Mathematical Sciences: Stable and Chaotic Quantum Motion

豪兰将研究量子力学中的稳定性和混沌 哈密顿量在时间上几乎是周期的系统; 疤痕波函数和共振态对应于 经典系统的不稳定周期轨道;摄动; 多光子交流理论斯塔克效应;以及 随机薛定谔算子的绝对连续谱 和其他系统。 现代物理学，量子力学和相对论，是一个 二十世纪的产物。 它牢固地建立在 上世纪人们试图研究物质的微观结构 并掌握远距离行动的概念， 电磁和热辐射。 数学 这些发展的基础，统称为 数学物理，范围从详细分析 薛定谔算子，控制着粒子的动力学， 统一场论，试图统一四个已知的 形成一个单一的理论。

Howland will investigate stability and chaos in quantum systems with Hamiltonians almost periodic in time; existence of scarred wave functions and resonant states corresponding to unstable periodic orbits of the classical system; perturbation theory of the multiphoton a.c. Stark effect; and existence of absolutely continuous spectra in random Schroedinger operators and other systems. 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.