Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On absolute continuity of the spectrum of periodic Schr\"odinger
  operators   In this paper we find a new condition on a real periodic potential for which
the self-adjoint Schr\"odinger operator may be defined by a quadratic form and
the spectrum of the operator is purely absolutely continuous. This is based on
resolvent estimates and spectral projection estimates in weighted $L^2$ spaces
on the torus, and an oscillatory integral theorem.

1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys