Instabilities in a Non-KAM System via Information Scrambling: A Note

Quantum Physics arXiv:2606.12761 (quant-ph) [Submitted on 11 Jun 2026] Title:Instabilities in a Non-KAM System via Information Scrambling: A Note Authors:Naga Dileep Varikuti View a PDF of the paper titled Instabilities in a Non-KAM System via Information Scrambling: A Note, by Naga Dileep Varikuti View PDF HTML (experimental) Abstract:We study operator growth in quantized non-KAM systems using out-of-time-ordered correlators (OTOCs), focusing on the kicked harmonic oscillator as a representative example. Since the classical harmonic oscillator is degenerate, the dynamics fall outside the usual Kolmogorov-Arnold-Moser (KAM) framework, and resonances play a central role in shaping the phase space. We examine the system near resonances, where the ratio between the oscillator and driving frequencies takes integer values. Even though the classical Lyapunov exponent remains small at these points, and hence no conventional chaos, the phase space still undergoes strong structural changes. The OTOCs are particularly sensitive to these resonances, with a quadratic-in-time growth at resonance compared to linear growth away from it. Within a perturbative treatment, we derive closed-form expressions for the OTOCs and uncover a number-theoretic structure emerging in the behavior of OTOCs, governed by the Euler totient function of the frequency ratio. Overall, the results we present in this short note imply that resonant structures can play an important role in controlling information spreading. Comments: Subjects: Quantum Physics (quant-ph); Chaotic Dynamics (nlin.CD) Cite as: arXiv:2606.12761 [quant-ph] (or arXiv:2606.12761v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.12761 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Naga Dileep Varikuti [view email] [v1] Thu, 11 Jun 2026 00:00:05 UTC (238 KB) Full-text links: Access Paper: View a PDF of the paper titled Instabilities in a Non-KAM System via Information Scrambling: A Note, by Naga Dileep VarikutiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: nlin nlin.CD 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?) 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?)