Transition from Pure Point to Continuous Spectrum for Random Schrödinger Equations: Some Examples

Abstract

I review some recent results on Schrodinger equations with random potentials, and specially discuss the known examples where a transition in the nature of the spectrum occurs when varying the coupling constant or the energy: a transition from pure point spectrum with power decaying eigenfunctions to purely continuous spectrum has been proven recently for two classes of disordered systems, a transition which differs from the Mott-Anderson transition proven in certain Anderson models.