Non-linearity and chaos in the kicked top

[2408.05869] Non-linearity and chaos in the kicked top Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Nonlinear Sciences > Chaotic Dynamics arXiv:2408.05869 (nlin) [Submitted on 11 Aug 2024] Title: Non-linearity and chaos in the kicked top Authors: Amit Anand , Robert B. Mann , Shohini Ghose View a PDF of the paper titled Non-linearity and chaos in the kicked top, by Amit Anand and Robert B. Mann and Shohini Ghose View PDF HTML (experimental) Abstract: Classical chaos arises from the inherent non-linearity of dynamical systems. However, quantum maps are linear; therefore, the definition of chaos is not straightforward. To address this, we study a quantum system that exhibits chaotic behavior in its classical limit: the kicked top model, whose classical dynamics are governed by Hamilton's equations on phase space, whereas its quantum dynamics are described by the Schrödinger equation in Hilbert space. We explore the critical degree of non-linearity signifying the onset of chaos in the kicked top by modifying the original Hamiltonian so that the non-linearity is parametrized by a quantity $p$. We find two distinct behaviors of the modified kicked top depending on the value of $p$. Chaos intensifies as $p$ varies within the range of $1\leq p \leq 2$, whereas it diminishes for $p > 2$, eventually transitioning to a purely regular oscillating system as $p$ tends to infinity. We also comment on the complicated phase space structure for non-chaotic dynamics. Our investigation sheds light on the relationship between non-linearity and chaos in classical systems, offering insights into their dynamic behavior. Subjects: Chaotic Dynamics (nlin.CD) ; Classical Physics (physics.class-ph); Quantum Physics (quant-ph) Cite as: arXiv:2408.05869 [nlin.CD] (or arXiv:2408.05869v1 [nlin.CD] for this version) https://doi.org/10.48550/arXiv.2408.05869 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Physica D 471 (2025) 134455 Related DOI : https://doi.org/10.1016/j.physd.2024.134455 Focus to learn more DOI(s) linking to related resources Submission history From: Amit Anand [ view email ] [v1] Sun, 11 Aug 2024 22:05:50 UTC (2,104 KB) Full-text links: Access Paper: View a PDF of the paper titled Non-linearity and chaos in the kicked top, by Amit Anand and Robert B. Mann and Shohini Ghose View PDF HTML (experimental) TeX Source view license Current browse context: nlin.CD < prev | next > new | recent | 2024-08 Change to browse by: nlin physics physics.class-ph quant-ph References & Citations INSPIRE HEP NASA ADS Google 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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