Abstract
The Mel'nikov-Meshkov (MM) turnover theory [J. Chem. Phys. 85, 1018 (1986)] for the escape rate of a particle from a metastable state is extended to a non-Markovian activated rate process in a potential with an arbitrary barrier shape. The key points of the extension are a generalized expression for the Kramers-Grote-Hynes transmission coefficient and a properly defined energy loss of the particle per oscillation. The former is derived by approximately solving the respective Fokker-Planck equation, while the latter is obtained from the deterministic particle dynamics. The resulting overall rate expression interpolates the correct limiting behavior for both weak and strong friction. Its validity is tested by comparing with exact numerical rates in potentials with parabolic, cusped, and quartic barriers. In all these cases we obtain excellent agreement between the theory and estimates of the rates from numerical calculations.
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