Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Energy estimates and symmetry breaking in attractive Bose-Einstein
  condensates with ring-shaped potentials
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio