Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean-Field Interacting Boson Random Point Fields in Weak Harmonic Traps   A model of the mean-field interacting boson gas trapped by a weak harmonic
potential is considered by the \textit{boson random point fields} methods. We
prove that in the Weak Harmonic Trap (WHT) limit there are two phases
distinguished by the boson condensation and by a different behaviour of the
local particle density. For chemical potentials less than a certain critical
value, the resulting Random Point Field (RPF) coincides with the usual boson
RPF, which corresponds to a non-interacting (ideal) boson gas. For the chemical
potentials greater than the critical value, the boson RPF describes a divergent
(local) density, which is due to \textit{localization} of the macroscopic
number of condensed particles. Notice that it is this kind of transition that
observed in experiments producing the Bose-Einstein Condensation in traps.

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The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex