Topological phase dynamics described by overtone-synthesized classical and quantum Adler equations
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Quantum Physics arXiv:2602.21451 (quant-ph) [Submitted on 25 Feb 2026] Title:Topological phase dynamics described by overtone-synthesized classical and quantum Adler equations Authors:Hiroshi Yamaguchi, Motoki Asano View a PDF of the paper titled Topological phase dynamics described by overtone-synthesized classical and quantum Adler equations, by Hiroshi Yamaguchi and Motoki Asano View PDF Abstract:The Adler equation is a well-known one-dimensional model describing phase locking and synchronization. Motivated by recent experiments using optomechanical oscillators, we extend the model to include overtone-synthesized sinusoidal coupling with adiabatic temporal modulation. This extension gives rise to unique topological features such as winding-number quantization, discontinuous phase-slip transitions, and hysteretic and non-reciprocal phase dynamics. We further extend the analysis to the quantum regime, where we find a counterintuitive result: the breakdown of winding-number quantization. This arises from the superposition of different winding-number states in a closed-space Thouless pump. Moreover, hysteretic dynamics, once eliminated in quantum adiabatic approximation, is recovered in non-adiabatic calculations, as the superposition of two Floquet states with different PT eigenvalues becomes the quantum counterpart of phase trajectory. Comments: Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall) Cite as: arXiv:2602.21451 [quant-ph] (or arXiv:2602.21451v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.21451 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Hiroshi Yamaguchi Dr. [view email] [v1] Wed, 25 Feb 2026 00:06:56 UTC (2,257 KB) Full-text links: Access Paper: View a PDF of the paper titled Topological phase dynamics described by overtone-synthesized classical and quantum Adler equations, by Hiroshi Yamaguchi and Motoki AsanoView PDF view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cond-mat cond-mat.mes-hall 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?)