Current control in a tilted washboard potential via time-delayed feedback

TL;DR

This paper demonstrates how time-delayed feedback can reverse, control, and halt particle current in a tilted washboard potential, providing a mechanism for directed transport manipulation over various temperatures.

Contribution

It introduces a novel control method using time-delayed feedback to manipulate particle current in a washboard potential, including reversal and stopping of transport.

Findings

Time-delayed feedback can reverse particle current against static bias.

The control mechanism induces a ratchet-like effect that prevents further current reversals.

Adjusting delay time allows continuous control or cessation of particle transport.

Abstract

We consider motion of an overdamped Brownian particle in a washboard potential exerted to a static tilting force. The bias yields directed net particle motion, i.e. a current. It is demonstrated that with an additional time-delayed feedback term the particle current can be reversed against the direction of the bias. The control function induces a ratchet-like effect that hinders further current reversals and thus the particle moves against the direction of the static bias. Furthermore, varying the delay time allows also to continuously depreciate and even stop the transport in the washboard potential. We identify and characterize the underlying mechanism which applies to current control in a wide temperature range.