95-544 Klein A.
Absolutely Continuous Spectrum in Random Schr\"odinger Operators (31K, AMS-LaTeX 1.1) 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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