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Hadamard regularization of open quantum systems coupled to unstructured environments in the Schwinger-Keldysh formalism

arXiv Quantum Physics
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A March 2026 preprint introduces a Hadamard regularization method to tackle computational bottlenecks in open quantum systems, where environmental interactions degrade coherence—a key challenge for quantum technologies and condensed-matter physics. The study leverages the Schwinger-Keldysh formalism, a functional-integral framework for nonequilibrium quantum systems, but notes its cubic time-step scaling renders simulations impractical for systems with disparate time scales, like slow quantum devices coupled to fast environments. Using a damped quantum harmonic oscillator as a testbed, the work proposes a separation-of-scales approach via Hadamard regularization to isolate slow system dynamics from rapid environmental fluctuations, reducing computational overhead. A novel time-stepping algorithm for Kadanoff-Baym equations is presented, operating on the system’s slow time scale while preserving non-Markovian effects and renormalization from the faster environment—critical for low-temperature regimes. The method bridges theoretical rigor and practical computation, offering a pathway to simulate complex open quantum systems more efficiently, with implications for quantum material design and error-mitigation strategies in near-term devices.
Hadamard regularization of open quantum systems coupled to unstructured environments in the Schwinger-Keldysh formalism

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Quantum Physics arXiv:2603.13462 (quant-ph) [Submitted on 13 Mar 2026] Title:Hadamard regularization of open quantum systems coupled to unstructured environments in the Schwinger-Keldysh formalism Authors:Jakob Dolgner View a PDF of the paper titled Hadamard regularization of open quantum systems coupled to unstructured environments in the Schwinger-Keldysh formalism, by Jakob Dolgner View PDF HTML (experimental) Abstract:The theory of open quantum systems addresses how coupling to external degrees of freedom modifies observables and quantum coherence, a situation central to fundamental condensed-matter research and emerging quantum technologies. Schwinger-Keldysh field theory is a natural framework for both open- and nonequilibrium quantum systems in terms of functional integrals. However, its numerical solution is limited by a cubic scaling with the number of time steps. This is particularly prohibitive for scenarios with widely separated time scales, as is often the case for system and environmental scales. We consider a damped quantum harmonic oscillator as a toy model to study a separation-of-scales ansatz based on Hadamard regularization. A time-stepping algorithm for the Kadanoff-Baym equations on the slow system time-scale is presented that captures both low-temperature non-Markovianity and renormalization effects arising from the much faster environment scale. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Computational Physics (physics.comp-ph) Cite as: arXiv:2603.13462 [quant-ph] (or arXiv:2603.13462v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.13462 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jakob Dolgner [view email] [v1] Fri, 13 Mar 2026 17:28:11 UTC (523 KB) Full-text links: Access Paper: View a PDF of the paper titled Hadamard regularization of open quantum systems coupled to unstructured environments in the Schwinger-Keldysh formalism, by Jakob DolgnerView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: cond-mat cond-mat.stat-mech physics physics.comp-ph 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)

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Source: arXiv Quantum Physics