Dynamics below the depinning threshold

TL;DR

This paper investigates the low-temperature steady-state dynamics of an elastic line in a disordered medium below the depinning threshold, revealing that the system is dominated by a single configuration with specific geometrical properties and no diverging length scale at the threshold.

Contribution

An exact algorithm is developed to identify the dominant configuration and analyze its geometrical properties below the depinning threshold.

Findings

The roughness exponent matches that at depinning.

No diverging length scale occurs in the steady state near the threshold.

A divergent length scale appears only during transient relaxation.

Abstract

We study the steady-state low-temperature dynamics of an elastic line in a disordered medium below the depinning threshold. Analogously to the equilibrium dynamics, in the limit T->0, the steady state is dominated by a single configuration which is occupied with probability one. We develop an exact algorithm to target this dominant configuration and to analyze its geometrical properties as a function of the driving force. The roughness exponent of the line at large scales is identical to the one at depinning. No length scale diverges in the steady state regime as the depinning threshold is approached from below. We do find, a divergent length, but it is associated only with the transient relaxation between metastable states.