Probing the Quantum Analog of Chaos with Atoms in External Fields
For a few years, considerable interest arises in the problem of the quantum analog of classical chaos for hamiltonian system. Among several other simple atomic physics systems, the atom in a magnetic field turns out to be the most promising prototype for tackling such questions. The classical and quantum motions are now well understood. The experimental study is possible in high Rydberg states of atoms. Throughout the study of some aspects of this problem, we demonstrate that the quantum analog of chaos presents a two-fold aspect. While the spectral properties at short range are conveniently described by Random matrix theories, a long-range order still exist in the quantum dynamics which indicates the existence of scars of symmetries. This in turn is quite clearly exhibited in the experimental data on Rydberg atoms. We finally indicate how to generalize the notions to any situation involving the Coulomb field and perturbing potentials.
KeywordsRandom Matrix Theory Dynamical Symmetry Rydberg Atom Quantum Analog Approximate Symmetry
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- For example J.C. Gay in Progress Atomic Spectroscopy. Vol. C.; H.J. Beyer and H. Kleinpoppen Ed. (Plenum 1984 ).Google Scholar
- A. Einstein, Ver. Deut. Phys. Ger. 19, 82 (1917).Google Scholar
- A more detailed discussion can be found in: J.C. Gay in Atoms in Unusual Situations, J.P. BRIAND Ed. (PLENUM 1986 ).Google Scholar
- A.R. Edmonds and R.A. Pullen, Preprints, Imperial College 79 - 801 (1981).Google Scholar
- D. Delande and J.C. Gay, J. Phys. B 17, L 335 (1984).Google Scholar
- D. Delande and J.C. Gay, J. Phys. B 19, L 173 (1986).Google Scholar
- See for example O. Bohigas and M.J. Giannoni in “Mathematical and Computational methods in nuclear Physics” J.S. Dehesa et al. Ed. (SPRINGER 1984 ).Google Scholar
- D. Delande and J.C. Gay, Phys. Rev. Lett. 57, 2006 (1986).Google Scholar
- D. Delande and J.C. Gay, submitted Phys. Rev. Lett.Google Scholar
- D. Delande, unpublished (1987).Google Scholar