Non-equilibrium relaxation of an elastic string in a random potential

TL;DR

This paper investigates the non-equilibrium relaxation dynamics of an elastic string in a disordered landscape, revealing universal growth behavior and barrier distributions through Langevin simulations.

Contribution

It introduces a detailed analysis of the relaxation process, including the universal distribution functions and scaling of barriers, for an elastic string in a random potential.

Findings

L(t) exhibits non-algebraic growth with a universal distribution.

The waiting time distribution is characterized and related to barrier scaling.

Barrier distribution is narrow, supporting scaling arguments.

Abstract

We study the non--equilibrium motion of an elastic string in a two dimensional pinning landscape using Langevin dynamics simulations. The relaxation of a line, initially flat, is characterized by a growing length, $L(t)$, separating the equilibrated short length scales from the flat long distance geometry that keep memory of the initial condition. We show that, in the long time limit, $L(t)$ has a non--algebraic growth with a universal distribution function. The distribution function of waiting times is also calculated, and related to the previous distribution. The barrier distribution is narrow enough to justify arguments based on scaling of the typical barrier.