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Dissipative transport in the localized regime

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Periodic and Ergodic Spectral Problems

Co-author: Jrg Frhlich (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. Frhlich.)

This talk is part of the Isaac Newton Institute Seminar Series series.

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