Semiclassical periodic-orbit theory for quantum spectra
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Quantum Physics arXiv:2605.19019 (quant-ph) [Submitted on 18 May 2026] Title:Semiclassical periodic-orbit theory for quantum spectra Authors:Sebastian Müller, Martin Sieber View a PDF of the paper titled Semiclassical periodic-orbit theory for quantum spectra, by Sebastian M\"uller and 1 other authors View PDF HTML (experimental) Abstract:Gutzwiller's trace formula has a central place in quantum chaos because it provides semiclassical approximations for quantum energy levels in classically chaotic systems by linking them to classical periodic orbits. In this didactic article, we discuss a derivation of the trace formula starting from the Feynman path integral. We then describe how the trace formula is used to explain universal features in the distribution of the quantum energy levels that are described by random matrix theory, and we give an overview of related work. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Chaotic Dynamics (nlin.CD) Cite as: arXiv:2605.19019 [quant-ph] (or arXiv:2605.19019v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.19019 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Sebastian Müller [view email] [v1] Mon, 18 May 2026 18:40:45 UTC (3,459 KB) Full-text links: Access Paper: View a PDF of the paper titled Semiclassical periodic-orbit theory for quantum spectra, by Sebastian M\"uller and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: math math-ph math.MP 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?)