Resonant Delocalization on the Bethe Strip

摘要

Recently, Aizenman and Warzel discovered a mechanism for the appearance of absolutely continuous spectrum for random Schr?dinger operators on the Bethe lattice through rare resonances (resonant delocalization). We extend their analysis to operators with matrix-valued random potentials drawn from ensembles such as the Gaussian Orthogonal Ensemble. These operators can be viewed as random operators on the Bethe strip, a graph (lattice) with loops.