A more accurate analysis of Bose-Einstein condensation in harmonic traps

Details A more accurate analysis of Bose-Einstein condensation in harmonic traps A more accurate analysis of Bose-Einstein condensation in harmonic traps

1996-05-16

arxiv.org/abs/cond-mat/9605100v1

Physics

Condensed Matter

10 pages, Latex, 5 Postscript figures

Scientific paper

10.1016/S0375-9601(96)08842-1

Using the Euler-Maclaurin summation we calculate analytically the internal energy for non-interacting bosons confined within a harmonic oscillator potential. The specific heat shows a sharp $\lambda$-like peak indicating a condensation into the ground state at a well-defined transition temperature. Full agreement is obtained with direct numerical calculation of the same quantities. When the number of trapped particles is very large and at temperatures near and above the transition temperature, the results also agree with previous approximate calculations. At extremely low temperatures both the specific heat and the number of particles excited from the condensate are exponentially suppressed.

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