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Prog. Theor. Phys. Vol. 69 No. 5 (1983) pp. 1403-1415
Chaotic Response of a Self-Interacting Pseudo-Spin Model
Masayoshi Inoue and
Hitoshi Koga
Department of Physics, Kagoshima University, Kagoshima 890
(Received November 26, 1982)
Abstract:
A new model for a conservative semi-quantum system is presented to study quantum aspects of chaotic behavior. The model is made up of a pseudo-spin which interacts with an external field and the reaction field of the polarization of the pseudo-spin. The reaction field is super-imposed upon the external field in the equations of motion and it brings nonlinear terms. Two isolating integrals, whose intersection curve gives an orbit, are obtained analytically in a static external field case, and phase plane plots are drawn using the integrals. The phase plane plots have three elliptic fixed points and one hyperbolic fixed point for a strong reaction field case and it has two elliptic ones and no hyperbolic one for a weak reaction field case. Only one single finite separatrix emanates from the hyperbolic fixed point in the strong reaction field case.
Chaotic motion is observed in a periodic external field case, and Poincaré mappings, Lyapunov exponents and power spectra of the polarization are calculated with the aid of computer simulations. The spectrum of 1-dimensional Lyapunov exponents takes a hyperbolic type ( +, 0, - ), namely the model has C-system like property.
URL :
http://ptp.ipap.jp/link?PTP/69/1403/
DOI : 10.1143/PTP.69.1403
References:
- M. Hénon and C. Heiles, Astron. J. 69 (1964), 73.
-
I. Prigognie and R. Lefever, J. Chem. Phys. 48 (1968), 1695[CrossRef].
R. Lefever, J. Chem. Phys. 48 (1968), 4977[AIP Scitation].
K. Tomita, T. Kai and F. Hikami, Prog. Theor. Phys. 57 (1977), 1159[PTP].
- K. Tomita and T. Kai, J. Stat. Phys. 21 (1979), 65.
- See, e. g., N. Minorsky, Nonlinear Oscillations (Robert E. Krieger Publishing Company, Huntington, New York, 1974).
-
R. M. Stratt, N. C. Handy and W. H. Miller, J. Chem Phys. 71 (1979), 3311[CrossRef].
- B. Barbanis, Astron. J. 71 (1966), 415.
-
G. Casati and J. Ford, Phys. Rev. A 12 (1975), 1702[APS].
- M. Inoue and S. Shiraishi, Prog. Theor. Phys. 68 (1982), 1470[PTP].
- See, e. g., M. Sargent III, M. O, Scully and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, 1974).
-
P. G. de Gennes, Solid State Commun. 1 (1963), 132[CrossRef].
M. Tokunaga and T. Matsubara, Prog. Theor. Phys. 35 (1966), 581[PTP].
- See, e. g., V. I. Arnold, Ordinary Differential Equations (M. I. T. Press, 1973).
- See, e. g., R. H. G. Helleman, Fundamental Problems in Statistical Mechanics Vol 5, edited by E. G. D. Cohen (North Holland Publ., Amsterdam and N. Y., 1980) and references cited therein.
- I. Shimada and T. Nagashima, Prog. Theor. Phys. 61 (1979), 1605[PTP].
-
T. Hogg and B. A. Huberman, Phys. Rev. Lett. 48 (1982), 711[APS].
-
U. Frisch and R. Morf, Phys. Rev. A 23 (1981), 2673[APS].
Y. F. Chang, M. Tabor and J. Weiss, Phys. Lett. A 85 (1981), 211[CrossRef].
M. Tabor and J. Weiss, Phys. Rev. A 24 (1981), 2157[APS].
Y. F. Chang, M. Tabor and J. Weiss, J. Math. Phys. 23 (1982) 531[CrossRef].
-
G. Benettin, L. Galgani and J. Strelcyn, Phys. Rev. A 14 (1976) 2338[APS].
