Geometrical Approach for the Mean-Field Dynamics of a Particle in a Short Range Correlated Random Potential

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.