Brownian motion in a quantizing magnetic field

A model previously discussed by the author to study Brownian motion of charged carriers in a quantizing magnetic field is extended to include a Landau level-dependent friction parameter. A phase-space Fokker-Planck equation is used to derive a generalized diffusion equation describing spatial diffusion of the carriers, coupled with random jumps between adjacent Landau levels. This partial differential-difference equation is solved analytically. The longitudinal “global” diffusion coefficient is calculated and shown to be enhanced over the value in the extreme quantum limit.