Kramers Approach Research Articles

Escape from a metastable state

Many important processes in science involve the escape of a particle over a barrier. In this review, we report, extend, and interpret various theories of noise-activated escape. We discuss the connection between many-body transition state theory and Kramers' original diffusive Brownian motion approach (both in one-and multidimensional potential fields) and emphasize the physical situation inherent in Kramers' rate for weak friction. A rate theory accounting for memory friction is presented together with a set of criteria which test its validity. The complications and peculiarities of noise-activated escape in driven systems exhibiting multiple, locally stable stationary nonequilibrium states are identified and illustrated. At lower temperatures, quantum tunneling effects begin to play an increasingly important role. Early approaches and more recent developments of the quantum version of Kramers approach are discussed, thereby providing a description for dissipative escape at all temperatures.

Numerical solution for diffusion in periodic potentials: A comparison with the theory of activated processes.

A numerical algorithm is implemented to explore Brownian particle diffusion in a periodic potential for the full viscosity range. The predictions of the theory of activated processes are checked. In particular, a recent refinement of the vanishingly small viscosity limit of the Kramers approach by Grote and Hynes [J. Chem. Phys. 77, 3736 (1982)] and B\"uttiker, Harris, and Landauer [Phys. Rev. B 28, 1268 (1983)] is found to fit our numerical results better.