EffectiveQuantum

The proposed French-German joint project “Effective Approximation and Dynamics of Many-Body Quantum Systems” aims at various important open questions in mathematical physics and partial differential equations (PDE). More specifically, we address the mathematical relations between the PDE describing a many-body quantum system at a microscopic level and effective approximations to this description at a macroscopic level. The three major foci are: 1. the derivation of effective equations related to Hartree-Fock theory and kinetic equations; 2. the study of dynamical and scattering properties of many-body systems and their effective descriptions; 3. spectral analysis and derivation of effective equations at positive temperature. This project is a joint cooperation between researchers in Braunschweig (Germany), Bremen (Germany), Metz (France) and Rennes (France).