Spatio-temporal scaling for out-of-equilibrium relaxation dynamics of an elastic manifold in random media: crossover between the Larkin regime and thermally activated regime

TL;DR

This paper investigates the relaxation dynamics of a 3D elastic manifold in a random medium, revealing a crossover from Larkin to thermally activated regimes through numerical simulations and scaling analysis.

Contribution

It introduces a compact scaling ansatz capturing the crossover between Larkin and random manifold regimes in out-of-equilibrium relaxation.

Findings

Short time regime matches Larkin model predictions.

Longer time regime shows slower growth consistent with random manifold behavior.

Identifies a crossover length scale between regimes.

Abstract

We study relaxation dynamics of a three dimensional elastic manifold in random potential from a uniform initial condition by numerically solving the Langevin equation.We observe growth of roughness of the system up to larger wavelengths with time.We analyze structure factor in detail and find a compact scaling ansatz describing two distinct time regimes and crossover between them. We find short time regime corresponding to length scale smaller than the Larkin length $L_c$ is well described by the Larkin model which predicts a power law growth of domain size $L(t)$. Longer time behavior exhibits the random manifold regime with slower growth of $L(t)$.