS, 46 allée d'Italie, 69364 Lyon Cedex 07, France.
Abstract:
We present the description of thermodynamic properties of a Bose gas by considering the hierarchy of equations satisfied by imaginary-time Green functions. In the case of an ideal gas the appearance of the off-diagonal long-range order (presence of condensate) is derived in a particularly simple way. The simplicity of the analysis persists at the level of the mean-field theory. Using Kac's scaling of the repulsive binary potential we then determine asymptotic corrections to the mean-field theory for thermodynamic states far from the region of the mean-field condensation. Our predictions are in accordance with rigorous results obtained previously, whereas the Hartree-Fock approximation is shown to neglect a whole class of equally important contributions.
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