Bose-Einstein condensation in arbitrarily shaped cavities

We discuss the phenomenon of Bose-Einstein condensation of an ideal nonrela tivistic Bose gas in an arbitrarily shaped cavity. The influence of the fin ite extension of the cavity on all thermodynamical quantities, especially o n the critical temperature of the system, is considered. We use two main me thods that are shown to be equivalent. The first deals with the partition f unction as a sum over energy levels and uses a Mellin-Barnes integral repre sentation 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 cav ities is discussed. [S1063-651X(99)03101-3].