The absolutely continuous spectrum of the almost Mathieu operator

Abstract

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 Schrödinger operator problems for the twenty-first century.

22 pages

References in corpus (1)

• Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrodinger operators

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