Zero Measure and Singular Continuous Spectra for Quantum Graphs
arXiv:1906.02088 · doi:10.1007/s00023-020-00920-6
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.
22 pages