Classical Chaos on Double Nonlinear Resonances in Diatomic Molecules

DOI: 10.4236/jmp.2015.64054   PDF   HTML   XML   3,633 Downloads   4,123 Views   Citations


Classical chaotic behavior in diatomic molecules is studied when chaos is driven by a circularly polarized resonant electric field and expanding up to fourth order of approximation the Morse’s potential and angular momentum of the system. On this double resonant system, we find a weak and a strong stationary (or critical) points where the chaotic characteristics are different with respect to the initial conditions of the system. Chaotic behavior around the weak critical point appears at much weaker intensity on the electric field than the electric field needed for the chaotic behavior around the strong critical point. This classical chaotic behavior is determined through Lyapunov exponent, separation of two nearby trajectories, and Fourier transformation of the time evolution of the system. The threshold of the amplitude of the electric field for appearing the chaotic behavior near each critical point is different and is found for several molecules.

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López, G. and Mercado, A. (2015) Classical Chaos on Double Nonlinear Resonances in Diatomic Molecules. Journal of Modern Physics, 6, 496-509. doi: 10.4236/jmp.2015.64054.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Burton, M. (1987) Ast. Soc., 28, 269.
[2] Chevalier, R. (1999) The Astrophysical Journal, 511, 798.
[3] Shuryak, E.V. (1976) Sov. Phys. JEPT, 44, 1070.
[4] Parson, R.P. (1987) The Journal of Chemical Physics, 88, 3655.
[5] Dardi, P.S. and Gray, K. (1982) The Journal of Chemical Physics, 77, 1345.
[6] Messiah, A. (1964) Quantum Mechanics I. North Holland, John Wiley & Sons, Inc., New York, London, 29.
[7] Lombardi, M., Labastie, P., Bordas, M.C. and Boyer, M. (1988) The Journal of Chemical Physics, 89, 3479.
[8] Berman, G.P. and Kolovsky, A.R. (1989) Sov. Phys. JEPT, 68, 898.
[9] Berman, G.P. and Kolovsky, A.R. (1992) Soviet Physics Uspekhi, 35, 303.
[10] Berman, G.P., Bulgakov, E.N. and Holm, D.D. (1995) Physical Review A, 52, 3074.
[11] López, G.V. and Zanudo, J.G.T. (2011) Journal of Modern Physics, 2, 472-480.
[12] Reichl, L.E. (2004) The Transition to Chaos. Springer-Verlag, Berlin.
[13] Lichtenberg, A.J. and Liberman, M.A. (1983) Regular and Stochastic Motion. Springer-Verlag, Berlin.
[14] Chirikov, B.V. (1979) Physics Reports, 52, 263-379.
[15] Drazin, P.G. (1992) Nonlinear Systems. Cambridge University Press, Cambridge.
[16] Gershitov, A.G., Spiridonov, V.P. and Butayev, B.S. (1978) Chemical Physics Letters, 55, 599-602.
[17] Morse, P.M. (1929) Physical Review, 34, 57.
[18] Perko, L. (1996) Differential Equations and Dynamical Systems. 2nd Edition, Springer, Berlin.
[19] Strogatz, S.H. (1994) Nonlinear Dynamics and Chaos. Perseus Books, New York City.

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