  Quantum Brownian motion in ratchet potentials is investigated by means of an
approach based on a duality relation. This relation links the long-time
dynamics in a tilted ratchet potential in the presence of dissipation with the
one in a driven dissipative tight-binding model. The application to quantum
ratchet yields a simple expression for the ratchet current in terms of the
transition rates in the tight-binding system.
