Effective Approximation and Dynamics of Many-Body Quantum Systems

法德联合项目“多体量子系统的有效逼近和动力学”旨在研究数学物理和偏微分方程（PDE）中各种重要的开放性问题。更具体地说，我们解决了在微观水平上描述多体量子系统的偏微分方程与宏观水平上描述的有效近似之间的数学关系。三个主要重点是：1。有关哈特里-福克、托马斯-费米和运动理论的有效方程的推导；2. 多体系统的动力学和散射特性及其有效描述的研究3. 正温度下的光谱分析和有效方程的推导。本项目由德国布伦瑞克、德国不莱梅、法国梅斯和法国雷恩的研究人员共同合作完成。

The 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, Thomas-Fermi, and kinetic theory; 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).