Cantor Spectrum for CMV Matrices With Almost Periodic Verblunsky Coefficients
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Publication:6386926
DOI10.1016/J.JFA.2022.109709arXiv2112.14376MaRDI QIDQ6386926
Qi Zhou, David Damanik, Long Li
Publication date: 28 December 2021
Abstract: We consider extended CMV matrices with analytic quasi-periodic Verblunsky coefficients with Diophantine frequency vector in the perturbatively small coupling constant regime and prove the analyticity of the tongue boundaries. As a consequence we establish that, generically, all gaps of the spectrum that are allowed by the Gap Labelling Theorem are open and hence the spectrum is a Cantor set. We also prove these results for a related class of almost periodic Verblunsky coefficients and present an application to suitable quantum walk models on the integer lattice.
Spectrum, resolvent (47A10) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20)
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