One-to-one correspondence between Hierarchical Equations of Motion and Pseudomodes for Open Quantum System Dynamics
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Quantum Physics arXiv:2604.06466 (quant-ph) [Submitted on 7 Apr 2026] Title:One-to-one correspondence between Hierarchical Equations of Motion and Pseudomodes for Open Quantum System Dynamics Authors:Kai Müller, Walter T. Strunz View a PDF of the paper titled One-to-one correspondence between Hierarchical Equations of Motion and Pseudomodes for Open Quantum System Dynamics, by Kai M\"uller and Walter T. Strunz View PDF HTML (experimental) Abstract:We unite two of the most widely used approaches for strongly damped, non-Markovian open quantum dynamics, the Hierarchical Equations of Motion (HEOM) and the pseudomode method by proving two statements: First, every physical bath correlation function (BCF) that can be written as a sum of $N$ exponential terms can be obtained from a physical model with $N$ interacting pseudomodes which are damped in Lindblad form. Second, for every such BCF there exists a non-unitary, linear transformation which mirrors the evolution of the system-pseudomode state onto the HEOM hierarchy, and vice versa. Our proofs are constructive and we give explicit expressions for the mirror transformation as well as for the pseudomode Lindbladian corresponding to a given exponential BCF. This approach also gives insight and provides elegant derivations of the corresponding Hierarchy of stochastic Pure States (HOPS) method and its nearly-unitary version, nuHOPS. Our result opens several avenues for further optimization of non-Markovian open quantum system dynamics methods. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.06466 [quant-ph] (or arXiv:2604.06466v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.06466 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Kai Müller [view email] [v1] Tue, 7 Apr 2026 21:08:53 UTC (120 KB) Full-text links: Access Paper: View a PDF of the paper titled One-to-one correspondence between Hierarchical Equations of Motion and Pseudomodes for Open Quantum System Dynamics, by Kai M\"uller and Walter T. StrunzView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)