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arXiv · 1906.02088

Zero Measure and Singular Continuous Spectra for Quantum Graphs

David Damanik·Licheng Fang·Selim Sukhtaiev
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Abstract

We introduce a dynamically defined class of unbounded, connected, equilateral metric graphs on which the Kirchhoff Laplacian has zero Lebesgue measure spectrum and a nontrivial singular continuous part. A new local Borg--Marchenko uniqueness result is obtained in order to utilize Kotani theory for aperiodic subshifts satisfying Boshernitzan's condition.

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BibTeXRIS

David Damanik, Licheng Fang, Selim Sukhtaiev. 2019-06-05. Zero Measure and Singular Continuous Spectra for Quantum Graphs. https://doi.org/10.1007/s00023-020-00920-6

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