Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absolutely continuous and pure point spectra of discrete operators with
  sparse potentials   We consider the discrete Schr\"odinger operator $H=-\Delta+V$ with a sparse
potential $V$ and find conditions guaranteeing either existence of wave
operators for the pair $H$ and $H_0=-\Delta$, or presence of dense purely point
spectrum of the operator $H$ on some interval $[\lambda_0,0]$ with
$\lambda_0<0$.

35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an