An upper bound on the condensate fraction in a Bose gas with weak repulsion

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Abstract

For a spinless Bose gasmoving in three-dimensional free space with an interaction V (r) which is everywhere positive, I show that the condensate fraction f is bounded above by an expression parametrized by the quantity nV0/kT(0)c = η, where n is the density, V0 the space integral of the interaction potential and T (0)c the critical temperature of the corresponding noninteracting gas. The only assumption needed is that fluctuations in the interacting system have the standard extensivity properties. In particular, for T = T(0)c the upper bound on f is proportional to η1/3, while for η1/3 ≪ 1 - T(0) c /T ≪ 1 it is proportional to η/(1 - (T(0) c /T)3/2)2.

Original languageEnglish (US)
Pages (from-to)23.1-23.6
JournalNew Journal of Physics
Volume3
DOIs
StatePublished - Dec 19 2001

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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