Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conserving Gapless Mean-Field Theory of a Multi-Component Bose-Einstein
  Condensate   We develop a mean-field theory for Bose-Einstein condensation of spin-1 atoms
with internal degrees of freedom. It is applicable to nonuniform systems at
finite temperatures with a plausible feature of satisfying the Hugenholtz-Pines
theorem and various conservation laws simultaneously. Using it, we clarify
thermodynamic properties and the excitation spectra of a uniform gas. The
condensate is confirmed to remain in the same internal state from T=0 up to
$T_{c}$ for both antiferromagnetic and ferromagnetic interactions. The
excitation spectra of the antiferromagnetic (ferromagnetic) interaction are
found to have only a single gapless mode, contrary to the prediction of the
Bogoliubov theory where three (two) of them are gapless. We present a detailed
discussion on those single-particle excitations in connection with the
collective excitations.

36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
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The categories of this paper are: atom-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph