Curvature as a control field in helicoidal two-body systems

Quantum Physics arXiv:2608.02659 (quant-ph) [Submitted on 1 Aug 2026] Title:Curvature as a control field in helicoidal two-body systems Authors:Abdullah Guvendi, Hassan Hassanabadi View a PDF of the paper titled Curvature as a control field in helicoidal two-body systems, by Abdullah Guvendi and 1 other authors View PDF HTML (experimental) Abstract:Geometry is increasingly recognized as an active physical resource capable of modifying the behavior of quantum systems beyond conventional external control mechanisms. Here, we establish a curvature--gauge framework in which the geometry of an embedded manifold functions as a tunable control field for classical trajectories and quantum states. By deriving an exact reduced Hamiltonian for a two-body system confined to a helicoidal surface, we demonstrate that curvature modifies the effective kinetic structure while a projected gauge field reconstructs the conserved momentum landscape. This geometric renormalization produces controllable transitions between distinct dynamical regimes, including bounded phase-space structures, zero-energy localization, symmetry-breaking bifurcations, and critical soft-mode behavior. Quantization of the geometry-dependent effective potential reveals a corresponding spectral reconstruction, where harmonic confinement evolves into quartic critical states at the localization threshold. These results establish engineered geometry as a general route for controlling localization and spectral organization in curved quantum, electronic, photonic, and synthetic platforms, where deformation itself becomes a functional degree of freedom rather than a passive constraint. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.02659 [quant-ph] (or arXiv:2608.02659v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.02659 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Abdullah Guvendi [view email] [v1] Sat, 1 Aug 2026 13:27:50 UTC (6,525 KB) Full-text links: Access Paper: View a PDF of the paper titled Curvature as a control field in helicoidal two-body systems, by Abdullah Guvendi and 1 other authorsView 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?)