Bulletin of the Chemical Society of Japan
Online ISSN : 1348-0634
Print ISSN : 0009-2673
ISSN-L : 0009-2673
Quasi-Action Variable for Chaos in Chemical Dynamics
Kazuo Takatsuka
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1993 Volume 66 Issue 11 Pages 3189-3202

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Abstract

Is proposed quasi-action variable as a means to analyze the onset of classical chaos in molecular vibrational systems. The basic idea rests on a symplectic area generated by a classical trajectory in phase space, from which the geometrical information of a torus and its breakdown in extracted. The Fourier spectrum of the time derivative of this symplectic area centers on the following definition and findings: (1) in an integrable system, the action variables can be simply calculated in terms of the above Fourier amplitudes, (2) the quasi-action variable is also defined in a similar way and is a good approximation to the corresponding action variable, but (3) the construction of the quasi-action variable does not depend on the integrability and hence it it defined as well even for a chaotic system, and (4) the characteristics of chaos can be analyzed in the continuous spectrum of the quasi-action variable. Some numerical examples of the quasi-action variable are presented for a system of what we call phase-space large amplitude motion. As a byproduct, a simple method has been devised to calculate very accurate frequencies and amplitudes from the so-called Fast-Fourier-Transform (FFT) spectra without resorting to the so-called window technique.

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© 1993 The Chemical Society of Japan
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