Dimensional Crossover for the Bose -- Einstein Condensation of an Ideal Bose Gas
Abstract
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}.
Keywords
Cite
@article{arxiv.cond-mat/9704087,
title = {Dimensional Crossover for the Bose -- Einstein Condensation of an Ideal Bose Gas},
author = {M. I. Molina and J. A Roessler},
journal= {arXiv preprint arXiv:cond-mat/9704087},
year = {2008}
}
Comments
19 pages, including 4 figures and one table. Latex source file