Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the eigenvalues for slowly varying perturbations of a periodic
  Schr\"{o}dinger operator   In this paper, I consider one-dimensional periodic Schr{\"o}dinger operators
perturbed by a slowly decaying potential. In the adiabatic limit, I give an
asymptotic expansion of the eigenvalues in the gaps of the periodic operator.
When one slides the perturbation along the periodic potential, these
eigenvalues oscillate. I compute the exponentially small amplitude of the
oscillations.

21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga