Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bose condensates in a harmonic trap near the critical temperature   The mean-field properties of finite-temperature Bose-Einstein gases confined
in spherically symmetric harmonic traps are surveyed numerically. The solutions
of the Gross-Pitaevskii (GP) and Hartree-Fock-Bogoliubov (HFB) equations for
the condensate and low-lying quasiparticle excitations are calculated
self-consistently using the discrete variable representation, while the most
high-lying states are obtained with a local density approximation. Consistency
of the theory for temperatures through the Bose condensation point requires
that the thermodynamic chemical potential differ from the eigenvalue of the GP
equation; the appropriate modifications lead to results that are continuous as
a function of the particle interactions. The HFB equations are made gapless
either by invoking the Popov approximation or by renormalizing the particle
interactions. The latter approach effectively reduces the strength of the
effective scattering length, increases the number of condensate atoms at each
temperature, and raises the value of the transition temperature relative to the
Popov approximation. The renormalization effect increases approximately with
the log of the atom number, and is most pronounced at temperatures near the
transition. Comparisons with the results of quantum Monte Carlo calculations
and various local density approximations are presented, and experimental
consequences are discussed.

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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: math
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org