Spectral Transitions and Singular Continuous Spectrum in A New Family of Quasi-periodic Quantum Walks

• URL: http://arxiv.org/abs/2601.20081v1
• Date: Tue, 27 Jan 2026 21:55:48 GMT
• Title: Spectral Transitions and Singular Continuous Spectrum in A New Family of Quasi-periodic Quantum Walks
• Authors: Xinyu Yang, Long Li, Qi Zhou,
• Abstract summary: This paper introduces and rigorously analyzes a new class of one-dimensional discrete-time quantum walks.<n>It provides the first example of a solvable quasi-periodic quantum walk that exhibits a stable region of purely singular continuous spectrum.
• Score: 17.90668458240918
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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