  The zero temperature relaxational dynamics of a particle in a short range
correlated random potential is addressed. We derive a set of "two-times"
mean-field dynamical equations, accounting for a possible mean displacement of
the particle when subject to an external force. We show first detailed results
from the numerical integration of the above mentionned equations. We mainly pay
attention to the exponentially decreasing spatial correlations case, for which
simple analytical arguments provide valuable results about the hessian of the
energy landscape, and we propose a geometrical description of the "mean-field
aging". Our numerical results and further analytical arguments give access to
the waiting time dependence of the main characteristic time scales.
