THE DIFFUSION EQUATION FOR A CLASSICAL MECHANICAL SYSTEM IN A NONLINEAR FIELD OF FORCE - A 2ND-ORDER TREATMENT

Following a previously proposed procedure, the equations of motion of a classical-mechanical system in a random field of force are solved by splitting the velocity into a deterministic plus a stochastic component whose average vanishes. Thus, the diffusion equation can be derived by known methods from the equation of continuity, by conditional averaging. Explicit expressions are derived for the diffusion coefficient in terms of the response function. This is subsequently evaluated by making use of a frozen-trajectory approximation. The diffusion equation for a Brownian particle is then derived, including the transients, in the limit of a large frictional constant. © 1990.