A generalized Faxén theorem for two-dimensional Brownian motion

The induced force method developed by Mazur and Bedeaux is applied here to two-dimensional Brownian motion. We obtain a generalized Faxén theorem which reduces to the Stokes-Basset drag force on a nonuniformly moving cylinder or disk in the special case where the fluid fluctuations are neglected. The resulting modified Langevin equation is solved numerically for the velocity autocorrelation Ø(t) and the expected long time result Ø(t)～1/t is obtained. It is perhaps surprising that the short time behavior of Ø(t) deviates considerably from that predicted on the basis of a modified Langevin equation incorporating the classic Oseen-Lamb drag force on a cylinder.