Asymmetry-controlled resonant transport in a Brownian flashing ratchet

Abstract

We investigate directed transport in a one-dimensional Brownian flashing ratchet with a piecewise-linear asymmetric periodic potential. Numerical solutions of the Fokker--Planck equation and Brownian dynamics simulations reveal a nonmonotonic dependence of the stationary current on the switching frequency, with a resonant maximum whose position depends on the potential asymmetry $\delta$ and barrier height $\Delta$. For moderate asymmetry, $|\delta|<0.5$, the current obeys a scaling form that separates the dependence on the potential parameters from a common frequency dependence, resulting in a data collapse upon appropriate scaling of the current and frequency. The current amplitude varies linearly with $\delta$, while the resonance frequency follows $\nu(\delta,\Delta)=\nu_0(\Delta)/ [1-b_0\, \delta^2]$. We interpret the resulting $(1-\delta^2)^{-1}$ scaling in terms of coupled relaxation along the two branches of the asymmetric potential, which provides a physical basis for the observed dependence of the resonant frequency on the potential asymmetry.