Mathematical Physics Seminar

Abstract: A quantum particle moving in a strongly disordered random environment is known to be subject to Anderson localization, which results in the complete suppression of transport. However, localization can be broken by a small perturbation, such as thermal noise from the environment, resulting in diffusive motion for the particle. I will discuss this phenomenon in a model in which the Schroedinger equation for a particle in the strongly localized regime is perturbed by a Lindblad operator describing the interaction with a heat bath in the Markov approximation. In this case, it can be proved that diffusive motion results with a strictly positive and finite diffusion constant. Furthermore, the diffusion constant tends continuously to zero at a calculable rate, as the strength of the perturbation is taken to zero. (Joint work with J. Fröhlich.)