Theory of Brownian Motion. IV. A Hydrodynamic Model for the Friction Factor

Abstract

The hydrodynamical theory of the velocity correlation function of a Brownian particle, due to Widom, is combined with the non‐Markovian generalized Fokker–Planck equation given by the molecular theory of Brownian motion. An expression for the friction kernel (force autocorrelation) is derived. On the basis of the model here considered, the friction kernel decays as $t^{\text{−3/2}}$ for long times.