Over-damped Limit Research Articles

Dynamics of Multidimensional Barrier Crossing in the Overdamped Limit

AbstractTwo methods for numerical solution of multidimensional diffusion problems are presented and applied to the two dimensional barrier crossing problem in the overdamped limit. One of these methods is based on evaluating the smallest non‐vanishing eigenvalue of the Smoluchowski equation, and the other is based on an adaption of Chandler's steady state correlation function approach. Both methods make use of the fast Fourier transform algorithm for solving a transformed version of the Smoluchowski equation. The numerical solutions are compared to results based on the Kramers theory and some observations concerning effects of the dynamics of barrier crossing problems are made.

Memory effect on thermally activated escape rates

Non-Markovian thermal Brownian motion of a particle over a barrier is studied using thermal noise with a small but finite bath-memory correlation time. Starting from the corresponding non-Markovian Smoluchowski master equation, valid in the over-damped limit, the rate of escape $\ensuremath{\lambda}$ is evaluated, and it is shown that a renormalization of the bare damping occurs. The modeling of the rate $\ensuremath{\lambda}$ for a special class of bistable, driven non-Markovian nonequilibrium systems is sketched.