  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.
