Optimal transport in a ratchet coupled to a modulated environment: The role of Levy walks

We consider a Brownian particle in a ratchet potential coupled to a modulated environment and subjected to an external oscillating force. The modulated environment is modelled by a finite number N of uncoupled harmonic oscillators. Superdiffusive motion and Levy walks (anomalous random walks) are observed for any N and for low values of the external amplitude F  . The coexistence of left and right running states enhances the power αα from the time dependence of the mean square displacement (MSD). It is shown that αα is twice the average of the power of the separated left and right MSDs. Normal random walks are obtained by increasing F. We show that the maximal mobility of particles along the periodic structure occurs just before superdiffusive motion disappears and Levy walks are transformed into normal random walks.