Controlling directed ratchet transport of driven overdamped Brownian particles subjected to a vibrating periodic potential: ratchet universality versus harmonic-mixing perturbation theory

Abstract

We study directed ratchet transport of a harmonically driven overdamped Brownian particle subjected to a harmonically shaken periodic potential. The existence of a frequency-dependent optimal value of the relative amplitude of the two harmonic excitations involved is theoretically predicted from the criticality scenario giving rise to ratchet universality and numerically confirmed by extensive numerical experiments. The robustness of the ratchet universality scenario is also demonstrated when the external harmonic excitation is replaced by a bounded chaotic excitation having the same underlying main frequency in its Fourier spectrum. We remark that our findings are in sharp contrast with the predictions from the standard harmonic-mixing perturbation theory.