Drift, creep and pinning of a particle in a correlated random potential

The motion of a particle in a correlated random potential under the influence of a driving force is investigated in mean field theory. The correlations of the disorder are characterized by a short distance cutoff and a power law decay with exponent $\gamma$ at large distances. Depending on temperature and $\gamma$ , drift with finite mobility, creep or pinning is found. This is in qualitative agreement with results in one dimension. This model is of interest not only in view of the motion of particles or manifolds in random media, it also improves the understanding of glassy non-equilibrium dynamics in mean field models. The results, obtained by numerical integration and analytic investigations of the various scaling regimes in this problem, are compared with previous proposals regarding the long time properties of such systems and with replica calculations.