Particle number counting statistics in ideal Bose gases
- 10 November 1997
- journal article
- Published by Optica Publishing Group in Optics Express
- Vol. 1 (10) , 272-283
- https://doi.org/10.1364/oe.1.000272
Abstract
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 [Navez et el, Phys. Rev. Lett. (1997)] and show that for large total number of particles the root-mean-square fluctuation of the condensate occupation scales δn 0 α [T/Tc ] rNs 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 σ 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.Keywords
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