 95544 Klein A.
 Absolutely Continuous Spectrum in Random Schr\"odinger Operators
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Dec 22, 95

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Abstract. The spectrum of the Anderson Hamiltonian $\;H_\lb=\De +\lb V$ on the Bethe
Lattice is absolutely continuous inside the spectrum of the Laplacian, if
the disorder $\lb$ is sufficiently small. More precisely, given any
closed interval $I$ contained in the interior of the spectrum of the
(centered) Laplacian $\De$ on the Bethe lattice, for small disorder
$H_\lb$ has purely absolutely continuous spectrum in $I$ with probability
one (i.e.,
$\si_{ac}( H_\lb) \cap I = I$ and $\si_{pp}( H_\lb) \cap I
=\si_{sc}( H_\lb) \cap I= \emptyset$
with probability one). The proof is discussed and regularity properties are
proven for the spectral measures restricted to such intervals of absolute
continuity.
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