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The fluctuations of the atom number between a Bose-Einstein condensate andthe surrounding thermal gas have been the subject of a long standingtheoretical debate. This discussion is centered around the appropriatethermodynamic ensemble to be used for theoretical predictions and the effect ofinteractions on the observed fluctuations. Here we introduce the so-called Fockstate sampling method to solve this classic problem of current experimentalinterest for weakly interacting gases. A suppression of the predicted peakfluctuations is observed when using a microcanonical with respect to acanonical ensemble. Moreover, interactions lead to a shift of the temperatureof peak fluctuations for harmonically trapped gases. The absolute size of thefluctuations furthermore depends on the total number of atoms and the aspectratio of the trapping potential. Due to the interplay of these effect, there isno universal suppression or enhancement of fluctuations.

Microcanonical and Canonical Fluctuations in Bose-Einstein Condensates -- Fock state sampling approach