Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Symmetry-controlled singlet-triplet transition in a double-barrier
  quantum ring
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex