Short time relaxation of a driven elastic string in a random medium

TL;DR

This paper investigates the short-time relaxation dynamics of a driven elastic string in a disordered medium, revealing universal behavior and a new method to measure critical exponents of the depinning transition.

Contribution

It introduces a novel numerical analysis of relaxation dynamics, showing universality and providing a practical way to determine critical exponents independently.

Findings

Identifies a universal short-time relaxation regime.

Demonstrates a method to extract critical exponents from relaxation data.

Shows differences in relaxation behavior above and below the depinning threshold.

Abstract

We study numerically the relaxation of a driven elastic string in a two dimensional pinning landscape. The relaxation of the string, initially flat, is governed by a growing length $L(t)$ separating the short steady-state equilibrated lengthscales, from the large lengthscales that keep memory of the initial condition. We find a macroscopic short time regime where relaxation is universal, both above and below the depinning threshold, different from the one expected for standard critical phenomena. Below the threshold, the zero temperature relaxation towards the first pinned configuration provides a novel, experimentally convenient way to access all the critical exponents of the depinning transition independently.