Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absolutely Continuous Spectrum for Random Schroedinger Operators on the
  Bethe Strip   The Bethe Strip of width $m$ is the cartesian product $\B\times\{1,...,m\}$,
where $\B$ is the Bethe lattice (Cayley tree). We prove that Anderson models on
the Bethe strip have "extended states" for small disorder. More precisely, we
consider Anderson-like Hamiltonians $\;H_\lambda=\frac12 \Delta \otimes 1 + 1
\otimes A + \lambda \Vv$ on a Bethe strip with connectivity $K \geq 2$, where
$A$ is an $m\times m$ symmetric matrix, $\Vv$ is a random matrix potential, and
$\lambda$ is the disorder parameter. Given any closed interval $I\subset
(-\sqrt{K}+a_{\mathrm{max}},\sqrt{K}+a_{\mathrm{min}})$, where
$a_{\mathrm{min}}$ and $a_{\mathrm{max}}$ are the smallest and largest
eigenvalues of the matrix $A$, we prove that for $\lambda$ small the random
Schr\"odinger operator $\;H_\lambda$ has purely absolutely continuous spectrum
in $I$ with probability one and its integrated density of states is
continuously differentiable on the interval $I$.

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The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat