Universität Potsdam Institut für Physik KarlLiebknechtStr. 24/25 14476 PotsdamGolm 



AbstractWe discuss the exact particle number counting statistics of degenerate ideal Bose gases in the microcanonical, canonical, and grandcanonical ensemble, respectively, for various trapping potentials. We then invoke the Maxwell's Demon ensemble [P. Navez et al., Phys. Rev. Lett. 79, 17891792 (1997)] and show that for large total number of particles the rootmeansquare fluctuation of the condensate occupation scales delta n_{0} proportional to [T/T_{c}]^{r} N^{s} 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 singleparticle energy spectrum. Our predictions also apply to systems where BoseEinstein condensation does not occur. We point out that the condensate fluctuations in the microcanonical and canonical ensemble respect the principle of thermodynamic equivalence. file generated: 28 Apr 2003


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