Quantum ratchets at high temperatures

Using the continued-fraction method we solve the Caldeira–Leggett master equation in the phase–space (Wigner) representation to study quantum ratchets. Broken spatial symmetry, irreversibility and periodic forcing allows for a net current in these systems. We calculate this current as a function of the force under adiabatic forcing. Starting from the classical limit we make the system quantal. In the quantum regime, tunnel events and over-barrier wave reflection phenomena modify the classical result. Finally, using the phase–space formalism we give some insights about the decoherence in these systems.