Delayed feedback induced directed inertia particle transport in a washboard potential

TL;DR

This paper demonstrates how delayed feedback can induce and enhance directed particle transport in a washboard potential under thermal noise, by phase-locking oscillations and desymmetrizing attractors.

Contribution

It introduces a novel feedback mechanism that sustains directed motion in a noisy environment, expanding understanding of transport control in stochastic systems.

Findings

Feedback induces phase-locked oscillations promoting directed motion.

Desymmetrization of attractors supports persistent transport.

Transport can be enhanced by thermal noise under certain conditions.

Abstract

We consider motion of an underdamped Brownian particle in a washboard potential that is subjected to an unbiased time-periodic external field. While in the limiting deterministic system in dependence of the strength and phase of the external field directed net motion can exist, for a finite temperature the net motion averages to zero. Strikingly, with the application of an additional time-delayed feedback term directed particle motion can be accomplished persisting up to fairly high levels of the thermal noise. In detail, there exist values of the feedback strength and delay time for which the feedback term performs oscillations that are phase locked to the time-periodic external field. This yields an effective biasing rocking force promoting periods of forward and backward motion of distinct duration, and thus directed motion. In terms of phase space dynamics we demonstrate that with applied feedback desymmetrization of coexisting attractors takes place leaving the ones supporting either positive or negative velocities as the only surviving ones. Moreover, we found parameter ranges for which in the presence of thermal noise the directed transport is enhanced compared to the noise-less case.