Partial survival and inelastic collapse for a randomly accelerated particle
Service de Physique Théorique, CEA Saclay -
91191 Gif-sur-Yvette cedex, France
2 Service de Physique de l'État Condensé, CEA Saclay 91191 Gif-sur-Yvette cedex, France
Accepted: 11 December 2000
We present an exact derivation of the survival probability of a randomly accelerated particle subject to partial absorption at the origin. We determine the persistence exponent and the amplitude associated to the decay of the survival probability at large times. For the problem of inelastic reflection at the origin, with coefficient of restitution r, we give a new derivation of the condition for inelastic collapse, , and determine the persistence exponent exactly.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise and Brownian motion / 02.50.Ey – Stochastic processes / 05.20.-y – Classical statistical mechanics
© EDP Sciences, 2001