Resonant steps and spatiotemporal dynamics in the damped dc-driven Frenkel-Kontorova chain

TL;DR

This paper investigates the complex kink dynamics and resonant velocity steps in a damped, externally driven Frenkel-Kontorova chain, revealing how resonances influence motion and can be modeled with mean-field theory.

Contribution

It introduces a mean-field approach to accurately predict resonant velocity steps and analyzes the spatiotemporal dynamics of kinks under damping and external driving.

Findings

Resonant velocity steps are caused by competition between kinks and radiated modes.

Mean-field theory accurately predicts the positions of resonant steps.

Spatiotemporal dynamics include slip-stick motion on resonant steps.

Abstract

Kink dynamics of the damped Frenkel-Kontorova (discrete sine-Gordon) chain driven by a constant external force are investigated. Resonant steplike transitions of the average velocity occur due to the competitions between the moving kinks and their radiated phasonlike modes. A mean-field consideration is introduced to give a precise prediction of the resonant steps. Slip-stick motion and spatiotemporal dynamics on those resonant steps are discussed. Our results can be applied to studies of the fluxon dynamics of 1D Josephson-junction arrays and ladders, dislocations, tribology and other fields.