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The driven three body Coulomb problem

Published online by Cambridge University Press:  01 April 2007

JAVIER MADROÑERO ,
LAURENT HILICO ,
BENOÎT GRÉMAUD ,
DOMINIQUE DELANDE  and
ANDREAS BUCHLEITNER
JAVIER MADROÑERO
Affiliation:
Physik Department, Technische Universität München, James-Franck-Straβe, D-85747 Garching Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden
LAURENT HILICO
Affiliation:
Laboratoire Kastler Brossel de l'Université Pierre et Marie Curie et de l'Ecole Normale Supérieure, 4, place Jussieu, F-75252 Paris Cedex 05
BENOÎT GRÉMAUD
Affiliation:
Laboratoire Kastler Brossel de l'Université Pierre et Marie Curie et de l'Ecole Normale Supérieure, 4, place Jussieu, F-75252 Paris Cedex 05
DOMINIQUE DELANDE
Affiliation:
Laboratoire Kastler Brossel de l'Université Pierre et Marie Curie et de l'Ecole Normale Supérieure, 4, place Jussieu, F-75252 Paris Cedex 05
ANDREAS BUCHLEITNER
Affiliation:
Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński, Reymonta 4, PL-30-059 Kraków
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Extract

The three body Coulomb problem is one of the oldest unsolved problems of theoretical physics, and holds a variety of puzzling problems, on both the classical and quantum levels. It is of paradigmatic importance since it bears dynamical and spectral features that establish a link between single and many-particle dynamics, with the absolute minimum of ingredients. When additionally exposed to a time-periodic external perturbation, the effective dimension of the classical phase space as well as of Hilbert space increases dramatically. This gives rise to new phenomena, which stimulate research in such remote areas as mathematical physics, semiclassics and intense-field laser–matter interactions. In the present review, we illustrate how these different areas are interconnected by three interacting particles.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 17 , Issue 2 , April 2007 , pp. 225 - 246
Copyright
Copyright © Cambridge University Press 2007

