Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral and Dynamical contrast on highly correlated Anderson-type
  models   We study spectral and dynamical properties of random Schr\"odinger operators
$H_{\mathrm{Vert}}=-A_{\mathbb{G}_{\mathrm{Vert}}}+V_{\omega}$ and
$H_{\mathrm{Diag}}=-A_{\mathbb{G}_{\mathrm{Diag}}}+V_{\omega}$ on certain two
dimensional graphs ${\mathbb{G}_{\mathrm{Vert}}}$ and
${\mathbb{G}_{\mathrm{Diag}}}$. Differently from the standard Anderson model,
the random potentials are not independent but, instead, are constant along any
vertical line, i.e $V_{\omega}(n)=\omega(n_1)$, for $n=(n_1,n_2)$. In
particular, the potentials studied here exhibit long range correlations. We
present examples where geometric changes to the underlying graph, combined with
high disorder, have a significant impact on the spectral and dynamical
properties of the operators, leading to contrasting behaviors for the
"diagonal" and "vertical" models. Moreover, the "vertical" model exhibits a
sharp phase transition within its (purely) absolutely continuous spectrum. This
is captured by the notions of transient and recurrent components of the
absolutely continuous spectrum, introduced by Avron and Simon.

18
The categories of this paper are: econ
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom