Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Condensate deformation and quantum depletion of Bose-Einstein
  condensates in external potentials   The one-body density matrix of weakly interacting, condensed bosons in
external potentials is calculated using inhomogeneous Bogoliubov theory. We
determine the condensate deformation caused by weak external potentials on the
mean-field level. The momentum distribution of quantum fluctuations around the
deformed ground state is obtained analytically, and finally the resulting
quantum depletion is calculated. The depletion due to the external potential,
or potential depletion for short, is a small correction to the homogeneous
depletion, validating our inhomogeneous Bogoliubov theory. Analytical results
are derived for weak lattices and spatially correlated random potentials, with
simple, universal results in the Thomas-Fermi limit of very smooth potentials.

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The categories of this paper are: math
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph