  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 the other one, and vice versa. We apply this duality
relation to investigate transport and rectification in ratchet potentials: From
the linear mobility we infer ground-state delocalization for weak dissipation.
We report reversals induced by adiabatic driving and temperature in the ratchet
current and its dependence on the potential shape.
