The random acceleration process in bounded geometries

Abstract

In the random acceleration process considered here, a point particle is accelerated byGaussian white noise with zero mean. Early work on first-passage and first-returnprobabilities and some recent applications are reviewed. Motion on the half linex > 0 and on thefinite line 0 < x < 1 is considered, with two types of boundary conditions, absorbing and inelastic.In colliding inelastically with the boundary, the kinetic energy of the particledecreases. Results for this boundary condition are of interest in connection withdriven granular matter. Some applications to semiflexible polymers are discussedwhere the statistics is the same as for the randomly accelerated particle. Finally,an introduction to the extreme statistics of the random acceleration process isgiven.