Brownian Motion

This chapter concentrates on small Brownian momentum fluctuations, described by the momentum auto-correlation function. The physical theory of Brownian motion was first considered by Einstein and Smoluchowsky, and later further developed by Langevin and others. It continues to be a fascinating subject of statistical physics. In setting up a microscopic theory of Brownian motion, this chapter introduces one simplification from the start, by treating both the fluid particles and the B-particle as mass points. While this is certainly not a good description of those large colloidal particles which are visible under a light microscope, the diffusion of heavy mass points contains the essence of the Brownian problem, and generalizations to particles of more complicated structure present no difficulties of principle. In an unpublished report, A. Rahman has performed such a calculation of the Brownian friction coefficient. The theory of Brownian motion is, formally, perfectly analogous to the hydrodynamic theory of, for example, spin diffusion.