  Using a path integral approach, we derive an analytical solution of a
nonlinear and singular Langevin equation, which has been introduced previously
by P.-G. de Gennes as a simple phenomenological model for the stick-slip motion
of a solid object on a vibrating horizontal surface. We show that the optimal
(or most probable) paths of this model can be divided into two classes of
paths, which correspond physically to a sliding or slip motion, where the
object moves with a non-zero velocity over the underlying surface, and a
stick-slip motion, where the object is stuck to the surface for a finite time.
These two kinds of basic motions underlie the behavior of many more complicated
systems with solid/solid friction and appear naturally in de Gennes' model in
the path integral framework.
