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

Quantum Physics [Submitted on 13 Mar 2026] Hadamard regularization of open quantum systems coupled to unstructured environments in the Schwinger-Keldysh formalism Jakob Dolgner 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: 28 pages, 7 figures 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 Submission history From: Jakob Dolgner [view email] [v1] Fri, 13 Mar 2026 17:28:11 UTC (523 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.stat-mech physics physics.comp-ph 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?)