Possible Evidence of Deterministic Chaos for the Sinusoidally-Driven Weakly-Bound Electron

  • James E. Bayfield
Part of the NATO ASI Series book series (NSSB, volume 144)


The theoretical search for quantum chaos in deterministic Hamiltonian systems has recently concentrated on two types of problems. The stationary states of autonomous two-dimensional classically—stochastic nonlinear systems have been investigated, examples being the Henon-Heiles model of two coupled one-dimensional anharmonic oscillators, and the bound electron in a strong static magnetic field (Harada and Hasegawa, 1983; Hose et al., 1985). Although the onset of classical stochastic behavior has been associated theoretically with changes in the quantum spectra of such systems, quantum calculations within their irregular regions have been hampered by a lack of convergence that may be characteristic of such stationary state problems.


Microwave Absorption Microwave Field Rydberg Atom Quantum Chaos Irregular Region 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bardsley, J. N., and Sundaram, B., 1985, Microwave Absorption by Hydrogen Atoms in High Rydberg States, Phys. Rev. A 32:689.ADSCrossRefGoogle Scholar
  2. Bardsley, J.N., Sundaram, B., Pinnaduwage, L. A., and Bayfield, J. E., 1985, Quantum Dynamics for Driven Weakly Bound Electrons near the Threshold for Classical Chaos, submitted for publication.Google Scholar
  3. Bayfield, J. E., and Pinnaduwage, L. A., 1985a, Diffusionlike Aspects of Multiphoton Absorption in Electrically Polarized Highly Excited Hydrogen Atoms, Phys. Rev. Lett. 54:313.ADSCrossRefGoogle Scholar
  4. Bayfield, J. E., and Pinnaduwage, L. A., 1985b, Microwave Multi-photon n-decreasing Transitions in Electrically Polarized Highly Excited Hydrogen Atoms, J. Phys. B. 18:L49.ADSCrossRefGoogle Scholar
  5. Casati, G., Chirikov, B. V., Izraelev, F. M., and Ford, J., Stochastic Behavior of a Quantum Penedulum under a Periodic Perturbation, in: “Stochastic Behavior in Classical and Quantum Hamiltonain Systems,” G. Casati and J. Ford, ed., Springer, New York (1979).CrossRefGoogle Scholar
  6. Casati, G., Chirikov, B. V., and Shepelyansky, 1984, Quantum Limitations for Chaotic Excitation of the Hydrogen Atom in a Monochromatic Field, Phys. Rev. Lett. 53:2525.ADSCrossRefGoogle Scholar
  7. Chang, S.-J., and Shi, K.-J., 1985, Time Evolution and Eigenstates of a Quantum Iterative System, Phys. Rev. Lett. 55:269.Google Scholar
  8. Harada, A. and Hasegawa, H., 1983, Correspondence between Classical and Quantum Chaos for Hydrogen in a Uniform Magnetic Field, J. Phys. A. l6:L259.Google Scholar
  9. Hose, G., Taylor, H. S., and Richards, D., 1985, Observations on the Regular and Irregular Motion as Exemplified by the Quadratic Zeeman Effect and Other Systems, J. Phys. B 18:51.ADSCrossRefGoogle Scholar
  10. Jensen, R. V., 1984, Stochastic Ionization of Surface-state Electrons: Classical Theory, Phys. Rev. A 30:386.Google Scholar
  11. Jensen, R. V., 1985a, Stochastic Ionization of Electrically Polarized Hydrogen Rydberg Atoms, Phys. Rev. Lett. 54:2057.Google Scholar
  12. Jensen, R. V., 1985b, private communication.Google Scholar
  13. Kleppner, D., Laboratory Studies of Rydberg Atoms, in: “Radio Recombination Lines,” P. Shaver, ed., Reidel Publ. Co., (1980).Google Scholar
  14. Pinnaduwage, L. A., and Bayfield, J. E., 1985, in preparation.Google Scholar
  15. Shepelyansky, D. L., Quantum Diffusion Limitation at Excitation of Rydberg Atom in Variable Field, in: “Chaotic Behavior in Quantum Systems,” G. Casati, ed., Plenum, New York (1985).Google Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • James E. Bayfield
    • 1
  1. 1.Department of Physics and AstronomyUniversity of PittsburghPittsburghUSA

Personalised recommendations