Unveiling Semiclassical Structures in Quantum Chaotic Eigenstates Using Neural Networks

Quantum Physics arXiv:2607.07874 (quant-ph) [Submitted on 8 Jul 2026] Title:Unveiling Semiclassical Structures in Quantum Chaotic Eigenstates Using Neural Networks Authors:J. Montes, F. Borondo, Gabriel G. Carlo View a PDF of the paper titled Unveiling Semiclassical Structures in Quantum Chaotic Eigenstates Using Neural Networks, by J. Montes and 2 other authors View PDF HTML (experimental) Abstract:Physics-informed neural networks and neural quantum states have consolidated a new paradigm to analyze and discover physical phenomena through constrained neural parametrizations. In this context, we investigate whether the semiclassical structure of the eigenfunctions of a quantum chaotic system can be unveiled through unsupervised learning. To this end, we train a "quantum dictionary", formulated as an overcomplete autoencoder, that sparsely represents the eigenstates of the system, using as an illustration the quantum baker map. The only explicit physical information imposed on the dictionary atoms is their localization in phase space, without providing any kind of information about the periodic orbits of the corresponding classical system. The model achieves high fidelity in reconstructing eigenstates not used during training. By comparing the learned atoms with an independently constructed "semiclassical dictionary", we find that they spontaneously localize on the periodic orbits and develop scar-like structures. This result is interesting in two ways: a localization constraint is sufficient to recover nontrivial semiclassical organization from spectral data and at the same time periodic orbits confirm their fundamental role in the structure of quantum chaotic eigenfunctions. More generally, our proposed architecture opens a new route to learning representations whose atoms optimize other chosen physical properties. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2607.07874 [quant-ph] (or arXiv:2607.07874v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.07874 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Gabriel Gustavo Carlo [view email] [v1] Wed, 8 Jul 2026 19:17:58 UTC (569 KB) Full-text links: Access Paper: View a PDF of the paper titled Unveiling Semiclassical Structures in Quantum Chaotic Eigenstates Using Neural Networks, by J. Montes and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 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?)