Constructing Fermionic Dynamics with Closed Moment Hierarchies

Quantum Physics [Submitted on 1 Apr 2026] Constructing Fermionic Dynamics with Closed Moment Hierarchies A. E. Teretenkov We construct a broad class of completely positive maps and Go\-rini--Kossakowski--Sudarshan-Lindblad generators for fermionic systems induced by linear transformations of system and environment modes. For these maps, we derive explicit Heisenberg-picture formulas for arbitrary normally ordered monomials in terms of minors of the underlying mode-transformation matrices and environment correlation tensors. We show that for even environment states the linear span of monomials up to any fixed order is invariant, which yields closed equations for low-order moments and makes their computation efficient. We also discuss the relation of this construction to second quantization of non-Hermitian one-particle contractions and extend the formalism to completely positive maps arising from post-selection. Comments: 21 pages Subjects: Quantum Physics (quant-ph) MSC classes: 81S22 (Primary) 81Q05, 81Q80 (Secondary) Cite as: arXiv:2604.01353 [quant-ph]   (or arXiv:2604.01353v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.01353 Focus to learn more Submission history From: Alexander Teretenkov [view email] [v1] Wed, 1 Apr 2026 20:07:02 UTC (19 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?)