Logarithmic relaxation and stress aging in the electron glass

Slow relaxation and aging of the conductance are experimental features of a range of materials, which are collectively known as electron glasses. We report dynamic Monte Carlo simulations of the standard electron glass lattice model. In a non-equilibrium state, the electrons will often form a Fermi distribution with an effective electron temperature higher than the phonon bath temperature. We study the effective temperature as a function of time in three different situations: relaxation after a quench from an initial random state, during driving by an external electric field and during relaxation after such driving. We observe logarithmic relaxation of the effective temperature after a quench from a random initial state as well as after driving the system for some time $t_w$ with a strong electric field. For not too strong electric field and not too long $t_w$ we observe that data for the effective temperature at different waiting times collapse when plotted as functions of $t/t_w$ -- the so-called simple aging. During the driving period we study how the effective temperature is established, separating the contributions from the sites involved in jumps from those that were not involved. It is found that the heating mainly affects the sites involved in jumps, but at strong driving, also the remaining sites are heated.