Crossover from dispersive to regular transport in biased maps

We investigate the influence of a weak uniform field ε on chaotic maps which in the absence of the field generate subdiffusion. The field breaks the symmetry of the maps and leads to a net drift. A crossover from an anomalous type of motion, valid at short times, to a normal behavior, at long times is found for any finite field. The diffusion coefficient behaves as D(ε)∼ε^γwhere γ depends on a single parameter of the map.