Dynamics of multidimensional barrier crossing in the overdamped limit

Two 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.

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