TIME SCALES AND DIFFUSION MECHANISMS IN THE KRAMERS EQUATION WITH PERIODIC POTENTIALS (I)

Noise-assisted diffusion on a periodic substrate is studied, solving the Klein-Kramers equation (KKE) by the matrix continued fraction method. Assuming a periodic cosine potential and a homogeneous friction, the one-particle dynamics is completely characterized, both at short and long times, calculating, up to large momentum transfer, the dynamic structure factor, its full width at half maximum, the velocity self-correlation spectrum and the mean square displacement. Four different dynamical regimes are found as the potential strength or the friction vary. At high potential barriers, diffusion proceeds by single or multiple jumps at high and low friction respectively, while two different kinds of continuous unactivated diffusion are found at lower barriers. These dynamical features are discussed in terms of three characteristic time scales whose relations determine the diffusion mechanisms.