Metal-insulator transition for the almost Mathieu operator
谱理论
2016-09-07 v1 数学物理
math.MP
摘要
We prove that for Diophantine \om and almost every \th, the almost Mathieu operator, (H_{\omega,\lambda,\theta}\Psi)(n)=\Psi(n+1) + \Psi(n-1) + \lambda\cos 2\pi(\omega n +\theta)\Psi(n), exhibits localization for \lambda > 2 and purely absolutely continuous spectrum for \lambda < 2. This completes the proof of (a correct version of) the Aubry-Andr\'e conjecture.
关键词
引用
@article{arxiv.math/9911265,
title = {Metal-insulator transition for the almost Mathieu operator},
author = {Svetlana Ya. Jitomirskaya},
journal= {arXiv preprint arXiv:math/9911265},
year = {2016}
}
备注
17 pages, published version