Klein A.
EXTENDED STATES IN THE ANDERSON MODEL ON THE BETHE LATTICE
(53K, LaTeX)
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 $I$.