Bose-Einstein condensation in arbitrarily shaped cavities

Details Bose-Einstein condensation in arbitrarily shaped cavities Bose-Einstein condensation in arbitrarily shaped cavities

1998-10-08

arxiv.org/abs/cond-mat/9810098v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, LaTeX, to appear in Physical Review E

Scientific paper

10.1103/PhysRevE.59.158

We discuss the phenomenon of Bose-Einstein condensation of an ideal non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the finite extension of the cavity on all thermodynamical quantities, especially on the critical temperature of the system, is considered. We use two main methods which are shown to be equivalent. The first deals with the partition function as a sum over energy levels and uses a Mellin-Barnes integral representation to extract an asymptotic formula. The second method converts the sum over the energy levels to an integral with a suitable density of states factor obtained from spectral analysis. The application to some simple cavities is discussed.

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