Scientific report

International Focus Workshop on Few Body Dynamics in Atoms, Molecules and Planetary Systems - FBD10
June 28 - July 1, 2010

Scientific Coordinators:
Andreas Buchleitner (Universität Freiburg, Germany)
Florin Diacu (University of Victoria, Canada)
Gregor Tanner (University of Nottingham, UK)
Organisation:
Katrin Lantsch (Max Planck Institute for the Physics of Complex Systems, Dresden, Germany)

Main Focus:
Celestial mechanics and atomic physics share a common interest in studying the dynamics of few-body systems interacting via 1/r potentials. The methods and techniques used in the two research areas could not be more different, however. While the motions of planetary bodies is governed by - in general - nonlinear ODE's with often complicated singularity structures, atomic and molecular systems are described by a linear PDE - Schrödinger's equation - and are solved by spectral methods, Green function expansions or complex rotation techniques etc. Recent advances in semiclassical techniques as well as steady experimental progress in short pulse laser and detector technology makes it necessary to consider the classical dynamics of charged particles in more detail. These efforts greatly benefit from techniques developed in nonlinear systems theory in general and in the context of gravitational few-body problems in particular. The focus of this workshop was to bring the two communities together and to discuss the state of the art in particular in the areas phase space structure of few-body planetary and atomic systems, dynamical aspects of the solar system and beyond, symbolic dynamics and chaos in few body systems, transition state theory, semiclassical treatment of few-body Coulomb systems and highly (multiply) excited states in atoms and molecules; experimental results and numerical techniques.

Summary of contributions by participants:
The conference benefited in general greatly from the efforts of the speakers to make their topic of research available to a general audience.
The talks by Robert Mackay on 2nd species orbits and Ernesto Perez-Chavez on relative equilibria in curved space gave fascinating insights in what can and can not be done in terms of rigourously proving the existence of dynamical features in few body planetary systems. Holger Dullin introduced us to a new geometric integrator for n-body problems and Florin Diacu gave an overview over singularity problems in the field in the colloquium talk. The transition to few-body Coulomb systems was provided by Andreas Knauf, Bruno Eckhard, Tobias Kramer and Agapi Emmanouilidou discussing electron-electron correlation effects in the classical dynamics of few and many body systems. Jaques Laskar worried us by demonstrating that the earth will collide with another planet at some point - it only has the choice to either do it with Mars or with Venus. Symbolic dynamics in 3-body problems was discussed by Mitsusada Sano and Kiyotaka Tanikawa and in a more general setting by Predrag Cvitanovic and modern transition state theory was explained to us by Holger Waalkens. Combining insight from classical dynamics with semiclassical techniques allows access to new quantum regimes for few electron atoms as demonstrated by Nark Nyul Choi and Joachim Burgdörfer. An overview over the state of the art of numerical and experimental techniques for analysing few-body quantum systems was given by Javier Madronero, José Luis Sanz-Vicario and Jan-Michael Rost as well as Lothar Schmidt, Hanns-Christoph Nägerl and Marcus Dahlström.

Contributions by young scientists:
Plenty of space was given to young scientists to present their work either in the form of posters (we had 16 poster contributions) or giving talks in the workshop itself. In fact, 5 talks were reserved for young scientist who are either still doing their PhD or are at an early post-doc stage. The newcomers had no problem to fill the allocated time of 45 min with interesting research ranging from applications of complex rotation methods (Celsus Bouri, Sören Roeren) to challenging dynamical features in 4D classical maps (Martin Richter) to chaos detection (Haris Skokos) and a new classification of equilibria in 3-body Coulomb problems (Florian Rupp).

Scientific results:
The main benefit of this workshop was certainly that people got to know each other who would not have met otherwise. A hallmark of the workshop were the many discussions after talks and in the lunch and coffee breaks and there was a general interest to get to know more about each others problems and ideas. In particular, the planetary systems community showed great interest in the many open problems posed by considering few-body Coulomb systems and possible quantum implications. Likewise, the results and deep insight in the dynamics of planetary systems impressed the 'quantum' community and the workshop may have helped that these techniques will cross disciplinary boundaries.

For further information please e-mail to: fbd10@pks.mpg.de