Beigie, Darin and Wiggins, Stephen (1992) Dynamics associated with a quasiperiodically forced Morse oscillator: Application to molecular dissociation. Physical Review A, 45 (7). pp. 48034829. ISSN 05562791. http://resolver.caltech.edu/CaltechAUTHORS:BEIpra92

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Abstract
The dynamics associated with a quasiperiodically forced Morse oscillator is studied as a classical model for molecular dissociation under external quasiperiodic electromagnetic forcing. The forcing entails destruction of phasespace barriers, allowing escape from bounded to unbounded motion. In contrast to the ubiquitous Poincaré map reduction of a periodically forced system, we derive a sequence of nonautonomous maps from the quasiperiodically forced system. We obtain a global picture of the dynamics, i.e., of transport in phase space, using a sequence of timedependent twodimensional lobe structures derived from the invariant homoclinic tangle of a persisting invariant saddletype torus in a Poincaré section of an associated autonomous system phase space. Transport is specified in terms of twodimensional lobes mapping from one to another within the sequence of lobe structures, and this provides the framework for studying basic features of molecular dissociation in the context of classical phasespace trajectories. We obtain a precise criterion for discerning between bounded and unbounded motion in the context of the forced problem. We identify and measure analytically the flux associated with the transition between bounded and unbounded motion, and study dissociation rates for a variety of initial phasespace ensembles, such as an even or weighted distribution of points in phase space, or a distribution on a particular level set of the unperturbed Hamiltonian (corresponding to a quantum state). A doublephaseslice sampling method allows exact numerical computation of dissociation rates. We compare single and twofrequency forcing. Infinitetime average flux is maximal in a particular singlefrequency limit; however, lobe penetration of the level sets of the unperturbed Hamiltonian can be maximal in the twofrequency case. The variation of lobe areas in the twofrequency problem gives one added freedom to enhance or diminish aspects of phasespace transport on finite time scales for a fixed infinitetime average flux, and for both types of forcing the geometry of lobes is relevant. The chaotic nature of the dynamics is understood in terms of a traveling horseshoe map sequence.
Item Type:  Article 

Additional Information:  ©1992 The American Physical Society Received 19 June 1991 This material is based upon work supporeted by the National Science Foundation and the Office of Naval Research. 
Record Number:  CaltechAUTHORS:BEIpra92 
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:BEIpra92 
Alternative URL:  http://dx.doi.org/10.1103/PhysRevA.45.4803 
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ID Code:  2763 
Collection:  CaltechAUTHORS 
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Deposited On:  25 Apr 2006 
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