Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimensional Crossover for the Bose -- Einstein Condensation of an Ideal
  Bose Gas   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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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: math
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph