Micro-local analysis applied to geometry and mathematical physics

应用于几何和数学物理的微观局部分析

• 批准号: 64755222
• 负责人: Dr. Brice Camus
• 金额: --
• 依托单位: Lehrstuhl Analysis, insbes. Differentialgeometrie und Dynamische Systeme
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2008
• 资助国家: 德国
• 起止时间: 2007-12-31 至 2008-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/64755222?language=en
• 关键词: Micro; local; analysis; applied; geometry

The first objective of this research project is to apply techniques of micro-local analysis in geometry and mathematical physics. The first problem we plan to investigate concerns the asymptotic properties of eigenvectors associated to self-adjoint operators: associated distributions and their relations with the classical flow.A second aspect is the study of statistical properties of the discrete spectrum in relation with the classical dynamics. This question has some important motivations in geometry, physics and in quantum chemistry where the semi-classical approximation and high-energy methods are intensively used. In mathematics several conjectures are open concerning the universal statistics of large eigenvalues for integrable and chaotic motions and we hope to contribute.

本研究计画的第一个目标是应用几何与数学物理中的微局部分析技术。第一个问题是研究自伴算子特征向量的渐近性质：自伴分布及其与经典流的关系;第二个方面是研究离散谱与经典动力学的关系.这个问题在几何学、物理学和量子化学中有着重要的意义，在量子化学中，半经典近似和高能方法被广泛应用。在数学上，关于可积运动和混沌运动的大特征值的普适统计，有几个命题是开放的，我们希望能有所贡献。