Comments on Kinetic Equation for Autocorrelation Functions

The non-Markoffian kinetic equation for the one-particle momentum autocorrelation function, derived by Zwanzig and studied in great detail recently by Berne, Boon, and Rice, is analyzed in the weak coupling limit. It is shown that, in this limit, this kinetic equation remains non-Markoffian because the kernel which determines the memory effects only decays very slowly. More precisely, it tends to zero over times of the order of the relaxation time itself and not, as could be expected, over the much shorter collision time. The comparison with the more traditional approach, based on the solution of a transport equation, is also discussed.