Mathematical Structures in Computer Science

Table of Contents - 2007 - Volume 17, Issue 02  

Paper

The driven three body Coulomb problem

JAVIER MADROÑEROa1a2, LAURENT HILICOa3, BENOÎT GRÉMAUDa3, DOMINIQUE DELANDEa3 and ANDREAS BUCHLEITNERa2a4

a1 Physik Department, Technische Universität München, James-Franck-Straβe, D-85747 Garching

a2 Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden

a3 Laboratoire Kastler Brossel de l'Université Pierre et Marie Curie et de l'Ecole Normale Supérieure, 4, place Jussieu, F-75252 Paris Cedex 05

a4 Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński, Reymonta 4, PL-30-059 Kraków

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.

(Received May 15 2006)

(Revised October 06 2006)

--