Fluctuations of the weakly interacting Bose-Einstein condensate

We consider the role of weak interatomic interactions on the fluctuations o f the number of condensed atoms within canonical and microcanonical ensembl es. Unlike the corresponding case of the ideal gas this is not a clean, wel l-defined problem of mathematical physics. Two related reasons are the foll owing: there is no unique way of defining the condensate fraction of the in teracting system and no exact energy levels of the interacting system are k nown. [S0031-9007(99)09269-8].