E. Barkai et V. Fleurov, BROWNIAN TYPE OF MOTION OF A RANDOMLY KICKED PARTICLE FAR FROM AND CLOSE TO THE DIFFUSION LIMIT, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 52(2), 1995, pp. 1558-1570
The motion of a classical test particle, which evolves deterministical
ly in a potential field and where at a given rate its velocity is rand
omized, is investigated. A path integral approach is used to find exac
t solutions for the free and harmonically bound particles. Both the ex
act solution and numerical solution for a nonlinear case show large de
viations from the diffusion limit.