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Theory of activated rate processes for arbitrary frequency dependent friction: Solution of the turnover problem

J. Chem. Phys. 91, 4073 (1989); doi:10.1063/1.456837

Issue Date: 1 October 1989

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Eli Pollak
Chemical Physics Department, The Weizmann Institute of Science, 76100 Rehovot, Israel

Hermann Grabert
Fachbereich Physik, Universität-GHS Essen, D-4300 Essen, Federal Republic of Germany

Peter Hänggi
Lehrstuhl für Theoretische Physik, Universität Augsburg, D-8900 Augsburg, Federal Republic of Germany
An analytical theory is formulated for the thermal (classical mechanical) rate of escape from a metastable state coupled to a dissipative thermal environment. The working expressions are given solely in terms of the quantities entering the generalized Langevin equation for the particle dynamics. The theory covers the whole range of damping strength and is applicable to an arbitrary memory friction. This solves what is commonly known as the Kramers turnover problem. The basic idea underlying the approach is the observation that the escape dynamics is governed by the unstable normal mode coordinate—and not the particle system coordinate. An application to the case of a particle moving in a piecewise harmonic potential with an exponentially decaying memory-friction is presented. The comparison with the numerical simulation data of Straub, Borkovec, and Berne [J. Chem. Phys. 84, 1788 (1986)] exhibits good agreement between theory and simulation. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
History: Received 8 March 1989; accepted 8 June 1989
Permalink: http://link.aip.org/link/?JCPSA6/91/4073/1
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KEYWORDS and PACS

Keywords
PACS
  • 82.20.Pm
    Physical chemistry Chemical kinetics Measurements of rate constants, reaction cross sections, and activation energies
  • 82.20.Wt
    Physical chemistry Chemical kinetics Computational modeling; simulation
  • YEAR: 1988-89

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (27)
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