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Absence of Bound States for Quantum Walks and CMV Matrices via Reflections

Published 16 Feb 2024 in math.SP, math-ph, math.MP, and quant-ph | (2402.11024v2)

Abstract: We give a criterion based on reflection symmetries in the spirit of Jitomirskaya--Simon to show absence of point spectrum for (split-step) quantum walks and Cantero--Moral--Vel\'azquez (CMV) matrices. To accomplish this, we use some ideas from a paper by the authors and their collaborators to implement suitable reflection symmetries for such operators. We give several applications. For instance, we deduce arithmetic delocalization in the phase for the unitary almost-Mathieu operator and singular continuous spectrum for generic CMV matrices generated by the Thue--Morse subshift.

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