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Reaction rate theory: weak- to strong-friction turnover in Kramers' Fokker-Planck model

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  • van den Brink, Alec Maassen
  • Dekker, H.

Abstract

We present a unified treatment for both weak and strong friction — including the turnover regime — of Kramers' Fokker-Planck model for activated rate processes. No recourse to a specific microscopic model (à la Grabert et al.) or Langevin dynamics (à la Graham) will be made. Upon introducing some new theoretical concepts such as a constrained Gaussian transformation (CGT) and a dynamical extension of phase space (EPS), the analysis proceeds in terms of the unstable-mode energy and is systematic in a small parameter. We also introduce a nonlinear toy model for barrier recrossing for a simplified discussion of aspects like finite-barrier corrections, the boundary layer approximation, and exact solution in the absence of potential conditions.

Suggested Citation

  • van den Brink, Alec Maassen & Dekker, H., 1997. "Reaction rate theory: weak- to strong-friction turnover in Kramers' Fokker-Planck model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(3), pages 515-553.
    • Handle: RePEc:eee:phsmap:v:237:y:1997:i:3:p:515-553
    DOI: 10.1016/S0378-4371(96)00425-6
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    Cited by:

    1. Philipp, Lucas & Shizgal, Bernie D., 2019. "A Pseudospectral solution of a bistable Fokker–Planck equation that models protein folding," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 158-166.

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