Effective One-Particle Equations for Correlated Many-Particle-(Coulomb) Systems: Derivation and Properties

相关多粒子（库仑）系统的有效单粒子方程：推导和性质

• 批准号: 318342445
• 负责人: Professorin Li Chen, Ph.D.
• 金额: --
• 依托单位: Arbeitsbereich Mathematische Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/318342445?language=en
• 关键词: Effective; Particle; Equations; Correlated; Many

We propose to derive effective one-particle equations for (fermionic) many particle systems. The emphasis will be on electrons that interact via Coulomb forces among each other and the nucleus. Both, the stationary and the dynamic case will be treated. In the stationary case the emphasis will be on relativistic Coulomb systems. in the dynamical case where there are few results for Coulomb systems even in the non-relativistic setting, we propose to develop mathematical methods which allow the treatment of Coulomb singularites. Finally, the effective one-particle equations will be investigated for the Coulomb case.

我们提出推导（费米子）多粒子系统的有效单粒子方程。重点将放在电子之间和原子核之间通过库仑力相互作用。静态和动态两种情况都将被处理。在静止的情况下，重点将放在相对论性库仑系统上。在动力学情况下，即使在非相对论环境下，库仑系统的结果也很少，我们建议发展允许处理库仑奇点的数学方法。最后，我们将研究库仑情况下的有效单粒子方程。

项目成果

The Maximal Negative Ion of the Time-Dependent Thomas-Fermi and the Vlasov Atom

时变托马斯-费米和弗拉索夫原子的最大负离子

• DOI: 10.1063/1.5026970
• 发表时间: 2018
• 期刊: arXiv: Mathematical Physics
• 作者: Siedentop

Combined mean field limit and non-relativistic limit of Vlasov–Maxwell particle system to Vlasov–Poisson system

VlasovâMaxwell 粒子系统到 VlasovâPoisson 系统的平均场极限和非相对论极限的组合

• DOI: 10.1063/1.5128369
• 发表时间: 2020
• 期刊: Journal of Mathematical Physics
• 影响因子: 1.3

Combined Mean-Field and Semiclassical Limits of Large Fermionic Systems

• DOI: 10.1007/s10955-021-02700-w
• 发表时间: 2019-10
• 期刊: Journal of Statistical Physics
• 影响因子: 1.6
• 作者: Li Chen;Jinyeop Lee;Matthew Liew