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Grand-canonical fluctuations of Bose-Einstein condensates of light areaccessible to state-of-the-art experiments [J. Schmitt et al., Phys. Rev. Lett.112, 030401 (2014).]. We phenomenologically describe these fluctuations byusing the grand-canonical ensemble for a weakly interacting Bose gas at thermalequilibrium. For a two-dimensional harmonic trap, we use two models for whichthe canonical partition functions of the weakly interacting Bose gas are givenby exact recurrence relations. We find that the grand-canonical condensatefluctuations for weakly interacting Bose gases vanish at zero temperature, thusbehaving qualitatively similar to an ideal gas in the canonical ensemble (ormicro-canonical ensemble) rather than the grand-canonical ensemble. For low butfinite temperatures, the fluctuations remain considerably higher than for thecanonical ensemble, as predicted by the ideal gas in the grand-canonicalensemble, thus clearly showing that we are not in a regime in which theensembles are equivalent.

Grand-canonical condensate fluctuations in weakly interacting Bose-Einstein condensates of light