Abstract

The Bethe strip of width m is the cartesian product B x{1,..., m}, where B is the Bethe lattice ( Cayley tree). We prove that Anderson models on the Bethe strip have extended states for small disorder. More precisely, we consider Anderson- like Hamiltonians H lambda = 1/2 Delta circle times 1+ 1 circle times A + lambda V on a Bethe strip with connectivity K >= 2, where A is an m x m symmetric matrix, V is a random matrix potential, and lambda is the disorder parameter. Given any closed interval I subset of (-root K + a(max), root K + a(min)), where a(min) and a(max) are the smallest and largest eigenvalues of the matrix A, we prove that for lambda small the random Schr odinger operator H(lambda) has purely absolutely continuous spectrum in I with probability one and its integrated density of states is continuously differentiable on the interval I (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim