# Resonant current in coupled inertial Brownian particles with delayed-feedback control

## TL;DR

This paper investigates how delayed-feedback control in coupled inertial Brownian particles within ratchets can induce resonant currents, negative mobility, and phase-locked motion, with potential for optimized transport control.

## Contribution

It introduces a novel delayed-feedback ratchet mechanism that produces resonant currents and negative mobility, supported by symmetry analysis and simulations.

## Key findings

- Resonant current steps are induced by phase-locked motion.
- Delayed feedback can lead to absolute negative mobility.
- Transport can be optimized by adjusting system parameters.

## Abstract

The transport of a walker in rocking feedback-controlled ratchets are investigated. The walker consists of two coupled "feet" that allow the interchange of the order of the particles while the walker moves. In the underdamped case, the deterministic dynamics of the walker in a tilted asymmetric ratchet with an external periodic force is considered. It is found that the delayed feedback ratchets with a switching-on-and-off dependence of the states of the system can lead to the absolute negative mobility (ANM). In such a novel phenomenon the particles move against the bias. Moreover, the walker can acquire a series of resonant steps for different values of the current. Remarkably, it is interesting to find that the resonant current of the walker are induced by the phase locked motion that corresponds to the synchronization of the motion with the change in the frequency of the external driving. These resonant steps can be well predicted in terms of time-space symmetry analysis, which is in good agreement with dynamics simulations. The transport performances can be optimized and furthermore controlled by suitably adjusting the parameters of the delayed-feedback ratchets.

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Source: https://tomesphere.com/paper/1702.02318