The absolutely continuous spectrum of the almost Mathieu operator
Dynamical Systems
2008-10-17 v1 Mathematical Physics
math.MP
Spectral Theory
Abstract
We prove that the spectrum of the almost Mathieu operator is absolutely continuous if and only if the coupling is subcritical. This settles Problem 6 of Barry Simon's list of Schr\"odinger operator problems for the twenty-first century.
Keywords
Cite
@article{arxiv.0810.2965,
title = {The absolutely continuous spectrum of the almost Mathieu operator},
author = {Artur Avila},
journal= {arXiv preprint arXiv:0810.2965},
year = {2008}
}
Comments
22 pages