Semiclassical quantization of a nonintegrable system: Pushing the Fourier method into the chaotic regime

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Permanent URL	http://hdl.lib.byu.edu/1877/1358
Title	Semiclassical quantization of a nonintegrable system: Pushing the Fourier method into the chaotic regime
BYU Creator	Sohlberg, Karl Shirts, Randall B.
Keywords	EBK; quantization; Henon-Heiles Hamiltonian; Fourier transform method; tunneling; quasiperiodicity
Description/Abstract	Semiclassical Einstein–Brillouin–Keller (EBK) quantization of the nonintegrable Hénon–Heiles Hamiltonian succeeds using the Fourier transform method of Martens and Ezra. Two innovations are required for this success: (1) the use of tunneling corrected quantizing actions obtained from an approximate, one-dimensional Hamiltonian and (2) exploitation of intermediate-time approximate quasiperiodicity or "vague tori'' wherein the Fourier transform of chaotic motion over 10–100 vibrational periods allows the determination of frequencies and amplitudes which approximate motion during the time interval. Approximate tori, actions, and EBK energy levels are then straightforward. We use an interpolation method to smooth over small resonance zones that are not expected to be important quantum mechanically.
Source	Sohlberg, Karl and Randall B. Shirts."Semiclassical quantization of a nonintegrable system: Pushing the Fourier method into the chaotic regime." The Journal of Chemical Physics 101 (1994): 7763-7778.;
Publisher	AIP
Date Original	1994-11-01
Language	English eng en
Publication Type	Articles
Type	Text
Format	application/pdf
Owning Institution	Brigham Young University
BYU College	College of Physical and Mathematical Sciences
BYU Department	Chemistry and Biochemistry
Copyright Status	(c) 1994 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in The Journal of Chemical Physics and may be found at http://link.aip.org/link/?JCPSA6/101/7763/1;
Copyright Use Information	http://www.lib.byu.edu/generic_copyright.html

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Semiclassical quantization of a nonintegrable system: Pushing the Fourier method into the chaotic regime

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