Local Complex Dependence and Separability in Madelung Hydrodynamics

Quantum Physics arXiv:2608.10019 (quant-ph) [Submitted on 8 Aug 2026] Title:Local Complex Dependence and Separability in Madelung Hydrodynamics Authors:Lorenzo Pirovano View a PDF of the paper titled Local Complex Dependence and Separability in Madelung Hydrodynamics, by Lorenzo Pirovano View PDF HTML (experimental) Abstract:For a many-particle pure state in a fixed position representation, we consider the mixed cross-particle derivatives of the logarithm of the wave function. Their real part is one half of the Holland-Wang local dependence function of the configuration density, while their imaginary part is the cross-Jacobian of the Madelung velocity field. On a node-free product region, vanishing of all cross blocks throughout the region is equivalent to local multiplicative separability. Under Schrodinger evolution with a real scalar potential, the initial growth of a cross block from a separable state is sourced by the corresponding mixed Hessian of the potential and is purely imaginary to first order in time. The construction is a local separability and dependence diagnostic, rather than a basis-independent entanglement measure. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.10019 [quant-ph] (or arXiv:2608.10019v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.10019 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Lorenzo Pirovano [view email] [v1] Sat, 8 Aug 2026 21:47:27 UTC (7 KB) Full-text links: Access Paper: View a PDF of the paper titled Local Complex Dependence and Separability in Madelung Hydrodynamics, by Lorenzo PirovanoView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 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?)