Double-Bracket Master Equations: Phase-Space Representation and Classical Limit
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Quantum Physics arXiv:2601.20925 (quant-ph) [Submitted on 28 Jan 2026] Title:Double-Bracket Master Equations: Phase-Space Representation and Classical Limit Authors:Ankit W. Shrestha, Budhaditya Bhattacharjee, Adolfo del Campo View a PDF of the paper titled Double-Bracket Master Equations: Phase-Space Representation and Classical Limit, by Ankit W. Shrestha and 2 other authors View PDF HTML (experimental) Abstract:We investigate the classical limit of quantum master equations featuring double-bracket dissipators. Specifically, we consider dissipators defined by double commutators, which describe dephasing dynamics, as well as dissipators involving double anticommutators, associated with fluctuating anti-Hermitian Hamiltonians. The classical limit is obtained by formulating the open quantum dynamics in phase space using the Wigner function and Moyal products, followed by a systematic $\hbar$-expansion. We begin with the well-known model of energy dephasing, associated with energy diffusion. We then turn to master equations containing a double anticommutator with the system Hamiltonian, recently derived in the context of noisy non-Hermitian systems. For both classes of double-bracket equations, we provide a gradient-flow representation of the dynamics. We analyze the classical limit of the resulting evolutions for harmonic and driven anharmonic quantum oscillators, considering both classical and nonclassical initial states. The dynamics is characterized through the evolution of several observables as well as the Wigner logarithmic negativity. We conclude by extending our analysis to generalized master equations involving higher-order nested brackets, which provide a time-continuous description of spectral filtering techniques commonly used in the numerical analysis of quantum systems. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2601.20925 [quant-ph] (or arXiv:2601.20925v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.20925 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ankit Wenju Shrestha [view email] [v1] Wed, 28 Jan 2026 19:00:00 UTC (924 KB) Full-text links: Access Paper: View a PDF of the paper titled Double-Bracket Master Equations: Phase-Space Representation and Classical Limit, by Ankit W. Shrestha and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cond-mat cond-mat.stat-mech 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?)