Effective Approximation and Dynamics of Many-Body Quantum Systems

多体量子系统的有效逼近和动力学

• 批准号: 505496137
• 负责人: Professor Dr. Volker Bach
• 金额: --
• 依托单位: Institut für Analysis und Algebra
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/505496137?language=en
• 关键词: Effective; Approximation; Dynamics; Many; Body

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).

法德联合项目“多体量子系统的有效近似和动力学”旨在解决数学物理和偏微分方程中的各种重要未决问题。更具体地说，我们解决的PDE描述多体量子系统在微观水平和有效的近似在宏观水平上的描述之间的数学关系。三大焦点是：1。导出与Hartree-Fock、Fermi和动力学理论相关的有效方程; 2.研究多体系统的动力学和散射特性及其有效描述; 3.谱分析和正温度下有效方程的推导。该项目是布伦瑞克（德国）、不莱梅（德国）、梅斯（法国）和雷恩（法国）研究人员之间的联合合作。