AIMR Math Group On-line Seminar

#6 FY2021

 

Date :August. 27th (Fri) 2021 10:00–11:00

Venue: Zoom

Speaker: Stefan Junk (WPI-AIMR, Tohoku University)
Title: Scaling limits for Mott variable-range hopping

 

Abstract

Mott variable-range hopping is a model for low-temperature electron transport in a disordered solid in the Anderson localization regime. The electron is modeled by a random walk on the atoms whose jump probabilities depend on the spatial separation and the energy separation between the atoms. The atoms of the solid are modeled by a random point process and we want to understand how inhomogeneities in the point process influence the diffusivity of the random walk, which can be interpreted as the conductivity of the material. I will review some of the literature and the methods used to analyze this model and present our new result, obtained jointly with David Croydon and Ryoki Fukushima, for a one-dimensional version of the model where the density of atoms is low. We find that the diffusivity is much smaller than in the high-density regime and that the inhomogeneity of the material does not disappear asymptotically, which is an example for the phenomenon of "disorder relevance" in the study of random media.

 

 

 

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