| 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. |
