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 jr demonstrates a variety of dynamic regimes depending on the range of correlations. In a gaussian potential with correlator C(x) = x ~, we find a transition from ohmic behavior (), < 0) to creep motion V ~ exp(- const/f ~) (0 < "y < 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.