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Theoretica chimica acta

, Volume 75, Issue 1, pp 33–52 | Cite as

Semiclassical analysis of Hénon-Heiles coupled oscillators: quasi-periodic and chaotic quantum behavior and the resonance model of unimolecular decay

  • Vincenzo Aquilanti
  • Simonetta Cavalli
  • Gaia Grossi
Article

Abstract

The quantum mechanics of the Hénon-Heiles potential is analyzed using an adiabatic representation in polar coordinates and exploiting the asymptotic separability of the radius. The procedure allows us to establish a correlation between quasiperiodic and chaotic classical behavior, and regular or irregular quantum modes: It is found that irregularity can be attributed to nonadiabatic effects at the potential ridge. The resonance widths for this prototypic system of coupled oscillators are studied with reference to the lifetime in the quantum theory of unimolecular decay. The near separability of the radius of the polar coordinate representation is exploited for discussing energy dependence and symmetry effects on the widths. The relevance of this analysis for the characterization of quantum mechanical behavior near an elliptic umbilic catastrophe point is also briefly considered.

Key words

Hénon-Heiles potential Coupled oscillators Adiabatic representation Chaotic quantum modes Elliptic umbilic catastrophes Resonance widths 

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Vincenzo Aquilanti
    • 1
  • Simonetta Cavalli
    • 1
  • Gaia Grossi
    • 1
  1. 1.Dipartimento di Chimica dell'UniversitàPerugiaItaly

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