Journal of Statistical Physics

, Volume 31, Issue 3, pp 623–637

On condensation in the free-boson gas and the spectrum of the Laplacian

  • M. van den Berg

DOI: 10.1007/BF01019501

Cite this article as:
van den Berg, M. J Stat Phys (1983) 31: 623. doi:10.1007/BF01019501


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 densityρc which is independent of the geometrical details of the sequence. We are led to define a second critical densityρm depending on the geometrical details of the sequence. For densities betweenρc andρm none of the single particle states is macroscopically occupied. We derive a sufficient condition on the sequence such thatρmc.

Key words

Free boson gas Laplacian second critical density 

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • M. van den Berg
    • 1
  1. 1.Dublin Institute for Advanced StudiesDublin 4Ireland

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