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References

Balslev, E. and Combes, J. M. (1971) Spectral properties of many-body Schrödinger operators with dilation-analytic interactions. Commun. math. Phys. 22 280.CrossRefGoogle Scholar
Bohigas, O. (1991) Random matrix theories and chaotic dynamics. In: Chaos and quantum physics, Les Houches Lectures, North-Holland 87.Google Scholar
Bohr, N. (1936) Nature 137 344.CrossRefGoogle Scholar
Buchleitner, A. and Delande, D. (1995) Nondispersive electronic wave packets in multiphoton processes. Phys. Rev. Lett. 75 1487.Google Scholar
Buchleitner, A., Delande, D. and Zakrzewski, J. (2002) Non-dispersive wave packets in periodically driven quantum systems. Phys. Rep. 368 409.Google Scholar
Buchleitner, A., Grémaud, B. and Delande, D. (1994) Wave functions of atomic resonances. J. Phys. B: Atom. Mol. Opt. Phys. 27 2663.Google Scholar
Chirikov, B. V. (1959) The passage of a nonlinear oscillating system through resonance. Sov. Phys. Dokl. 4 390.Google Scholar
Cohen-Tannoudji, C., Dupont-Roc, J. and Grynberg, G. (1992) Atom-Photon Interactions, John Wiley and Sons Inc.Google Scholar
Corkum, P. (1993) Plasma perspective on strong field multiphoton ionization. Phys. Rev. Lett. 71 1994.CrossRefGoogle ScholarPubMed
Einstein, A. (1917) Zum Quantensatz von Sommerfeld und Epstein. Verh. Dtsch. Phys. Ges. 19 82.Google Scholar
Esra, G., Richter, K., Tanner, G. and Wintgen, D. (1991) Semiclassical cycle expansion for the helium atom. J. Phys. B 24 L413.Google Scholar
Floquet, M. G. (1883) Équations différentielles linéaires à coefficients périodiques. Annales de l'École Normale Supérieure 12 47.Google Scholar
Greiner, M., Mandel, O., Esslinger, T., W.Hänsch, T. and Bloch, I. (2002) Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415 39.Google Scholar
Hilico, L., Grémaud, B., Jonckheere, T., Billy, N. and Delande, D. (2002) Quantum three-body Coulomb problem in two dimensions. Phys. Rev. A 66 22101.Google Scholar
Holthaus, M. (1995) On the classical-quantum correspondence for periodically time dependent systems. Chaos, Solitons and Fractals 5 1143.Google Scholar
Kramer, B. and MacKinnon, A. (1993) Localization: Theory and experiment. Rep. Prog. Phys. 56 1469.CrossRefGoogle Scholar
Lappas, D. G., Sanpera, A., Watson, J. B., Burnett, K. and Knight, P. L. (1996) Two-electron effects in harmonic generation and ionization from a model He atom. J. Phys. B: Atom. Mol. Opt. Phys. 29 L619.Google Scholar
Lein, M., Gross, E. and Engel, V. (2000) Intense-field double ionization of helium: Identifying the mechanism. Phys. Rev. Lett. 85 4707.Google Scholar
Lichtenberg, A. J. and Lieberman, M. A. (1983) Regular and Stochastic Motion, Applied Mathematical Sciences 38, Springer-Verlag.Google Scholar
Madroñero, J. (2004) Spectral structure of planar helium under periodic driving, Ph.D. thesis, Ludwig-Maximilians-Universität München. (Available at http://edoc.ub.uni-muenchen.de/archive/00002187/.)Google Scholar
Madroñero, J. and Buchleitner, A. (2004) Planar helium under electromagnetic driving. In: High Performance Computing in Science and Engineering, Munich 2004 – Transactions of the Second Joint HLRB and KONWIHR Result and Reviewing Workshop, March 2nd and 3rd, 2004, Technical University of Munich, Springer-Verlag.Google Scholar
Madroñero, J., Schlagheck, P., Hilico, L., Grémaud, B., Delande, D. and Buchleitner, A. (2005) Decay rates of planar helium. Europhys. Lett. 70 183.Google Scholar
Maeda, H. and Gallagher, T. (2004) Nondispersing wave packets. Phys. Rev. Lett. 92 133004.CrossRefGoogle ScholarPubMed
Maeda, H., Norum, D. and Gallagher, T. F. (2005) Microwave manipulation of an atomic electron in a classical orbit. Science 307 1757.Google Scholar
Nikolopoulos, L. and Lambropoulos, P. (2001) Multichannel theory of two-photon single and double ionization of helium. J. Phys. B: Atom. Mol. Opt. Phys. 34 545.CrossRefGoogle Scholar
Ostrovsky, V. N. and Prudov, N. V. (1995) Adiabatic theory for the doubly excited asymmetric states of the helium atom. Phys. Rev. A51 1936.Google Scholar
Parker, J. S., Moore, L. R., Dundas, D. and Taylor, K. T. (2000) Double ionization of helium at 390 nm. J. Phys. B 33 L691.Google Scholar
Raman, C., Weihnacht, T. and Bucksbaum, P. (1997) Stark wave packets viewed with half-cycle pulses. Phys. Rev. A 55 R3995.Google Scholar
Reed, M. and Simon, B. (1990) Analysis of Operators, Methods of Modern Mathematical Physics, Academic Press.Google Scholar
Richter, K., Tanner, G. and Wintgen, D. (1993) Classical mechanics of two-electron atoms. Phys. Rev. A48 4182.CrossRefGoogle Scholar
Richter, K. and Wintgen, D. (1990) Stable planetary atom configurations. Phys. Rev. Lett. 65 1965.Google Scholar
Ritus, V. I. (1966) Shift and splitting of atomic levels caused by the field of an electromagnetic wave. Zh. Eksp. Teor. Fiz. 51 1492.Google Scholar
Ruiz, C., Plaja, L., Roso, L. and Becker, A. (2006) Ab initio calculation of the double ionization of helium in a few-cycle laser pulse beyond the one-dimensional approximation. Phys. Rev. Lett. 96 053001.Google Scholar
Russell, B. (1970) Das ABC der Relativitätstheorie, Fischer Verlag.Google Scholar
Schlagheck, P. and Buchleitner, A. (1999) Stable configurations in the strongly driven helium atom. Physica D 131 110.Google Scholar
Schlagheck, P. and Buchleitner, A. (2003) Nondispersive two-electron wavepackets in driven helium. Eur. Phys. J. D 22 401.Google Scholar
Schrödinger, E. (1926) Der stetige Übergang von der Mikro- zur Makromechanik. Die Natur-wissenschaften 14 664.Google Scholar
Scrinzi, A. and Piraux, B. (1997) Ionization and double excitation of helium by short intense laser pulses. Phys. Rev. A 56 R13.Google Scholar
Shirley, J. H. (1965) Solution of the Schrödinger equation with a Hamiltonian periodic in time. Phys. Rev. 138 B979.Google Scholar
Störzer, M., Gross, P., Aegerter, C. M. and Maret, G. (2006) Observation of the critical regime near Anderson localization of light. Phys. Rev. Lett. 96 063904.Google Scholar
Tanner, G., Richter, K. and Rost, J. (2000) The theory of two-electron atoms: between ground state and complete fragmentation. Rev. Mod. Phys. 72 497.Google Scholar
von Brentano, P., Ernst, J., Hausser, O., Mayer-Kuckuk, T., Richter, A. and von Witsch, W. (1964) Statistical fluctuations in the cross sections of the reactions Cl-35 (p, alpha) S-32 and Cl-37 (p, alpha) S-34. Phys. Lett. 9 48.Google Scholar
Walker, B., Sheehy, B., DiMauro, L. F., Agostini, P., Schafer, K. J. and Kulander, K. C. (1994) Precision measurement of strong field double ionization of helium. Phys. Rev. Lett. 73 1227.Google Scholar
Wellens, T., Grémaud, B., Delande, D. and Miniatura, C. (2005) Coherent backscattering of light by nonlinear scatterers. Phys. Rev. A 71 55603.Google Scholar
Wigner, E. (1959) Group Theory and its Application to the Quantum Mechanics, Academic Press.Google Scholar
Zeldovich, Y. B. (1967) The quasienergy of a quantum-mechanical system subjected to a periodic action. JETP (Soviet Physics) 24 1006.Google Scholar