Extended States in the Andersonmodel On
نویسنده
چکیده
We prove that the Anderson Hamiltonian H = ? + 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 has purely absolutely continuous spectrum in I with probability one (i.e., ac (H)\I = I and pp (H)\I = sc (H)\I = ; with probability one), and its integrated density of states is continuously diierentiable on the interval I.
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