Vibrational ratchets

TL;DR

This paper investigates how bi-harmonic drives, including high-frequency modulations, can activate transport in symmetric one-dimensional systems, revealing new mechanisms and potential applications beyond traditional linear response theory.

Contribution

It introduces the concept of vibrational mixing, showing how high-frequency modulations influence device response and challenges existing linear response assumptions.

Findings

High-frequency modulations can affect slow or dc device responses.

Rescaling Fourier components accurately reproduces vibrational mixing effects.

High-frequency beating signals can be analytically and numerically analyzed.

Abstract

Transport in a one-dimensional symmetric device can be activated by the combination of thermal noise and a bi-harmonic drive. For the study case of an overdamped Brownian particle diffusing on a periodic one-dimensional substrate, we distinguish two apparently different bi-harmonic regimes: (i) Harmonic mixing, where the two drive frequencies are commensurate and of the order of some intrinsic dynamical relaxation rate. A comparison of new simulation results with earlier theoretical predictions shows that the analytical understanding of this frequency mixing mechanism is not satisfactory, yet; (ii) Vibrational mixing, where one harmonic drive component is characterized by a high frequency but finite amplitude-to-frequency ratio. Its effect on the device response to either a static or a low-frequency additional input signal is accurately reproduced by rescaling each spatial Fourier component of the substrate potential, separately. Contrary to common wisdom based on the linear response theory, we show that extremely high-frequency modulations can indeed influence the response of slowly (or dc) operated devices, with potential applications in sensor technology and cellular physiology. Finally, the mixing of two high-frequency beating signal is also investigated both numerically and analytically.