Speaker
Description
The random Schrodinger equation and its discrete analogue, the tight-binding model, have been studied as models of electron transport in disordered systems. It is conjectured that the long-time behavior is either localized or diffusive. In the localized regime, solutions remain trapped near their initial position. This phase has been established rigorously near the spectral edges, and is known as Anderson localization. The other possibility is that solutions transport diffusively for all time, and this is related to delocalization of eigenfunctions. In these lectures I will present a simple proof of diffusive transport up to a nontrivial timescale, though far from resolving the question of delocalization. The proof involves random matrix theory arguments combined with estimates from dispersive PDE. Based on joint work with Adam Black and Reuben Drogin.
