Kramers' Turnover Theory: Improvement and Extension to Low Barriers

Kramers' turnover theory as derived by Pollak, Grabert, and Hanggi (PGH) suffers from a few drawbacks. First, the energy loss in PGH theory is not a monotonic function of the friction. Second, the theory is not applicable to surface diffusion, because the effective potential for the system does not conserve the periodicity of the potential. Third, when the reduced barrier height is low, it is rather inaccurate. In this paper, we present a modification of PGH theory that alleviates these drawbacks. We also introduce a finite barrier correction term which takes into consideration that the energy interval of the escaping particle is bounded from below. The resulting theory is tested for motion on a cubic potential and relatively low reduced barriers.