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In the previous paper [Nenashev et al., arXiv:0912.3161] an analytical theoryconfirmed by numerical simulations has been developed for the field-dependenthopping diffusion coefficient D(F) in one-dimensional systems with Gaussiandisorder. The main result of that paper is the linear, non-analytic fielddependence of the diffusion coefficient at low electric fields. In the currentpaper, an analytical theory is developed for the field-dependent diffusioncoefficient in three- and two-dimensional Gaussian disordered systems in thehopping transport regime. The theory predicts a smooth parabolic fielddependence for the diffusion coefficient at low fields. The result is supportedby Monte Carlo computer simulations. In spite of the smooth field dependencesfor the mobility and for the longitudinal diffusivity, the traditional Einsteinform of the relation between these transport coefficients is shown to beviolated even at very low electric fields.

Effect of Electric Field on Diffusion in Disordered Materials II. Two- and Three-dimensional Hopping Transport