On mean field theory for ac-driven elastic interfaces exposed to disorder

TL;DR

This paper develops a mean field theoretical framework for ac-driven elastic interfaces in disordered media, proving the regularity of perturbation theory and matching numerical results, with insights into velocity Fourier components.

Contribution

It introduces a systematic cancellation scheme for divergent graphs in perturbation theory and validates the approach against numerical simulations.

Findings

Perturbation theory is shown to be regular at all orders.

The mean velocity's Fourier coefficients depend on model parameters.

The theoretical results agree with numerical simulations in applicable regimes.

Abstract

The analytic description of ac-driven elastic interfaces in random potentials is desirable because the problem is experimentally relevant. This work emphasises on the mean field approximation for the problem at zero temperature. We prove that perturbation theory is regular in all orders by giving an inductive scheme how to find groups of ill-behaved graphs that mutually cancel, leaving a regular expression. In the parameter regimes for which perturbation theory is applicable it agrees with numerical results. Further, we determine the dependence of the Fourier coefficients of the mean velocity on the parameters of the model.