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We investigate directed motion in non-adiabatically rocked ratchet systems sustaining few bands below the barrier. Upon restricting the dynamics to the lowest M bands, the total system-plus-bath Hamiltonian is mapped onto a discrete tight-binding model containing all the information both on the intra- and inter-well tunneling motion. A closed form for the current in the incoherent tunneling regime is obtained. In effective single-band ratchets, no current rectification occurs. We apply our theory to describe rectification effects in vortex quantum ratchets devices. Current reversals upon variation of the ac-field amplitude or frequency are predicted.
A duality relation between the long-time dynamics of a quantum Brownian particle in a tilted ratchet potential and a driven dissipative tight-binding model is reported. It relates a situation of weak dissipation in one model to strong dissipation in
Unidirectional motion of solitons can take place, although the applied force has zero average in time, when the spatial symmetry is broken by introducing a potential $V(x)$, which consists of periodically repeated cells with each cell containing an a
We study a general model of granular Brownian ratchet consisting of an asymmetric object moving on a line and surrounded by a two-dimensional granular gas, which in turn is coupled to an external random driving force. We discuss the two resulting Bol
We demonstrate transport rectification in a hermitian Hamiltonian quantum ratchet by a dissipative, dynamic impurity. While the bulk of the ratchet supports transport in both directions, the properly designed loss function of the local impurity acts
We investigate the quantum ratchet effect under the influence of weak dissipation which we treat within a Floquet-Markov master equation approach. A ratchet current emerges when all relevant symmetries are violated. Using time-reversal symmetric driv