Stochastic resonance and Brownian ratchets

We discuss the connections between Brownian ratchets (BR) and stochastic resonance (SR). We consider a periodic potential energy landscape with no left–right symmetry that is driven by an external force which can be derived from a potential that is periodic both in time and space. We show that this system presents two thermal enhancements within two different windows of the temperature. One is associated with a “coherent diffusion” by which particles jump back and forth between the minima of the periodic potential in synchrony with the external driving. The other is instead associated with a “coherent directional transport” by which particles hop synchronically from one minimum of the ratchet to the next. We calculate the current and the diffusion coefficients and show how transport undergoes a resonant enhancement. While the former is always present, the second only appears when left–right symmetry is broken.