Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling

被引：0

作者：

Artur Avila

David Damanik

机构：

[1] Université Pierre et Marie Curie,CNRS UMR 7599, Laboratoire de Probabilités et Modèles aléatoires

[2] Rice University,Department of Mathematics

来源：

Inventiones mathematicae | 2008年 / 172卷

关键词：

Lyapunov Exponent; Absolute Continuity; Jacobi Matrice; Pure Point Spectrum; Unique Ergodicity;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：439 / 453

页数：14

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