Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiclassical asymptotics and gaps in the spectra of periodic
  Schr\"odinger operators with magnetic wells   We show that, under some very weak assumption of effective variation for the
magnetic field, a periodic Schr\"odinger operator with magnetic wells on a
noncompact Riemannian manifold $M$ such that $H^1(M, \R)=0$ equipped with a
properly disconnected, cocompact action of a finitely generated, discrete group
of isometries has an arbitrarily large number of spectral gaps in the
semi-classical limit.

28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an