Inelastic collapse of a randomly forced particle

We consider a randomly forced particle moving in a finite, one-dimensional region, which rebounds inelastically with coefficient of restitution r on collision with the boundaries. We show that there is a transition at a critical value of r, r(c) = e(-pi/root 3), above which the dynamics is ergodic but beneath which the particle undergoes inelastic collapse, coming to rest after an infinite number of collisions in a finite time. The value of r, is argued to be independent of the size of the region or the presence of a viscous damping term in the equation of motion. [S0031-9007(98)06788-X].