Correlation functions for the diffusive motion of particles in a periodic potential

The diffusive motion of particles in a one-dimensional periodic potential is treated using the Fokker-Planck equation method. First, a concise form of the Fokker-Planck equation and of the correlation function for this problem is set up. By expanding the distribution function into suitable eigenfunctions, a general method for calculating the correlation functions is then given. Finally, explicit calculations are presented for the velocity correlation functions, some of these are compared with those which were obtained by continued fraction methods.