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.