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Spectral Transitions and Singular Continuous Spectrum in A New Family of Quasi-periodic Quantum Walks
Xinyu Yang, Long Li, Qi Zhou·January 27, 2026
Quantum Physicsmath.SP
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Abstract
This paper introduces and rigorously analyzes a new class of one-dimensional discrete-time quantum walks whose dynamics are governed by a parametrized family of extended CMV matrices. The model generalizes the unitary almost Mathieu operator (UAMO) and exhibits a richer spectral phase diagram, closely resembling the extended Harper's model. It provides the first example of a solvable quasi-periodic quantum walk that exhibits a stable region of purely singular continuous spectrum.