Overdamped transport of particles in a periodic ratchet potential

Abstract

We have employed overdamped Langevin dynamics to study the driven transport of particles in a tilted ratchet potential. The system subject to an applied direct force undergoes an asymmetrical dynamic transition from a static state to a sliding state at different bidirectional critical forces. When an additional alternating force is applied to the system, the mean velocity shows steps as the direct force increases. These plateaus appear whenever the system’s natural frequency given by the direct force matches an integer multiple of the alternating frequency, and are similar to the Shapiro steps on the current-voltage characteristics in rf-driven Josephson junctions. For a rocking ratchet without a direct force, the rectification effect occurs when the alternating force exceeds a certain critical value.