Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absolute continuity of the spectrum of the periodic Schr\"odinger
  operator in a layer and in a smooth cylinder   We consider the Schr\"odinger operator $H = -\Delta + V$ in a layer or in a
$d$-dimensional cylinder. The potential $V$ is assumed to be periodic with
respect to some lattice. We establish the absolute continuity of $H$, assuming
$V \in L_{p, \loc}$, where $p$ is a real number greater than $d/2$ in the case
of a layer, and $p > \max (d/2, d-2)$ for the cylinder.

28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas