Using numerical simulations we studied the long-time relaxation of the hopping conductivity. We perturbed the system through insertion of electrons and monitored the conductivity as a function of time. Even though employing numerical simulations one can only follow the system for very short time scales we have shown that during such available times we can reach an apparent saturation of conductivity and energy. In order to investigate the long-time relaxation of the system we studied the difference between the saturated values of the conductivities obtained by the short-time relaxation from initial excited states with different electron distribution. We have related these two typical time scales to relaxation in one pseudoground state and to very slow transitions between pseudoground states. By employing two different two-dimensional models with electron-electron interactions we were able to show the effect of disorder on the relaxation of conductivity. In the strong-disorder case the universality of the Coulomb gap, which is responsible for the universal Efros-Shklovskii law for the conductivity, suppresses the long-time relaxation of conductivity since the universality strongly decreases the dispersion of conductivities of the pseudoground states. In the second model with a weak external disorder we found a difference between saturated values of conductivity in agreement with the experimental data. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. [References: 15]
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