Kink in a periodically modulated disordered system

TL;DR

This paper investigates how a periodically modulated weak spatial disorder affects the depinning of a kink in a damped sine-Gordon system, revealing a larger critical depinning force than mean-field predictions.

Contribution

It demonstrates that second-order perturbation theory introduces an effective periodic potential, significantly impacting kink depinning in disordered systems.

Findings

Critical depinning force exceeds mean-field predictions.

Effective periodic potential arises from second-order disorder effects.

Analytical results align with numerical simulations.

Abstract

We consider a dc-driven damped sine-Gordon model with a small nonlinear spatial-disorder term, onto which a sinusoidal modulation is superimposed. It describes, e.g., a weakly disordered system with a regular grain structure. We demonstrate that, at the second order of the perturbation theory (with respect to the weak spatial disorder), the periodically modulated disorder gives rise to an effective periodic potential. Dynamics of a kink moving in this potential is studied in the overdamped limit, using the adiabatic approximation, the main objective being to consider depinning of a trapped kink. The analytical results are compared with direct dynamical simulations of the underlying model, as well as with numerical results using the collective-coordinate approach but without the mean-field approximation. It is found that a critical force for the depinning of a kink trapped by the periodically modulated weak spatial disorder is much larger than that predicted by the mean-field approximation.