Chaos in Kicked Ratchets

TL;DR

This paper introduces a simple deterministic model of a kicked ratchet that demonstrates chaos and complex transport, with an analytical method predicting key behaviors like current reversals and bifurcations.

Contribution

The study presents a minimal overdamped ratchet model with analytical predictions of chaotic dynamics and transport phenomena, extendable to various periodic forces.

Findings

Chaotic behavior observed in the model.

Analytical predictions match key features like current reversals.

Model can be extended to different periodic forcing functions.

Abstract

We present a minimal one-dimensional deterministic continuous dynamical system that exhibits chaotic behavior and complex transport properties. Our model is an overdamped rocking ratchet that is periodically kicked with a delta function potential. We develop an analytical approach that predicts many key features of the system, such as current reversals, as well as the presence of chaotic behavior and bifurcation. We show that our approach can be easily extended to other types of periodic forces, including the square wave.