On the Dynamics of Multiparticle Carroll-Schr\"dinger Quantum Systems

Quantum Physics arXiv:2512.00247 (quant-ph) [Submitted on 28 Nov 2025] Title:On the Dynamics of Multiparticle Carroll-Schrdinger Quantum Systems Authors:José Rojas, Melvin Arias View a PDF of the paper titled On the Dynamics of Multiparticle Carroll-Schr\"dinger Quantum Systems, by Jos\'e Rojas and Melvin Arias View PDF HTML (experimental) Abstract:We study the dynamics of multiparticle Carroll-Schrödinger (CS) quantum systems in $1{+}1$ dimensions, where $x$ acts as the evolution variable and $t$ as the configuration coordinate. We derive the $N$-body theory on equal-$x$ slices as the Carrollian limit of a relativistic multi-time Klein-Gordon model, introducing temporal interactions via minimal coupling to the temporal energy operators. An $x$-dependent gauge transformation maps this to an equivalent description with explicit many-body potentials, illustrated by a temporal coupled-oscillator model that exhibits synchronization. Adopting a complementary spatial viewpoint with a static potential $U_{\!tot}(\mathbf x)$, we show that the evolution is driven by the collective force $\sum_j\partial_{x_j}U_{\!tot}$; for any translation-invariant interaction (such as a regularized Coulomb potential), these internal forces cancel, rendering the collective dynamics free and highlighting Carrollian ultralocality. We also construct a coordinate duality mapping separable Schrödinger Hamiltonians to CS generators via Schwarzian derivatives. Exchange symmetry is formulated in the time domain, yielding temporal bunching for bosons and antibunching for fermions via the second-order coherence function $g^{(2)}(t,t')$. In second quantization, the contact limit yields a temporal derivative cubic--quintic nonlinear Schrödinger equation with a theoretically fixed nonlinearity coefficient $\beta=-3/16$. Finally, by coupling canonical pairs to external scalar and gauge fields, we establish an isomorphism with one-dimensional current-density functional theory, outlining a Carrollian Hohenberg-Kohn mapping and Kohn-Sham scheme. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2512.00247 [quant-ph] (or arXiv:2512.00247v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.00247 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Melvin Arias [view email] [v1] Fri, 28 Nov 2025 23:36:04 UTC (1,223 KB) Full-text links: Access Paper: View a PDF of the paper titled On the Dynamics of Multiparticle Carroll-Schr\"dinger Quantum Systems, by Jos\'e Rojas and Melvin AriasView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 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?)