Abstract
We prove the convergence of the thermodynamic functions of a free boson gas for ad-dimensional (d=3,4,...) van Hove sequence of convex regions. The thermodynamic functions behave singularly at a critical densityρ c which is independent of the geometrical details of the sequence. We are led to define a second critical densityρ m depending on the geometrical details of the sequence. For densities betweenρ c andρ m none of the single particle states is macroscopically occupied. We derive a sufficient condition on the sequence such thatρ m =ρ c .
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van den Berg, M. On condensation in the free-boson gas and the spectrum of the Laplacian. J Stat Phys 31, 623–637 (1983). https://doi.org/10.1007/BF01019501
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DOI: https://doi.org/10.1007/BF01019501