Dissipative transport in dc-ac-driven tight-binding lattices

We investigate the incoherent dissipative quantum transport of a particle in a periodic lattice being driven nonlinearly by dc-ac fields. The particle always diffuses slower, as compared to the force-free case, and the minimal diffusion is found for zero de-bias and ac-field parameters that lead to dynamical localization (DL) in the nondissipative case. A current inversion occurs at weak dissipation. The amplitude of the negative current is maximal for a characteristic value of the dissipative strength, resembling a ''stochastic resonance'' like effect. For intermediate dissipation the current is positive and widely independent of both the ac-frequency and the dissipation. The negative current, as well as the stability of DL against dissipation are universal effects, in the sense that they are largely independent of the dissipative mechanism.