Canonical Statistics of Occupation Numbers for Ideal and Weakly Interacting Bose-Einstein Condensates

Abstract

We give a self-contained, tutorial review of recent works on the statistics of the number of particles contained in a Bose-Einstein condensate within the canonical ensemble, both for ideal and weakly interacting Bose gases. While in the case of the ideal gas there exists a general mathematical framework for computing the fluctuation of the condensate particles in any trap, the analysis of the weakly interacting case is restricted to a homogeneous gas in the framework of the Bogoliubov theory. In particular, we present a simplified derivation of the pair characteristic function which governs the condensate statistics, first obtained by Kocharovsky, Kocharovsky, and Scully [Physical Review A 61, 053606 (2000)].KeywordsOccupation NumberEinstein CondensateMicrocanonical EnsembleExcited ParticleGrand Partition FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.