Absolute Continuity of the Integrated Density of States for the Almost Mathieu Operator with Non-Critical Coupling
Dynamical Systems
2015-02-24 v1 Mathematical Physics
math.MP
Spectral Theory
Abstract
We show that the integrated density of states of the almost Mathieu operator is absolutely continuous if and only if the coupling is non-critical. We deduce for subcritical coupling that the spectrum is purely absolutely continuous for almost every phase, settling the measure-theoretical case of Problem 6 of Barry Simon's list of Schr\"odinger operator problems for the twenty-first century.
Keywords
Cite
@article{arxiv.0711.4291,
title = {Absolute Continuity of the Integrated Density of States for the Almost Mathieu Operator with Non-Critical Coupling},
author = {Artur Avila and David Damanik},
journal= {arXiv preprint arXiv:0711.4291},
year = {2015}
}
Comments
13 pages, to appear in Inv. Math