One-to-one correspondence between Hierarchical Equations of Motion and Pseudomodes for Open Quantum System Dynamics

Quantum Physics [Submitted on 7 Apr 2026] One-to-one correspondence between Hierarchical Equations of Motion and Pseudomodes for Open Quantum System Dynamics Kai Müller, Walter T. Strunz 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 Submission history From: Kai Müller [view email] [v1] Tue, 7 Apr 2026 21:08:53 UTC (120 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 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?)