Creep motion of an elastic string in a random potential

TL;DR

This study investigates the creep motion of an elastic string in a disordered landscape using simulations, confirming theoretical predictions at high temperatures and revealing deviations at lower temperatures.

Contribution

It provides numerical validation of the creep formula and explores the behavior of creep and roughness exponents across temperature regimes.

Findings

At high temperature, the creep exponent μ ≈ 1/4 and roughness exponent ζ ≈ 2/3.

At low temperature, μ and ζ increase, indicating a breakdown of the quasi-equilibrium creep picture.

Velocity-force characteristics align with phenomenological scaling predictions.

Abstract

We study the creep motion of an elastic string in a two dimensional pinning landscape by Langevin dynamics simulations. We find that the Velocity-Force characteristics are well described by the creep formula predicted from phenomenological scaling arguments. We analyze the creep exponent $\mu$, and the roughness exponent $\zeta$. Two regimes are identified: when the temperature is larger than the strength of the disorder we find $\mu \approx 1/4$ and $\zeta \approx 2/3$, in agreement with the quasi-equilibrium-nucleation picture of creep motion; on the contrary, lowering enough the temperature, the values of $\mu$ and $\zeta$ increase showing a strong violation of the latter picture.