Rupert Frank: On the spectrum of the Kronig–Penney model in a constant electric field

Speaker
Rupert Frank, LMU Muenchen

Abstract
We consider two models of one-dimensional Schroedinger operators with periodically arranged delta functions in a constant electric field. In the first model the coupling constants of the delta functions are iid random with zero mean and we prove a sharp transition, depending on the variance, between dense pure point and purely singular continuous spectrum. In the second model the coupling constants are constant and under a rationality assumption on the field we show purely absolutely continuous spectrum away from certain explicit discrete points. We also make some progress towards the behavior in the irrational case. The talk is based on joint work with S. Larson.