Absolute Continuity of the Integrated Density of States for the Almost Mathieu Operator with Non-critical Coupling

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 Schrödinger operator problems for the twenty-first century.

Cite this paper

@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} }