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Integrable, Mixed, and Chaotic Dynamics in a Single All-to-All Ising Spin Model

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arXiv:2604.14798v1 Announce Type: new Abstract: We demonstrate that the Ising all-to-all (ATA) model exhibits a range of dynamics, from integrable to chaotic, including mixed behaviour across symmetry blocks within a single system. While other works have explored the dynamics of all-to-all systems by varying parameters, we analyse a fixed set of parameters and examine the dynamics within different blocks. In addition to investigating the dynamical properties, we show that the system remains resi

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Quantum Physics [Submitted on 16 Apr 2026] Integrable, Mixed, and Chaotic Dynamics in a Single All-to-All Ising Spin Model David Amaro-Alcalá, Carlos Pineda We demonstrate that the Ising all-to-all (ATA) model exhibits a range of dynamics, from integrable to chaotic, including mixed behaviour across symmetry blocks within a single system. While other works have explored the dynamics of all-to-all systems by varying parameters, we analyse a fixed set of parameters and examine the dynamics within different blocks. In addition to investigating the dynamical properties, we show that the system remains resilient to noise when the norm of the Hamiltonian representing the noise is close to 1. Our results are presented by mapping each symmetry sector of the system to a kicked top (KT) and observing that KT parameters for each sector depend on its dimension. This system, similar to the Bunimovich billiard for classical chaos, provides a new platform for studying dynamics determined by the symmetry sector, advancing quantum chaos research. Comments: 18 pages, 7 figures. Accepted in Journal of Physics A: Mathematical and Theoretical Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Chaotic Dynamics (nlin.CD) Cite as: arXiv:2604.14798 [quant-ph] (or arXiv:2604.14798v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.14798 Focus to learn more Related DOI: https://doi.org/10.1088/1751-8121/ae5ff8 Focus to learn more Submission history From: David Amaro-Alcalá [view email] [v1] Thu, 16 Apr 2026 09:21:17 UTC (867 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev | next > new | recent | 2026-04 Change to browse by: math math-ph math.MP nlin nlin.CD References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

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