Periodic-orbit formula for quantum reactions through transition states

Roman Schubert, Holger Waalkens, Arseni Goussev, and Stephen Wiggins
Phys. Rev. A 82, 012707 – Published 23 July 2010

Abstract

Transition state theory forms the basis of computing reaction rates in chemical and other systems. Recently, it has been shown how transition state theory can rigorously be realized in phase space by using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov-Siegert resonances. In this paper, these results are used to express the cumulative reaction probability as an absolutely convergent sum over periodic orbits contained in the transition state.

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  • Received 22 January 2010

DOI:https://doi.org/10.1103/PhysRevA.82.012707

©2010 American Physical Society

Authors & Affiliations

Roman Schubert1, Holger Waalkens1,2, Arseni Goussev1, and Stephen Wiggins1

  • 1School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom
  • 2Johann Bernoulli Institute for Mathematics and Computer Sciences, University of Groningen, P.O. Box 407, 9700 AK Groningen, the Netherlands

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Vol. 82, Iss. 1 — July 2010

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