Creep dynamics of elastic manifolds via exact transition pathways

TL;DR

This paper provides an exact analysis of the steady state and transition pathways of driven elastic strings in disordered media below the depinning threshold, revealing a non-divergent length scale and a detailed dynamical phase diagram.

Contribution

It introduces an exact method to determine the dominant configuration and transition pathways in the low-temperature steady state of elastic manifolds below depinning.

Findings

Steady state dominated by a single configuration at low temperatures.

Depinning transition lacks a divergent length scale in steady state.

The dynamical phase diagram remains valid at finite temperatures and broken tilt symmetry.

Abstract

We study the steady state of driven elastic strings in disordered media below the depinning threshold. In the low-temperature limit, for a fixed sample, the steady state is dominated by a single configuration, which we determine exactly from the transition pathways between metastable states. We obtain the dynamical phase diagram in this limit. At variance with a thermodynamic phase transition, the depinning transition is not associated with a divergent length scale of the steady state below threshold, but only of the transient dynamics. We discuss the distribution of barrier heights, and check the validity of the dynamic phase diagram at small but finite temperatures using Langevin simulations. The phase diagram continues to hold for broken statistical tilt symmetry. We point out the relevance of our results for experiments of creep motion in elastic interfaces.