Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the absence of absolutely continuous spectra for Schr\"{o}dinger
  operators on radial tree graphs   The subject of the paper are Schr\"odinger operators on tree graphs which are
radial having the branching number $b_n$ at all the vertices at the distance
$t_n$ from the root. We consider a family of coupling conditions at the
vertices characterized by $(b_n-1)^2+4$ real parameters. We prove that if the
graph is sparse so that there is a subsequence of $\{t_{n+1}-t_n\}$ growing to
infinity, in the absence of the potential the absolutely continuous spectrum is
empty for a large subset of these vertex couplings, but on the the other hand,
there are cases when the spectrum of such a Schr\"odinger operator can be
purely absolutely continuous.

12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg