Semiclassical quantization of a nonintegrable system: Pushing the Fourier method into the chaotic regime
EBK, quantization, Henon-Heiles Hamiltonian, Fourier transform method, tunneling, quasiperiodicity
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.
Original Publication Citation
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 11 (1994): 7763-7778.
BYU ScholarsArchive Citation
Sohlberg, Karl and Shirts, Randall B., "Semiclassical quantization of a nonintegrable system: Pushing the Fourier method into the chaotic regime" (1994). Faculty Publications. 693.
Physical and Mathematical Sciences
Chemistry and Biochemistry
© 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
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