Spectral Transitions and Singular Continuous Spectrum in A New Family of Quasi-periodic Quantum Walks
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Quantum Physics arXiv:2601.20081 (quant-ph) [Submitted on 27 Jan 2026] Title:Spectral Transitions and Singular Continuous Spectrum in A New Family of Quasi-periodic Quantum Walks Authors:Xinyu Yang, Long Li, Qi Zhou View a PDF of the paper titled Spectral Transitions and Singular Continuous Spectrum in A New Family of Quasi-periodic Quantum Walks, by Xinyu Yang and 1 other authors View PDF HTML (experimental) 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. Comments: Subjects: Quantum Physics (quant-ph); Spectral Theory (math.SP) MSC classes: 81Q99, 47B36, 81Q35 Cite as: arXiv:2601.20081 [quant-ph] (or arXiv:2601.20081v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.20081 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Long Li [view email] [v1] Tue, 27 Jan 2026 21:55:48 UTC (40 KB) Full-text links: Access Paper: View a PDF of the paper titled Spectral Transitions and Singular Continuous Spectrum in A New Family of Quasi-periodic Quantum Walks, by Xinyu Yang and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: math math.SP References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)