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

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

2007-11-27

arxiv.org/abs/0711.4291v1

Mathematics

Dynamical Systems

13 pages, to appear in Inv. Math

Scientific paper

10.1007/s00222-007-0105-7

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.

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