Kinetic equation for a weakly coupled test particle. II. Approach to equilibrium

We study the Fokker-Planck equation for the distribution in velocity of a test particle uniformly distributed through a weakly coupled classical fluid. The diffusion tensor, described first by Landau and by Chandrasekhar, is a complicated function of velocity. We discuss the manner in which the distribution function approaches, in time, its final Maxwellian form. The angle-averaged ($l=0$) and the ($l=1$) components are particularly interesting, the latter governing the autocorrelation function for velocity. Both relax as tᵃexp(-tᵇ). Our analysis is based upon R. E. Langer's method of comparison equations. The two-dimensional case is remarkably like the three-dimensional.