Glassy properties of Anderson localization: pinning, avalanches and chaos

Gabriel Lemarié

Published 2018-09-07Version 1

I present the results of extensive numerical simulations which reveal the glassy properties of Anderson localization in dimension two at zero temperature: pinning, avalanches and chaos. I first show that the directed paths taken by the transport in the strongly localized regime are pinned by disorder and perform avalanches when a parameter like the energy is varied. I determine the roughness exponent $\zeta=2/3$ characterizing the wandering of these paths and find that it is the same as that of the directed polymer problem. Finally, I characterize the disorder chaos property: Two replicas with infinitesimally perturbed disorder configurations have their conductance correlation which vanishes at the thermodynamic limit. Chaos is the result of the interplay between two distinct mechanisms: a spin glass chaos effect at strong disorder characteristic of directed polymer physics and an interference effect at weak disorder characteristic of universal conductance fluctuations.