Classical Chaos in One Dimensional Hydrogen in Strong DC and AC Electric Fields

  • D. C. Humm
  • Munir H. Nayfeh
Part of the NATO ASI Series book series (NSSB, volume 212)


We present studies of highly excited atomic hydrogen in the presence of DC and AC external fields. In particular, we analyze the effect of a DC electric field on classical chaos in one-dimensional hydrogen in a microwave field in the n nonmixing regime and also in the inter-n mixing regime where significant DC field induced ionization occurs. We study the AC field induced nonlinear classical resonances, the threshold of chaos, and the number of states trapped in the resonances. In the strong n mixing and ionizing regime (unclamping DC field), we find the chaotic dynamics depend sharply on the DC field and the number of states trapped in the resonances, allowing the system to undergo a transition from a regime of classical behavior to a regime of uniquely quantum behavior as the DC field is changed. We show that ionization by classical chaos competes favorably with ionization by tunneling in the transition region, and that tunneling allows very sensitive spectroscopy of this region.


Stark Shift Nonlinear Resonance Threshold Curve Quantum Regime Classical Chaos 
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  1. 1.
    J.E. Bayfield and P.M. Koch, Phys. Rev. Lett. 33:258 (1974).ADSCrossRefGoogle Scholar
  2. 2.
    P.M. Koch, Fundamental Aspects of Quantum Theory, eds. V. Gorini and A. Frigerio (Plenum 1986).Google Scholar
  3. 3.
    J. Ford, in The New Physics, eds. S. Capelin and P.C.W. Davies (Cambridge University Press 1986).Google Scholar
  4. 4.
    For examples, see Stochastic Behavior in Classical and Quantum Hamiltonian Systems, Lecture Notes in Physics V. 93. eds. G. Casati and J. Ford (Springer-Verlag 1979); Chaotic Behavior in Quantum Systems, ed. G. Casati (Plenum 1985).Google Scholar
  5. 5.
    G. Casati, J. Ford, I Guarneri, and F. Vivaldi, Phys Rev. A34. 1413 (1986).ADSCrossRefGoogle Scholar
  6. 6.
    G.P. Berman, G.M. Zaslavsky, and A.R. Kolovsky, Phys. Lett. 87A:152 (1982).ADSCrossRefGoogle Scholar
  7. 7.
    G. Casati, B. Chirikov, D. Shepelyansky, and I. Guarneri, Phvs. Rep. 154:79 (1987).ADSGoogle Scholar
  8. 8.
    I.C. Percival, J. Phvs. B 6:L229 (1973).ADSGoogle Scholar
  9. N. Pomphrey, J. Phvs. B 7:1909 (1974).ADSGoogle Scholar
  10. 9.
    R.V. Jensen, Phvs. Rev. A 30, 386 (1984).ADSCrossRefGoogle Scholar
  11. 10.
    J.E. Bayfield and L.A. Pinnaduwage, Phvs. Rev. Lett. 54:313 (1985).ADSCrossRefGoogle Scholar
  12. 11.
    R.V. Jensen and S.M. Susskind, Photons and Continuum States of Atoms and Molecules, eds. N.K. Rahman, C. Guidotti, and M. Allegrini, 13 (Springer-Verlag 1987).Google Scholar
  13. 12.
    M.H. Nayfeh, D.C. Humm, and M.S. Peercy, proc. symposium “The Hydrogen Atom,” Pisa, Italy, June 30-July 2, 1988, eds. F. Bassani, T.W. Hänsch, and M. Inguscio.Google Scholar
  14. 13.
    R.V. Jensen, Phys. Rev. Lett. 54, 2057 (1985).ADSCrossRefGoogle Scholar
  15. 14.
    G.P. Berman, G.M. Zaslavsky, and A.R. Kolovsky, Zh. Eksp. Teor. Fiz. 88:1551 (1985).Google Scholar
  16. G.P. Berman, G.M. Zaslavsky, and A.R. Kolovsky, [Sov. Phvs. JETP 61:925 (1985)].Google Scholar
  17. 15.
    MJ. Stevens and B. Sundaram, Phys. Rev. A 36,417(1987).ADSCrossRefGoogle Scholar
  18. 16.
    B.V. Chirikov, Phys. Rep. 52:263 (1979).MathSciNetADSCrossRefGoogle Scholar
  19. 17.
    G.M. Zaslavsky and B.V. Chirikov, Usp. Fiz. Nauk. 105:3 (1971).CrossRefGoogle Scholar
  20. G.M. Zaslavsky and B.V. Chirikov, [Sov. Phvs. Usp. 14:549 (1971)].ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • D. C. Humm
    • 1
  • Munir H. Nayfeh
    • 1
  1. 1.Department of PhysicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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