Mathematical Sciences: Itinerant Electron Systems and Quantum Mechanical Spin Systems

肯尼迪将研究巡回费米子和量子自旋系统。我们将详细研究最简单的巡回费米子系统之一的基态的性质。特别是，他将研究是否存在与最近的二维结果类似的三维结果，即对于中性模型，在一定密度范围内，离子总是以对角线排列。他还将研究在随机势中运动的粒子系统的局部化问题。现代物理学，量子力学和相对论，是二十世纪的产物。它是在上个世纪试图解决物质的微观结构并掌握远距离作用力、电磁学和热辐射等概念的过程中建立起来的。这些发展的数学基础统称为数学物理，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。

Kennedy will study itinerant fermion and quantum spin systems. The nature of the ground state of one of the simplest itinerant fermion systems will be studied in detail. In particular he will investigate whether there is a 3-dimensional analog of the recent 2-dimensional result that for the neutral model in a certain range of densities the ions are always arranged in diagonal lines. He will also study the localization problem for a system of particles moving in a random potential. Modern physics, quantum mechanics and relativity, is a product of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concepts 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 Schroedinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory.