Mathematical study of non-relativistic QED: The Link between Resonances and Poles of the Scattering Matrix

• Applicant: Dr. Dirk - André Deckert
• Subject Area: Mathematics
• Term: from 2017 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 350174934

We will investigate the mathematical relation between resonances and poles of the scattering matrix in non-relativistic quantum electrodynamics (QED). As it is well-understood, non-interacting atomic systems which have stable excited states decay to lower energy states and eventually into the ground state when switching on the interaction with their radiation fields. Mathematically, this behavior can be described by means of eigenstates of non-interacting Hamiltonians turning into resonances. The aim of this project is to provide a rigorous proof of the conjecture that the only poles of the integral kernel of the transition matrix lie at the position of the resonances. In a first part, this behavior shall be proven in the Spin-Boson model. In a second part, the attained results shall be generalized to the Pauli-Fierz model.

• DFG Programme: Research Grants
• International Connection: Mexico
• Cooperation Partner: Professor Dr. Miguel Arturo Ballesteros Montero