The absolutely continuous spectrum of the almost Mathieu operator

Details The absolutely continuous spectrum of the almost Mathieu operator The absolutely continuous spectrum of the almost Mathieu operator

2008-10-16

arxiv.org/abs/0810.2965v1

Mathematics

Dynamical Systems

22 pages

Scientific paper

We prove that the spectrum of the almost Mathieu operator is absolutely
continuous if and only if the coupling is subcritical. This settles Problem 6
of Barry Simon's list of Schr\"odinger operator problems for the twenty-first
century.

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