Non-equilibrium relaxation of an elastic string in random media

TL;DR

This paper investigates how an elastic string relaxes in a disordered medium, revealing non-algebraic growth of the relaxation length due to thermally activated barrier crossings, using Langevin dynamics simulations.

Contribution

It provides new insights into the non-equilibrium relaxation dynamics of elastic strings in random media, emphasizing non-algebraic growth behavior.

Findings

Growth of relaxation length is non-algebraic at long times.

Relaxation involves thermally activated jumps over barriers.

Barrier height scales as a power law with length, U(L) ~ L^θ.

Abstract

We study the relaxation 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 find that, in the long time limit, $L(t)$ has a non--algebraic growth, consistent with thermally activated jumps over barriers with power law scaling, $U(L) \sim L^\theta$.