Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bose-Einstein transition temperature in a dilute repulsive gas   We discuss certain specific features of the calculation of the critical
temperature of a dilute repulsive Bose gas. Interactions modify the critical
temperature in two different ways. First, for gases in traps, temperature
shifts are introduced by a change of the density profile, arising itself from a
modification of the equation of state of the gas (reduced compressibility);
these shifts can be calculated simply within mean field theory. Second, even in
the absence of a trapping potential (homogeneous gas in a box), temperature
shifts are introduced by the interactions; they arise from the correlations
introduced in the gas, and thus lie inherently beyond mean field theory - in
fact, their evaluation requires more elaborate, non-perturbative, calculations.
One illustration of this non-perturbative character is provided by the solution
of self-consistent equations, which relate together non-linearly the various
energy shifts of the single particle levels k. These equations predict that
repulsive interactions shift the critical temperature (at constant density) by
an amount which is positive, and simply proportional to the scattering length
a; nevertheless, the numerical coefficient is difficult to compute. Physically,
the increase of the temperature can be interpreted in terms of the reduced
density fluctuations introduced by the repulsive interactions, which facilitate
the propagation of large exchange cycles across the sample.

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The categories of this paper are: gr-qc
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The categories of this paper are: math
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: cs