Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A matrix-valued point interactions model   We study a matrix-valued Schr\"odinger operator with random point
interactions. We prove the absence of absolutely continuous spectrum for this
operator by proving that away from a discrete set its Lyapunov exponents do not
vanish. For this we use a criterion by Gol'dsheid and Margulis and we prove the
Zariski denseness, in the symplectic group, of the group generated by the
transfer matrices. Then we prove estimates on the transfer matrices which lead
to the H\"older continuity of the Lyapunov exponents. After proving the
existence of the integrated density of states of the operator, we also prove
its H\"older continuity by proving a Thouless formula which links the
integrated density of states to the sum of the positive Lyapunov exponents.

1
The categories of this paper are: cs
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat