Diffusion in periodic potentials

We discuss the static and dynamic phenomena connected with the Brownian motion of a particle in a periodic potential. Specifically we consider the dynamic mobility and the dynamic structure factor. We show with numerical examples how translational and oscillatory motion show up in these quantities. The calculations are done for the onedimensional case. A main tool is the continued fraction expansion of the relevant correlation functions. It enables us, for example, to obtain numerically accurate results for the mobility in a cosine potential. Possible applications of this model lie in the fields of superionic conductors and molecular crystals with rotational diffusion.