Creep in One Dimension and Phenomenological Theory of Glass Dynamics

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.