The Spectrum of the Almost Mathieu Operator
نویسنده
چکیده
The notes are based on a series of six lectures, given during my stay at the CRC 701 in June/July 2008. The lecture series intended to give a survey of some of the results for the almost Mathieu operator that have been obtained since the early 1980’s. Specifically, the metalinsulator transition is discussed in detail, along with its relation to the ten Martini problem via duality and reducibility.
منابع مشابه
The Absolutely Continuous Spectrum of the Almost Mathieu Operator
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.
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