Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Quantum Phases of Ultracold Bosonic Atoms in two Bands of an
  Optical-Lattice coupled by a Cavity Field
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int