Underdamped quantum ratchets
  We investigate the quantum ratchet effect under the influence of weak dissipation which we treat within a Floquet-Markov master equation approach. A ratchet current emerges when all relevant symmetries are violated. Using time-reversal symmetric driving we predict a purely dissipation-induced quantum ratchet current. This directed quantum transport results from bath-induced superpositions of non-transporting Floquet states. 
S. Denisov, S. Kohler, and P. Hanggi