Mathematical Sciences: RUI: Spectral Properties of Some Random Schrodinger Operators

[401735 Shubin]这一提议涉及到谱逆理论和随机薛定谔算子理论中的问题。在逆谱理论部分中提出的问题围绕着从特征值集合中恢复薛定谔算子势的某些类型的奇异性。随机薛定谔算子理论中的问题涉及到安德森和泊松型模型在d维欧几里德空间中的局部化问题。现代物理学、量子力学和相对论都是二十世纪的产物。它坚定地建立在对物质微观结构的研究和对超距作用、电磁和热辐射等概念的把握上。这些发展的数学基础，统称为数学物理学，范围从控制粒子动力学的薛定谔算符的详细分析，到试图将四种已知力统一为单一理论的统一场论。本课题主要对数学物理中的薛定谔算子分量进行研究。＊＊＊

9401735 Shubin This proposal concerns problems from inverse spectral theory and random Schrodinger operator theory. The problems proposed in the inverse spectral theory section center around recovering certain types of singularities of the potential of a Schrodinger operator from the set of eigenvalues. The problems from random Schrodinger operator theory concern localization in d-dimensional Euclidean space for Anderson and Poisson type models. Modern physics, quantum mechanics and relativity is a product of the twentieth century. It is founded firmly in the attempt to address the microstructure of matter and to come to grips with the concept of action-at-a distance, electro-magnetism, and heat radiation. The mathematical foundations for these developments, collectively called mathematical physics, ranges from detailed analysis of Schrodinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory. This project is focused on the Schrodinger operator component of mathematical physics research. ***