Deterministic transport in biased maps: Crossover from dispersive to regular transport

We investigate the influence of a weak uniform field epsilon on chaotic diffusion generated by iterated maps which, in the absence of the field, lead to subdiffusion. When epsilon=0, the probability density psi(t) of the escape times from the vicinity of the fixed points of the maps decays as a pourer law. When a field is switched on, psi(t) decays exponentially at long enough times, with a decay rate that diverges when epsilon becomes small. The mean displacement and mean squared displacement show a transition from an anomalous type of motion, valid at short times, to a normal behavior at long times.