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 conditions. 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. 
D. Zueco, J. L. Garcia-Palacios