Mathematical Physics
[Submitted on 8 Sep 2023
]
Title: MFO Report: The dry ten Martini problem for Sturmian dynamical systems
Title: MFO 报告：Sturmian 动力系统中的干十问题
Abstract: This extended Oberwolfach report (to appear in the proceedings of the MFO Workshop 2335: Aspects of Aperiodic Order) announces the full solution to the Dry Ten Martini Problem for Sturmian Hamiltonians. Specifically, we show that all spectral gaps of Sturmian Hamiltonians (as predicted by the gap labeling theorem) are open for all nonzero couplings and all irrational rotations. We present here the proof strategy.
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