A periodic orbit formula for quantum reactions through transition states

A. Goussev*, R. Schubert, H. Waalkens, S. Wiggins

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


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 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. These results are used here to derive a formula which expresses the cumulative reaction probability as an absolutely convergent sum over periodic orbits contained in the transition state.

Original languageEnglish
Pages (from-to)1593-1596
Number of pages4
JournalAIP Conference Proceedings
Publication statusPublished - 17 Sept 2010
EventInternational Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010 - Rhodes, Greece
Duration: 19 Sept 201025 Sept 2010


  • quantum reactions
  • semiclassics
  • transition state theory


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