13.02.2023 15:30 David Zettler:
Miller-Abrahams random resistor network2.02.01 (Parkring 11, 85748 Garching-Hochbrück)

Based on a collection of works by Alessandra Faggionato, I will give a short introduction to Mott's Law and its rigorous derivation. It states that the conductivity in amorphous materials scales like $\exp( -c\beta^{1/4})$ for low temperatures, where $\beta$ denotes the inverse temperature. Using the Miller-Abrahams resistor network, A. Faggionato developed two approaches to rigorously prove such a limiting behavior. One via scaling limit of the conductivity of random resistor networks on simple point processes, and one via critical conductance of the Miller-Abrahams resistor network. A recent work of her presented at Paris CIRS connects these two approaches, showing that they both lead to the same sub-exponential decay of conductivity. Although, for a complete proof, a lower bound on LR-crossings in the supercritical regime for energy marks of both signs is still missing, and I will comment on this issue.