Abstract
For a harmonically trapped dilute Bose gas with uniformly repulsive interactions which is assumed to satisfy a certain condition on the extensivity of fluctuations, I find on upper bound on the condensate fraction f. If BEC is defined by the condition that f>const.N −α, α<1/2, I argue that in the limit N→∞, V o →0, NV o →const. where V o is the space integral of the potential, the interactions cannot increase the critical temperature over that of the noninteracting gas.
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Leggett, A.J. Bose–Einstein Condensation in a Harmonic Trap: Effect of Interactions on T c . Journal of Statistical Physics 110, 903–910 (2003). https://doi.org/10.1023/A:1022124222128
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DOI: https://doi.org/10.1023/A:1022124222128