Model $I$--$V$ curves and figures of merit of underdamped deterministic   Josephson ratchets
  We propose simple models for the current-voltage characteristics of typical Josephson ratchets. We consider the case of a ratchet working against a constant applied counter force and derive analytical expressions for the key characteristics of such a ratchet: rectification curve, stopping force, input and output powers and rectification efficiency. Optimization of the ratchet performance is discussed. 
E. Goldobin, R. Menditto, D. Koelle, R. Kleiner
cond-mat.mes-hall cond-mat.supr-con