半经典酉算子的谱渐近
谱理论
2018-04-10 v4 偏微分方程分析
辛几何
摘要
本文针对交换的半经典酉算子，确立了玻尔对应原理的一个方面，即量子力学在高频极限下收敛于经典力学。我们在极小假设下证明，一组交换半经典酉算子的量子谱凸包的半经典极限收敛于这些算子的主符号的经典谱凸包。
引用
@article{arxiv.1506.02873,
title = {Spectral asymptotics of semiclassical unitary operators},
author = {Yohann Le Floch and Alvaro Pelayo},
journal= {arXiv preprint arXiv:1506.02873},
year = {2018}
}
备注
32 pages. Presentation substantially revised and reorganized for clarity. Main Theorem is now in in the introduction, and non central materialshave been moved to appendix 1 and appendix 2. Small mistake in the application of Cayley transform has been fixed