A Schwinger-Keldysh Formulation of Semiclassical Operator Dynamics

[2602.02106] A Schwinger-Keldysh Formulation of Semiclassical Operator Dynamics Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2602.02106 (quant-ph) [Submitted on 2 Feb 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: A Schwinger-Keldysh Formulation of Semiclassical Operator Dynamics Authors: Jeff Murugan , Hendrik J. R. van Zyl View PDF HTML (experimental) Abstract: In this work we develop a real-time Schwinger-Keldysh formulation of Krylov dynamics that treats Krylov complexity as an in-in observable generated by a closed time contour path integral. The resulting generating functional exposes an emergent phase-space description in which the Lanczos coefficients define an effective Hamiltonian governing operator motion along the Krylov chain. In the semiclassical limit, exponential complexity growth arises from hyperbolic trajectories, and asymptotically linear Lanczos growth appears as a universal chaotic fixed point, with sub-leading deformations classified as irrelevant, marginal or relevant. Going beyond the saddle, the Schwinger-Keldysh framework provides controlled access to fluctuations and large deviations of Krylov complexity, revealing sharp signatures of integrability-chaos crossovers that are invisible at the level of the mean. This formulation reorganises Krylov complexity into a dynamical field-theoretic framework and identifies new fluctuation diagnostics of operator growth in closed quantum systems. Comments: 30+4 pages, 2 figures and 2 appendices Subjects: Quantum Physics (quant-ph) ; Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph) Cite as: arXiv:2602.02106 [quant-ph] (or arXiv:2602.02106v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.02106 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hendrik Van Zyl [ view email ] [v1] Mon, 2 Feb 2026 13:51:01 UTC (162 KB) [v2] Fri, 28 Aug 2026 08:21:38 UTC (164 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-02 Change to browse by: cond-mat cond-mat.str-el hep-th math math-ph math.MP 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 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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