Motion in a rocked ratchet with spatially periodic friction
  We present a detailed study of the transport and energetics of a Brownian particle moving in a periodic potential in the presence of an adiabatic external periodic drive. The particle is considered to move in a medium with periodic space dependent friction with the same periodicity as that of the potential but with a phase lag. We obtain several results, most of them arising due to the medium being inhomogeneous and are sensitive to the phase lag. When the potential is symmetric we show that efficiency of energy transduction can be maximised as a function of noise strength or temperature. However, in the case of asymmtertic potential the temperature may or may not facilitate the energy conversion but current reversals can be obtained as a function of temperature and the amplitude of the periodic drive. The reentrant behaviour of current can also be seen as a function of phase lag. 
Debasis Dan, Mangal C. Mahato and A. M. Jayannavar