Transport and localization in random media: theory and applications

Two Classical models of Quantum Dynamics

Thomas Spencer

Institute for Advanced Study
[SLIDES]

The talk will start with an elementary introduction to the quantum dynamics of a Schr\"odinger operator with a random potential. Certain features of this model are believed to be reflected in classical models. In two dimensions one such model is described by the motion of a classical particle on the Manhattan lattice which is deflected by randomly placed obstructions. The second model is the linearly edge reinforced random walk on a d dimensional lattice. In three dimensions this model has a localization - diffusion transition as one varies the strength of reinforcement.