Drift and trapping in biased diffusion on disordered lattices

We re-examine the theory of transition from drift to no-drift in biased diffusion on percolation networks. We argue that for the bias field B equal to the critical value B,, the average velocity at large times t decreases to sero as 1/log(t). For B < B-c, the time required to reach the steady-state velocity diverges as exp(const/\B-c - B\). We propose an extrapolation form that describes the behavior of average velocity as a function of time at intermediate time scales. This form is found to have a very good agreement with the results of extensive Monte Carlo simulations on a three-dimensional site-percolation network and moderate bias.