Born-Oppenheimer approximation for resonances

• Applicant: Professor Dr. Stefan Teufel
• Subject Area: Mathematics
• Term: from 2006 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 25330812

Separation of scales plays a fundamental role for the understanding of the dynamical behavior of complex systems in physics and other sciences. It is often possible to derive simple laws for certain slow variables from the underlying fast dynamics whenever the scales are well separated. Recently there has been considerable progress in the mathematical analysis of quantum mechanical systems which display such a separation of scales. Depending on whether the Hamiltonian of the fast degrees of freedom has a gap in its spectrum or not, one speaks of adiabatic theory with or without spectral gap. Adiabatic perturbation theory with spectral gap is highly developed, mathematically controlled and was successfully applied in different physical contexts. Adiabatic theory without gap is still in a rudimentary form, although it has important applications for example in quantum electrodynamics and in quantum statistical mechanics, both active fields at the focus of the Mathematical Physics community. The aim of this project is to systematically develop adiabatic perturbation theory without gap abstractly and in connection with its main applications.

• DFG Programme: Research Grants