Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Excited states of a dilute Bose-Einstein condensate in a harmonic trap   The low-lying hydrodynamic normal modes of a dilute Bose-Einstein gas in an
isotropic harmonic trap determine the corresponding Bogoliubov amplitudes. In
the Thomas-Fermi limit, these modes have large low-temperature occupation
numbers, and they permit an explicit construction of the dynamic structure
function $S(q,\omega)$. The total noncondensate number $N'(0)$ at zero
temperature increases like $R^6$, where $R$ is the condensate radius measured
in units of the oscillator length. The lowest dipole modes are constructed
explicitly in the Bogoliubov approximation.

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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: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: math
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th