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Kramers' activation rate for a sharp edged potential barrier: The double oscillator

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  • Dekker, H.

Abstract

Using Rayleigh's identity for the pertinent eigenvalue of Kramers' Fokker-Planck model, the noise activated rate of escape over a sharp edged potential barrier is obtained for the symmetric double oscillator. The rate is shown in its dependence on barrier height and on viscosity. Both the weak and strong damping ranges are treated by asymptotic methods in such a way that they can be properly connected in the moderate damping regime by means of a generalized Galerkin method. In the limit of an extremely high barrier the reaction rate tends to the standard transition state results for almost all values of the dissipation, as expected from Kramers' smooth parabolic barrier result. In general, however, the sharp edged barrier dynamics is found to be quite unlike that of the parabolic barrier.

Suggested Citation

  • Dekker, H., 1986. "Kramers' activation rate for a sharp edged potential barrier: The double oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 136(1), pages 124-146.
    • Handle: RePEc:eee:phsmap:v:136:y:1986:i:1:p:124-146
    DOI: 10.1016/0378-4371(86)90046-4
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