- Published 2008

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 Schrödinger operator problems for the twenty-first century.

@inproceedings{Avila2008AbsoluteCO,
title={Absolute Continuity of the Integrated Density of States for the Almost Mathieu Operator with Non-critical Coupling},
author={Artur Avila and David Damanik},
year={2008}
}