Numerical study of relaxation in electron glasses

TL;DR

This study uses numerical simulations to analyze energy relaxation in three-dimensional electron glasses, revealing a universal power-law decay and long exponential relaxation times influenced by system parameters.

Contribution

It provides the first comprehensive numerical analysis of relaxation dynamics in electron glasses with various interactions, highlighting universal power-law behavior and long relaxation times.

Findings

Power-law relaxation with an exponent of 0.15 independent of parameters

Exponential relaxation regime at very long times with temperature-dependent timescales

Interacting samples exhibit relaxation times much larger than measurement times

Abstract

We perform a numerical simulation of energy relaxation in three-dimensional electron glasses in the strongly localized regime at finite temperatures. We consider systems with no interactions, with long-range Coulomb interactions and with short-range interactions, obtaining a power law relaxation with an exponent of 0.15, which is independent of the parameters of the problem and of the type of interaction. At very long times, we always find an exponential regime whose characteristic time strongly depends on temperature, system size, interaction type and localization radius. We extrapolate the longest relaxation time to macroscopic sizes and, for interacting samples, obtain values much larger than the measuring time. We finally study the number of electrons participating in the relaxation processes of very low energy configurations.