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Dissipative transport in the localized regime

Presented by: 
J Schenker Michigan State University
Tuesday 23rd June 2015 - 13:30 to 14:30
INI Seminar Room 1
Co-author: Jürg Fröhlich (ETH)

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 two models in which the Schroedinger equation for a particle in the strongly localized regime is perturbed by (1) a time dependent fluctuating random potential and (2) a Lindblad operator incorporating the interaction with a heat bath in the Markov approximation. In each 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. (Partially based on joint work with J. Fröhlich.)

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons