Quantum diffusion and random band matrices

Wednesday, June 27, 2012 - 2:00pm - 3:15pm
Lind 305
Antti Knowles (Harvard University)
I give an introduction to quantum diffusion and localization properties of eigenvectors of random band matrices. I give a short overview of the Anderson model, followed by a more in-depth discussion of random band matrices. After a survey of recent results, I sketch the main ideas of the proofs. I focus on two approaches: perturbative renormalization and self-consistent equations for the resolvent combined with fluctuation averaging.