Universal non stationary dynamics at the depinning transition

TL;DR

This paper investigates the universal non-stationary dynamics of elastic interfaces at the depinning transition, combining theoretical calculations and simulations to reveal critical exponents and crossover phenomena relevant to magnetic and wetting systems.

Contribution

It provides the first comprehensive analysis of two-time response and correlation functions at depinning, demonstrating universality and validating two-loop FRG with molecular dynamics.

Findings

Universal two-time response and correlation functions characterized by two critical exponents.

Agreement between FRG calculations and molecular dynamics simulations.

Identification of a dynamical dimensional crossover at long times.

Abstract

We study the non-stationary dynamics of an elastic interface in a disordered medium at the depinning transition. We compute the two-time response and correlation functions, found to be universal and characterized by two independent critical exponents. We find a good agreement between two-loop Functional Renormalization Group calculations and molecular dynamics simulations for the scaling forms, and for the response aging exponent $\theta_R$. We also describe a dynamical dimensional crossover, observed at long times in the relaxation of a finite system. Our results are relevant for the non-steady driven dynamics of domain walls in ferromagnetic films and contact lines in wetting.