Spectral Transitions and Singular Continuous Spectrum in A New Family of Quasi-periodic Quantum Walks
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915758634696704 |
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| author | Yang, Xinyu Li, Long Zhou, Qi |
| author_facet | Yang, Xinyu Li, Long Zhou, Qi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20081 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral Transitions and Singular Continuous Spectrum in A New Family of Quasi-periodic Quantum Walks Yang, Xinyu Li, Long Zhou, Qi Quantum Physics Spectral Theory 81Q99, 47B36, 81Q35 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. |
| title | Spectral Transitions and Singular Continuous Spectrum in A New Family of Quasi-periodic Quantum Walks |
| topic | Quantum Physics Spectral Theory 81Q99, 47B36, 81Q35 |
| url | https://arxiv.org/abs/2601.20081 |