Creep in One Dimension and Phenomenological Theory of Glass Dynamics

TL;DR

This paper models glass transition dynamics using a one-dimensional correlated random potential, revealing different regimes like ohmic and creep motion depending on correlation range, with implications for elastic systems and superconductors.

Contribution

It introduces an exact calculation of particle velocity in a correlated random potential, elucidating dynamic regimes and transitions relevant to glassy systems.

Findings

Transition from ohmic to creep motion depending on correlation exponent

Exact velocity calculation in correlated random potential

Implications for elastic manifolds and vortex glass in superconductors

Abstract

The dynamics of a glass transition is discussed in terms of the motion of a particle in a one dimensional correlated random potential. An exact calculation of the velocity $V$ under an applied force $f$ demonstrates a variety of dynamic regimes depending on the range of correlations. In a gaussian potential with correlator $C(x) = x^{\gamma}$, we find a transition from ohmic behaviour ($\gamma <0$) to creep motion $V \sim \exp(- const/f^{\mu} )$ ($0<\gamma <1$). This provides a generic picture of the glass transition in systems where long range correlations in the effective disorder develop due to elasticity such as elastic manifolds subject to quenched disorder and the vortex glass transition in superconductors.