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arXiv · 2112.14376

Cantor Spectrum for CMV Matrices With Almost Periodic Verblunsky Coefficients

Long Li·David Damanik·Qi Zhou
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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.

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Long Li, David Damanik, Qi Zhou. 2021-12-29. Cantor Spectrum for CMV Matrices With Almost Periodic Verblunsky Coefficients. https://arxiv.org/abs/2112.14376

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