Dimensional Crossover for the Bose -- Einstein Condensation of an Ideal Bose Gas

Details Dimensional Crossover for the Bose -- Einstein Condensation of an Ideal Bose Gas Dimensional Crossover for the Bose -- Einstein Condensation of an Ideal Bose Gas

1997-04-10

arxiv.org/abs/cond-mat/9704087v1

Physics

Condensed Matter

Statistical Mechanics

19 pages, including 4 figures and one table. Latex source file

Scientific paper

We study an ideal Bose gas of N atoms contained in a box formed by two identical planar and parallel surfaces S, enclosed by a mantle of height a perpendicular to them. Calling r0 the mean atomic distance, we assume S >> r0^2 while a may be comparable to r0. In the bidimensional limit (a/r0 << 1) we find a macroscopic number of atoms in the condensate at temperatures T ~1/log(N); therefore, condensation cannot be described in terms of intensive quantities; in addition, it occurs at temperatures not too low in comparison to the tridimensional case. When condensation is present we also find a macroscopic occupation of the low--lying excited states. In addition, the condensation phenomenon is sensitive to the shape of S. The former two effects are significant for a nanoscopic system. The tridimensional limit is slowly attained for increasing (a/r0), roughly at (a/r0) ~ 10^{2}-10^{3}.

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