Force-dependent motion reversal in quantum rocking ratchets

It is well known that at low temperatures, the direction of motion for a quantum rocking ratchet in an asymmetric periodic potential (with a period (Formula presented.) and an energy barrier (Formula presented.)), driven by an external fluctuating force (Formula presented.) ((Formula presented.)), can be opposite to the direction for the analogous classical ratchet operating at high temperature (Reimann et al, Phys. Rev. Lett. 1997, 79, 10). In the present work, within the semiclassical approximation and taking into account zero-point fluctuations of a quantum particle in the minima of a sawtooth potential of an arbitrary asymmetry at the temperature of absolute zero, we obtain analytical expressions for the tunneling current in the rocking ratchet. These expressions allowed us to obtain the dependencies of the ratio (Formula presented.), at which the motion direction is reversed, on the asymmetry parameter and other parameters of the system. Similar results are obtained for a particle in a two-sinusoidal potential.