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Divergences of the semiclassical S-matrix beyond hyperbolic systems

  • Krzysztof Stefański
Part II: Seminars
Part of the Lecture Notes in Physics book series (LNP, volume 457)

Abstract

It is shown that the absolute convergence of the semiclassical S-matrix formula in the case of irregular inelastic scattering depends only on the fractal dimension of the corresponding singular set of the scattering function, and the critical fractal dimension is derived. Ways of handling divergences are discussed.

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References

  1. 1.
    W.H. Miller, Adv. Chem. Phys. 25, 69 (1974).Google Scholar
  2. 2.
    C.C. Rankin and W.H. Miller, J. Chem. Phys. 55, 3150 (1971).Google Scholar
  3. 3.
    L. Gottdiener, Mol. Phys. 29, 1585 (1975).Google Scholar
  4. 4.
    D.A. Noid, S.K. Gray and S.A. Rice, J. Chem. Phys. 84, 2649 (1986).Google Scholar
  5. 5.
    R.T. Skodje, J. Chem. Phys. 90, 6193 (1989).Google Scholar
  6. 6.
    K. Someda, R. Ramaswamy and H. Nakamnra, J. Chem. Phys. 98, 1156 (1993).Google Scholar
  7. 7.
    J.M. Bowman (ed.) Advances in Molecular Vibrations and Collision Dynamics: Quantum Reactive Scattering, JAI Press, Greenwich 1993.Google Scholar
  8. 8.
    S. Levit and U. Smilansky, Ann. Phys. 108, 165 (1977).Google Scholar
  9. 9.
    K. Stefański, K. Someda and H. Nakamura, Divergencies of the Classical S-Matrix Formula in Irregular Scattering to be published.Google Scholar
  10. 10.
    J.H. Jensen, Phys. Rev. Lett. 73, 244 (1994).Google Scholar
  11. 11.
    M.V. Berry, in: Lectures at Les Houches 1989, Session LII, Chaos and Quantum Physics (eds. M.-J. Giannoni, A. Voros, J. Zinn-Justin), North Holland, Amsterdam 1991, p. 251.Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Krzysztof Stefański
    • 1
  1. 1.Institute of AstronomyNicholas Copernicus UniversityTorunPoland

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