Ratchet behavior in nonlinear Klein-Gordon systems with point-like inhomogeneities

TL;DR

This paper explores how nonlinear Klein-Gordon kinks behave like rocking ratchets in asymmetric inhomogeneous lattices, revealing mechanisms for directed motion and the influence of noise on transport.

Contribution

It introduces a collective coordinate model explaining kink ratchet behavior and demonstrates noise-induced unidirectional motion in such systems.

Findings

Kinks exhibit ratchet-like directed motion in asymmetric lattices.

Noise can activate unidirectional transport where none occurs without noise.

The collective coordinate approach effectively describes the observed phenomena.

Abstract

We investigate the ratchet dynamics of nonlinear Klein-Gordon kinks in a periodic, asymmetric lattice of point-like inhomogeneities. We explain the underlying rectification mechanism within a collective coordinate framework, which shows that such system behaves as a rocking ratchet for point particles. Careful attention is given to the kink width dynamics and its role in the transport. We also analyze the robustness of our kink rocking ratchet in the presence of noise. We show that the noise activates unidirectional motion in a parameter range where such motion is not observed in the noiseless case. This is subsequently corroborated by the collective variable theory. An explanation for this new phenomenom is given.