Quantum, Stochastic, and Classical Dynamics Within A Single Geometric Framework

Quantum Physics arXiv:2510.27170 (quant-ph) [Submitted on 31 Oct 2025] Title:Quantum, Stochastic, and Classical Dynamics Within A Single Geometric Framework Authors:Partha Ghose View a PDF of the paper titled Quantum, Stochastic, and Classical Dynamics Within A Single Geometric Framework, by Partha Ghose View PDF HTML (experimental) Abstract:Nelson's stochastic mechanics links quantum mechanics to an underlying Brownian motion with the identification $\hbar = m\sigma$. Ghose's interpolating equation introduces a continuous parameter $\lambda$ that suppresses the quantum potential $Q[\psi]$ and yields a smooth transition between quantum ($\lambda=0$) and classical ($\lambda=1$) regimes. In this short note, we show that the Koopman--von Neumann (KvN) Hilbert-space formulation of classical mechanics emerges naturally as the $\lambda \to 1$ limit of this stochastic $\sigma$--$\lambda$ hierarchy. The KvN phase-space amplitude provides an operator representation of the classical Liouville equation, while the $\lambda$ parameter acts as a projection flow from the complex projective Hilbert manifold $\mathbb{C}P^n$ to its classical quotient $\mathbb{C}P^*/U(1)$, implementing phase superselection. This unified picture links quantum, stochastic, and classical dynamics within a single continuous framework. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2510.27170 [quant-ph] (or arXiv:2510.27170v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.27170 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Partha Ghose Professor [view email] [v1] Fri, 31 Oct 2025 04:46:39 UTC (4 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum, Stochastic, and Classical Dynamics Within A Single Geometric Framework, by Partha GhoseView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)