Mathematical Sciences: Random Quantum Systems

本研究将集中在三个方面：1)具有密集点谱和奇异谱的量子哈密顿量的稳定性和不稳定性；2)随机势薛定谔算子绝对连续谱的存在性；3)与随机哈密顿量有关的对易子不等式的解。这项工作属于数学物理的一般领域。在某种程度上，这位研究者研究的问题是经典力学中KAM问题的一个简单的量子模拟。这类具有时间周期势的问题具有相当大的物理意义，特别是与激光场中的原子有关的问题。

This research will focus on three areas: 1) Stability and instability of quantum Hamiltonians with dense point and singular spectra; 2) Existence of absolutely continuous spectra of Schrodinger operators with random potential; and 3) Solutions of a commutator inequality which arose in connection with random Hamiltonians. This work is in the general area of mathematical physics. The problem examined by this researcher is to some extent a simple quantum analogue of the KAM problem in classical mechanics. Problems of this sort with time-periodic potentials are of considerable physical interest, particularly in connection with atoms in laser fields.