On condensation in the free-boson gas and the spectrum of the Laplacian |
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Authors: | M van den Berg |
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Institution: | 1. Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4, Ireland
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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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