A general interpretation of nonlinear connected time crystals: quantum self-sustaining combined with quantum synchronization
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Quantum Physics arXiv:2601.20186 (quant-ph) [Submitted on 28 Jan 2026] Title:A general interpretation of nonlinear connected time crystals: quantum self-sustaining combined with quantum synchronization Authors:Song-hai Li, Najmeh Es'haqi-Sani, Xingli Li, Wenlin Li View a PDF of the paper titled A general interpretation of nonlinear connected time crystals: quantum self-sustaining combined with quantum synchronization, by Song-hai Li and 3 other authors View PDF HTML (experimental) Abstract:Although classical nonlinear dynamics suggests that sufficiently strong nonlinearity can sustain oscillations, quantization of such model typically yields a time-independent steady state that respects time-translation symmetry and thus precludes time-crystal behavior. We identify dephasing as the primary mechanism enforcing this symmetry, which can be suppressed by intercomponent phase correlations. Consequently, a sufficient condition for realizing a continuous time crystal is a nonlinear quantum self-sustaining system exhibiting quantum synchronization among its constituents. As a concrete example, we demonstrate spontaneous oscillations in a synchronized array of van der Pol oscillators, corroborated by both semiclassical dynamics and the quantum Liouville spectrum. These results reduce the identification of time crystals in many-body systems to the evaluation of only two-body correlations and provide a framework for classifying uncorrelated time crystals as trivial. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.20186 [quant-ph] (or arXiv:2601.20186v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.20186 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Wenlin Li [view email] [v1] Wed, 28 Jan 2026 02:36:56 UTC (1,944 KB) Full-text links: Access Paper: View a PDF of the paper titled A general interpretation of nonlinear connected time crystals: quantum self-sustaining combined with quantum synchronization, by Song-hai Li and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?)