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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