Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proof of Bose-Einstein Condensation for Interacting Gases with a
  One-Particle Spectral Gap   Using a specially tuned mean-field Bose gas as a reference system, we
establish a positive lower bound on the condensate density for continuous Bose
systems with superstable two-body interactions and a finite gap in the
one-particle excitations spectrum, i.e. we prove for the first time standard
homogeneous Bose-Einstein condensation for such interacting systems.

28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci