No abstract available

[en] For a few years, considerable interest arose 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, the authors 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. Finally the authors indicate how to generalize the notions to any situation involving the Coulomb field and perturbing potentials. 21 refs.; 8 figs

[en] In the presence of a strong state magnetic field, the classical dynamics of a Rydberg atomic state turns chaotic. This has important consequences on the energy levels and eigenstates of the quantum system. These are analysed in connection with the recent experimental results. (orig.)

[en] We propose a new theoretical scheme for exciting atoms in circular Rydberg states with high efficiency whatever the atomic species. It only requires the use of a weak magnetic field crossed to a weak time-varying electric field. The scheme is based on the symmetry properties of the Coulomb interaction

[en] Atomic systems played a major role in the birth and growth of quantum mechanics. One central idea was to relate the well-known classical motion of the electron of a hydrogen atom--an ellipsis around the nucleus--to the experimentally observed quantization of the energy levels. This is the aim of the Bohr and Bohr-Sommerfeld models. These simple semiclassical models were unable to make any reliable prediction on the energy spectrum of the next simplest atom, helium. Because of the great success of quantum mechanics, the problem of correspondence between the classical and the quantal dynamics has not received much attention in the last 60 years. The fundamental question is (Gutzwiller, 1990). How can classical mechanics be understood as a limiting case within quantum mechanics? For systems with time-independent one-dimensional dynamics like the harmonic oscillator and the hydrogen atom, the correspondence is well understood. The restriction to such simple cases creates the erroneous impression that the classical behavior of simple systems is entirely comprehensible and easily described. During the last 20 years it has been recognized that this in not true and that a complex behavior can be obtained from simple equations of motion. This usually happens when the motion is chaotic, that is, unpredictable on a long time scale although perfectly deterministic (Henon, 1983). A major problem is that of understanding how the regular or chaotic behavior of the classical system is manifest in its quantum properties, especially in the semiclassical limit. 53 refs., 15 figs., 1 tab

[en] A formalism is presented based on the non-invariance algebra for the Coulomb problem that allows an effective Hamiltonian to be deduced for a wide variety of perturbing potentials. Applications to the problem of the hydrogen atom in a magnetic field are performed. The exact first- and second-order expressions of the effective diamagnetic Hamiltonian are derived under a general operatorial form. Some of the consequences and further developments are briefly indicated. (author)

[en] We report the results of experimental measurements on atomic diamagnetism in inter-l and inter-n mixing conditions. They have been obtained using high resolution techniques on highly hydrogenic M = +-3 states of cesium, providing a pure experimental situation. Comparison with straightforward hydrogenic calculations and semi-classical predictions allow identification of the dominant lines of the spectrum which are shown to behave as precursors of the quasi Landau spectrum. (orig.)

No abstract available

[en] The photoionization spectrum of helium near the double-ionization threshold shows structure which indicated a transition towards quantum chaos

[en] We calculate the photo-ionization cross-section from the ground state of the helium atom, using the complex rotation method and diagonalization of sparse matrices. This produces directly the positions and widths of the doubly excited ¹P^o resonances together with the photo-ionization cross-section. Our calculations up to the N = 9 threshold are in perfect agreement with recent experimental data and show the transition from a regular structure at low energy to a chaotic one at high energy, where various resonances strongly overlap. (orig.)