Resonant delocalization of the eigenfunctions of random Schroedinger operators on tree graphs

TYPETheor./Math. Physics Seminar
Speaker:Prof. M. Aizenman
Location:Lewiner Seminar Room (412)
Remark:(Joint work with S. Warzel)
Abstract:We resolve an existing question concerning the location of the mobility edge for operators with a hopping term and a random potential on the Bethe lattice. The model has been among the earliest studied for Anderson localization, and it continues to attract attention because of analogies which have been suggested with localization issues for many particle systems. For unbounded potential we find that extended states appear through disorder enabled resonances well beyond the energy band of the operator’s hopping term, including in a Lifshitz tail regime of very low density of states. For bounded potentials the analysis yields the surprising finding that at weak disorder there is no mobility edge in the form that was envisioned before.