- We discuss the exact particle number counting statistics of degenerate ideal Bose gases in the microcanonical, canonical, and grand-canonical ensemble, respectively, for various trapping potentials. We then invoke the Maxwell's Demon ensemble [P. Navez et al., Phys. Rev. Lett.(1997)] and show that for large total number of particles the root-mean-square fluctuation of the condensate occupation scales delta n0 proportional to [T/Tc]r Ns with scaling exponents r=3/2, s=1/2 for the 3D harmonic oscillator trapping potential, and r=1, s=2/3 for the 3D box. We derive an explicit expression for r and s in terms of spatial dimension D and spectral index sigma of the single- particle energy spectrum. Our predictions also apply to systems where Bose-Einstein condensation does not occur. We point out that the condensate fluctuations in the microcanonical and canonical ensemble respect the principle of thermodynamic equivalence.
