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

Noise-assisted diffusion on a periodic substrate is studied, solving t he Klein-Kramers equation (KKE) by the matrix continued fraction metho d. Assuming a periodic cosine potential and a homogeneous friction, th e one-particle dynamics is completely characterized, both at short and long times, calculating, up to large momentum transfer, the dynamic s tructure factor, its full width at half maximum, the velocity self-cor relation spectrum and the mean square displacement. Four different dyn amical regimes are found as the potential strength or the friction var y. At high potential barriers, diffusion proceeds by single or multipl e jumps at high and low friction respectively, while two different kin ds of continuous unactivated diffusion are found at lower barriers. Th ese dynamical features are discussed in terms of three characteristic time scales whose relations determine the diffusion mechanisms.