Mathematical Sciences: Stable and Chaotic Quantum Motion

霍兰德将研究哈密顿量在时间上几乎是周期性的量子系统的稳定性和混沌；经典系统的不稳定周期轨道对应的疤痕波函数和共振态的存在；多光子A.C.的微扰理论。斯塔克效应；随机薛定谔算子和其他系统绝对连续谱的存在性。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。

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.