title: Kramers' theory for diffusion on a periodic potential.
abstract: Kramers' turnover theory, based on the dynamics of the collective unstable normal mode (also known as PGH theory), is extended to the motion of a particle on a periodic potential interacting bilinearly with a dissipative harmonic bath. This is achieved by considering the small parameter of the problem to be the deviation of the collective bath mode from its value along the reaction coordinate, defined by the unstable normal mode. With this change, the effective potential along the unstable normal mode remains periodic, albeit with a renormalized mass, or equivalently a renormalized lattice length. Using second order classical perturbation theory, this not only enables the derivation of the hopping rates and the diffusion coefficient, but also the derivation of finite barrier corrections to the theory. The analytical results are tested against numerical simulation data for a simple cosine potential, ohmic friction, and different reduced barrier heights.
authors.affiliation: Chemical Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel. eli.pollak@weizmann.ac.il and Shenkar College of Engineering and Design, Ramat Gan, Israel.
authors.forename: Reuven
authors.initials: R
authors.lastname: Ianconescu
authors.affiliation: Chemical Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel. eli.pollak@weizmann.ac.il.
authors.forename: Eli
authors.initials: E
authors.lastname: Pollak