Abstract: We review recent results on dynamical localization for a Delone-Anderson operator in the context of non-ergodic random Schrödinger operators, using the Bootstrap Multiscale Analysis adapted to the non-ergodic setting. We consider a randomly perturbed Laplacian or Landau operator, where the random perturbation is of Anderson-type with the impurities lying in an aperiodic Delone set, which yields a break of ergodicity. In order to apply the multiscale analysis we prove a uniform Wegner estimate and a uniform initial length scale estimate at the bottom of the spectrum, using a spatial averaging that enables us to bypass the use of periodicity as in previous approaches. As a result, we obtain dynamical localization at the bottom of the spectrum. Furthermore, we prove the almost-sure existence of the Integrated Density of States (IDS) for this model under some assumptions on the "extent of aperiodicity'' of the Delone set. The IDS is proven to be Lipschitz continuous and to exhibit Lifshitz tails at the bottom of the spectrum. We also mention previews result on Delone-Anderson type perturbations of the Landau Hamiltonian with a constant magnetic field. Reference: C. Rojas-Molina, arXiv:1110.4652v1.
Seminarsko predavanje bo v petek 13. januarja 2012 ob 15:15 uri v seminarski sobi CAMTP, Krekova 2, pritličje desno. Vljudno vabljeni vsi zainteresirani, tudi študentje.