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Quantum Systems Periodically Perturbed in Time

  • J. Bellissard
Part of the NATO ASI Series book series (NSSB, volume 144)

Abstract

In 1974, J.E. Bayfield and P.M. Koch [1] performed a puzzling experiment on microwave ionization of hydrogen atoms. A beam of hydrogen atoms in a highly excited state (typically 50≤n≤80) crosses a microwave chamber. At the end of the cavity a counter measures the ionization rate. The results shown in fig. 1 below exhibit a transition between a regime of low field amplitude where almost all atoms are stable and a regime of high field amplitude where almost all atoms are ionized. Several frequencies were used but even the highest one represents only about 1% of the photon frequency for excitation to the continuum. This means that a perturbation theory is useless since it would require at least the calculation of hundred orders, and even in this case it would give significant predictions only in a very small range of values of the field amplitude. All other methods of spectroscopy failed to explain this effect. In 1978, following a suggestion by Lamb, J.6. Leopold and I.e. Percival [2] showed from a numerical simulation, that a purely classical treatment was quite efficient in describing quantitatively the experimental datas. Following this idea, R. Jensen [3] proposed in 1982 a theoretical scheme using the classical evolution of a one dimensional hydrogen atom in order to estimate the critical field amplitude: restricting the motion to the negative energy configurations the ionization occurs when the field amplitude is sufficiently high to create a transition to classical chaos.

Keywords

Field Amplitude Rydberg Atom Pure Point Scatter Theory Pure Point Spectrum 
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.

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Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • J. Bellissard
    • 1
  1. 1.Université de Provence and Centre de Physique ThéoriqueMarseilleFrance

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