Asymmetric step-like characteristics in a tilted rocking ratchet potential

The overdamped Langevin dynamics has been employed to study the directional transport of particles driven in a tilted rocking ratchet potential. The system subjected to a constant direct force undergoes an asymmetrical dynamic transition from a static state to a sliding state at two different critical forces that are consistent with the predicted values. When an additional alternating force is applied to the system, the time-averaged velocity shows several steps of equal height as the direct force increases. These steps are similar to the Shapiro steps in an rf-driven Josephson junction, and appear whenever the system's natural frequency given by the direct force matches an integer multiple of the applied frequency. When the alternating force exceeds a certain critical value which can be also estimated for a slow rocking, a directional motion known as the rectification effect occurs even at zero direct force.