Applications of singular analysis to quantum many-particle models in chemistry

奇异分析在化学量子多粒子模型中的应用

• 批准号: 204409314
• 负责人: Privatdozentin Dr. Gohar Flad-Harutyunyan
• 金额: --
• 依托单位: Lehrstuhl für Analysis (M7)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2011
• 资助国家: 德国
• 起止时间: 2010-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/204409314?language=en
• 关键词: Applications; singular; analysis; quantum; many

Many interesting problems in condensed matter physics and large parts of chemistry can be described by quantum many-particle systems interacting via singular Coulomb potentials. The subject of this proposl is to study the asymptotic behaviour of such systems, in particular in electronic structure theory, near coalescence ponts of particles using methods from singular analysis. It is intended to provide explicit asymptotic constructions for parametrices of quantum echanical Hamiltonians which encode the asymptotic behaviour of the corresponding solutions of Schrödinger’s equation This can be achieved in the framework of a general pseudo-differential calculus on manifolds with geometric singularities. Here, the Coulomb potentials introduce a natural hierachry of singularities which can be described within the calculus by embedded conical, edge and higher-order corner singularities. A new important feature of the project is to consider not only the Schrödlinger’s equation but also some simplifie many-particle models in the framework of coupled cluster theory. This provides a new perspective concerning the asymptotic behaviour of these models and reveals possible shortcomings which in turn might lead to improved models for electronic structure calculations.

凝聚态物理和化学中的许多有趣问题都可以通过奇异库仑势描述量子多粒子系统的相互作用。本论文的主要目的是研究这类系统的渐近行为，特别是在电子结构理论中，用奇异分析的方法研究粒子聚结蓬茨附近的渐近行为。它的目的是提供明确的渐近结构参数的量子力学哈密顿编码的渐近行为相应的解决方案薛定谔方程这可以实现的框架内的一般伪微分流形上的几何奇点。在这里，库仑势引入了一个自然的奇点层次，可以在微积分中通过嵌入的圆锥奇点、边缘奇点和高阶角奇点来描述。该项目的一个新的重要特点是不仅考虑薛定谔方程，而且考虑耦合集团理论框架内的一些非线性多粒子模型。这提供了一个新的视角，这些模型的渐近行为，并揭示了可能的缺点，这反过来可能导致改进的模型，电子结构计算。