Zero Measure and Singular Continuous Spectra for Quantum Graphs
Spectral Theory
2020-07-15 v1 Mathematical Physics
Dynamical Systems
math.MP
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.
Cite
@article{arxiv.1906.02088,
title = {Zero Measure and Singular Continuous Spectra for Quantum Graphs},
author = {David Damanik and Licheng Fang and Selim Sukhtaiev},
journal= {arXiv preprint arXiv:1906.02088},
year = {2020}
}
Comments
22 pages