Chaos in One-Dimensional Hydrogen

  • D. C. Humm
  • Munir H. Nayfeh
Part of the Physics of Atoms and Molecules book series (PAMO)

Abstract

We analyze the effect of a DC electric field on classical chaos in one-dimensional hydrogen in a microwave field. We show that, under ordinary experimental conditions, the system is expected to undergo a transition from a regime of classical behavior to a regime of uniquely quantum behavior as the DC field is increased, for an unclamping DC field. We also 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.

Keywords

Microwave Helium Schiff Berman 

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References

  1. 1.
    J. Ford, in The New Physics, eds. S. Capelin and P. C. W. Davies Cambridge Univ. Press 1986).Google Scholar
  2. 2.
    For example, 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
  3. 3.
    G. Casati, J. Ford, I. Guarneri, and F. Vivaldi, Phys. Rev. A 34:1413 (1986).ADSCrossRefGoogle Scholar
  4. 4.
    G. P. Berman, G. M. Zaslavsky, and A. R. Kolovsky, Phys. Lett. 87A:152 (1982).ADSGoogle Scholar
  5. 5.
    G. Casati, B. Chirikov, D. Shepelyansky, and I. Guarneri, Phys. Rep. 154:79 (1987).ADSCrossRefGoogle Scholar
  6. 6.
    I. C. Percival, J. Phys. B 6:L229 (1973), and N. Pomphrey, J. Phys. B 7:1909 (1974).ADSCrossRefGoogle Scholar
  7. 7.
    R. V. Jensen, Phys. Rev. A 30:386 (1984).ADSGoogle Scholar
  8. 8.
    J. E. Bayfield and L. A. Pinnaduwage, Phys. Rev. Lett. 54:313 (1985).ADSCrossRefGoogle Scholar
  9. 9.
    M. H. Nayfeh, D. C. Humm, and M. S. Peercy, presented to the APS March meeting, K3 3 (1988).Google Scholar
  10. 10.
    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
  11. 11.
    J. E. Bayfield, Photons and Continuum States of Atoms and Molecules, eds. Rahman, Guidotti, and Allegrini, 8 (Springer-Verlag 1987).Google Scholar
  12. 12.
    P. M. Koch, Fundamental Aspects of Quantum Theory, eds. V. Gorini and A. Frigerio (Plenum 1986).Google Scholar
  13. 13.
    G. P. Berman, G. M. Zaslavsky, and A. R. Kolovsky, Zh. Eksp. Teor. Fiz. 88:1551 (1985) [Sov. Phys. JETP 61:925 (1985)]. Also see M. H. Nayfeh and D. Humm, Photons and Continuum States of Atoms and Molecules, eds. N. K. Rahman, C. Guidotti, and M. Allegrini, 28 (Springer-Verlag 1987).Google Scholar
  14. 14.
    W. L. Glab, K. Ng, D. Yao, and M. H. Nayfeh, Phys. Rev. A 31:3677 (1985).ADSGoogle Scholar
  15. 15.
    H. Rottke and K. H. Welge, Phys. Rev. A 33:301 (1986).ADSGoogle Scholar
  16. 16.
    D. A. Harmin, Phys. Rev. A 26:2656 (1982).ADSGoogle Scholar
  17. 17.
    B. V. Chirikov, Phys. Rep. 52:263 (1979).MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    G. M. Zaslavsky and B. V. Chirikov, Usp. Fiz. Nauk. 105:3 (1971) [Sov. Phys. Usp. 14:549 (1971)].Google Scholar
  19. 19.
    L. I. Schiff, Quantum Mechanics, 3rd ed., 268 (McGraw-Hill 1968).Google Scholar
  20. 20.
    O. Bohigas, M. J. Gianonni, and C. Schmit, Phys. Rev. Lett. 52:1 (1984).MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1988

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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