Perturbations of semi-classical completely integrable systems with singularities

• Applicant: Dr. Nicolas Roy
• Subject Area: Mathematics
• Term: from 2004 to 2008
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5437892

Among all physical systems (in classical mechanics, as well as in quantum mechanics) there exists a very special class: the so-called completely integrable systems. On the one hand these systems were studied intensively and are now quite well understood, but on the other hand they are highly non-generic. Nevertheless, many systems can be considered to be nearly integrable, i.e. close to a completely integrable system. This feature allows one to develop a fruitful perturbation theory and to obtain very precise information about the perturbed system. In the classical mechanical context, this is the celebrated K.A.M. theory. In the quantum mechanical context there have been several contributions, including ours, but they concern the special case where the completely integrable system under consideration is regular. However, completely integrable systems usually comprise singularities and this makes their analysis much more difficult. The main aim of this project is the study of the perturbations of quantum completely integrable systems with singularities.

• DFG Programme: Research Fellowships
• Cooperation Partner: Professor Dr. Jochen Brüning