Schrödinger and Dirac equations in disordered media
Wave propagation in a random medium is modeled by adding a random potential to the wave equation. The resulting model is very well known in the Schrödinger case and well understood in dimension one. In higher dimensions, the most interesting questions are still open, at least from the rigorous mathematical point of view. The Dirac equation case has been much less studied, but it is known that in this case response to disorder is different. This may be relevant for interpreting recent experiments with conductivity of graphene sheets. I will compare the two disordered equations and show a plan of study of the discretized one-dimensional Dirac equation with a random potential. This is a joint project with the groups of M. Dudynski in Warsaw and of M. Lewenstein in Barcelona.