Random Schrödinger Operators on discrete structures
arXiv:1710.02293
Abstract
The Anderson model serves to study the absence of wave propagation in a medium in the presence of impurities, and is one of the most studied examples in the theory of quantum disordered systems. In these notes we give a review of the spectral and dynamical properties of the Anderson Model on discrete structures, like the -dimensional square lattice and the Bethe lattice, and the methods used to prove localization. These notes are based on a course given at the CIMPA School "Spectral Theory of Graphs and Manifolds" in Kairouan, 2016.
41 pages, diagrams and figures, lecture notes, typos corrected in v2