Amplitude-dependent quantum hydrodynamics from a \(\coth\)-Madelung ansatz
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Quantum Physics arXiv:2606.06561 (quant-ph) [Submitted on 4 Jun 2026] Title:Amplitude-dependent quantum hydrodynamics from a \(\coth\)-Madelung ansatz Authors:C. Dedes View a PDF of the paper titled Amplitude-dependent quantum hydrodynamics from a \(\coth\)-Madelung ansatz, by C. Dedes View PDF HTML (experimental) Abstract:We investigate a nonlinear extension of the Madelung transformation based on a hyperbolic phase--amplitude coupling of the form \[ \Psi = R e^{\imath\theta \coth R}, \] where \(R\) is a real amplitude field and \(\theta\) is an auxiliary phase coordinate governed by Schrödinger's equation. In contrast to the conventional polar decomposition, this construction imposes a singular hyperbolic relation between amplitude and phase, thereby endowing the Bohmian or hydrodynamic description with an intrinsically geometric structure. We show that the associated velocity field acquires a density-gradient contribution, producing generalized continuity equations and modified quantum force terms. When interpreted as a complex macroscopic order parameter, this generalized phase structure leads to modified superconducting electrodynamics; in particular, the London equations acquire additional contributions that render the Meissner response sensitive to spatial density gradients. The proposed framework is motivated by broader developments involving complex group velocities, dissipative wave propagation, and amplitude-sensitive transport in quantum systems. Subjects: Quantum Physics (quant-ph); Superconductivity (cond-mat.supr-con); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph) Cite as: arXiv:2606.06561 [quant-ph] (or arXiv:2606.06561v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.06561 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: C Dedes [view email] [v1] Thu, 4 Jun 2026 14:51:14 UTC (18 KB) Full-text links: Access Paper: View a PDF of the paper titled Amplitude-dependent quantum hydrodynamics from a \(\coth\)-Madelung ansatz, by C. DedesView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cond-mat cond-mat.supr-con gr-qc math math-ph math.MP 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?)