Glassy Motion of Elastic Manifolds

TL;DR

This paper investigates the low-temperature dynamics of elastic manifolds in random media, revealing a power-law distribution of waiting times that leads to a nonlinear, glassy response under driving forces.

Contribution

It introduces a model explaining the glassy dynamics and nonlinear response of elastic manifolds driven through disordered media at low temperatures.

Findings

Waiting times follow a power-law distribution.

The driven medium exhibits a nonlinear velocity-force relationship.

The model explains glassy behavior in disordered elastic systems.

Abstract

We discuss the low-temperature dynamics of an elastic manifold driven through a random medium. For driving forces well below the $T=0$ depinning force, the medium advances via thermally activated hops over the energy barriers separating favorable metastable states. We show that the distribution of waiting times for these hopping processes scales as a power-law. This power-law distribution naturally yields a nonlinear glassy response for the driven medium, $v\sim\exp(-{\rm const}\times F^{-\mu})$.