94-236 Klein A.

EXTENDED STATES IN THE ANDERSON MODEL ON THE BETHE LATTICE (53K, LaTeX) Jul 15, 94

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Abstract. We prove that the Anderson Hamiltonian $\;H_\lb=-\De +\lb V$ on the Bethe Lattice has ``extended states'' for small disorder. More precisely, given any closed interval $I$ contained in the interior of the spectrum of the Laplacian on the Bethe lattice, we prove that 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), and its integrated density of states is continuously differentiable on the interval $I$.

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