Kinetic equation for a weakly-coupled test particle

This paper is concerned with the generalized kinetic equation for the motion of a test particle in a weakly-coupled classical fluid. The distribution function for the test particle satisfies a generalized Fokker-Planck equation in velocity. The equation has "memory" and a diffusion tensor that is time and velocity dependent. We study the case of the relaxation of a spatially uniform distribution in considerable detail. In particular, we find that the coupling of interaction, velocity, time, and mass ratio make questionable the traditional methods of solution by expansion in a small parameter.