Three or More Degrees of Freedom

Lichtenberg, Anna; Lieberman, Melvyn

doi:10.1007/978-1-4757-4257-2_6

Cited by 1 publication

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“…Note that the contributing states: 6, 7, 16 and 17, are completely assignable ͑see Fig. 15͒, corresponding to the quantum states (n R ,n ) ϭ(0,8),(0,10), (1,8) and (1,10), respectively.…”

Section: B Results and Discussionmentioning

confidence: 99%

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Saddle-node bifurcations in the LiNC/LiCN molecular system: Classical aspects and quantum manifestations

Borondo

Zembekov

Benito

1996

The Journal of Chemical Physics

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A classical-quantum correspondence study of a saddle-node bifurcation in a realistic molecular system is presented. The relevant classical structures ͑periodic orbits and manifolds͒ and its origin are examined in detail. The most important conclusion of this study is that, below the bifurcation point, there exists an infinite sequence of precursor orbits, which mimic for a significant period of time the ͑future͒ saddle-node orbits. These structures have a profound influence in the quantum mechanics of the molecule and several vibrational wave functions of the system present a strong localization along the saddle-node periodic orbits. A striking result is that this scarring effect also takes place well below the bifurcation energy, which constitutes a manifestation of the so-called ''ghost'' orbits in configuration and phase space. This localization effect has been further investigated using wave packet dynamics.

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Section: B Results and Discussionmentioning

confidence: 99%

“…1 The KAM ͑Kolmogorov-Arnold-Moser͒ theorem and the widespread possibility of numerical experiments have played an important role in this development. The importance of phase space structures such as periodic orbits ͑PO͒, 1,2 cantori 3 or broken separatrices 4 has been realized, and the phenomenon of classical chaos well characterized.…”

Section: Introductionmentioning

confidence: 99%