Abstract:

The Random Displacement Model (RDM) describes the motion of an electron in a spatially disordered medium. This is in contrast to the Anderson model where the disorder is in the coupling constants. A proof of localization for the RDM near the edge of the deterministic spectrum will be outlined. Localization is meant in both senses, pure point spectrum with exponentially decaying eigenfunctions as well as dynamical localization. The proof relies on a well established multi-scale analysis and the main problem is to verify the necessary ingredients, such as a Lifshitz tail estimate and a Wegner estimate. This work is jointly with J. Baker, F. Klopp, S. Nakamura and G. Stolz.