Exact Universal Excitation Waveform for Optimal Enhancement of Directed Ratchet Transport

Abstract

We show the existence and properties of an exact universal excitation waveform for optimal enhancement of directed ratchet transport (in the sense of the average velocity) by providing three alternative derivations. Specifically, it is deduced from the criticality scenario giving rise to ratchet universality as well as from an approach based on Fokker–Planck’s equation. Numerical experiments confirmed the existence of such exact universal excitation waveform in the context of a driven overdamped Brownian particle subjected to a periodic potential. While the universality scenario holds regardless of the waveform of the periodic vibratory excitations involved, it is shown that the enhancement of directed ratchet transport is optimal when the impulse transmitted by those excitations (time integral over a half-period) is maximum.