Toda-like Hamiltonian as a probe for quantized prey-predator dynamics
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Quantum Physics arXiv:2603.09071 (quant-ph) [Submitted on 10 Mar 2026] Title:Toda-like Hamiltonian as a probe for quantized prey-predator dynamics Authors:Alex E. Bernardini, Orfeu Bertolami View a PDF of the paper titled Toda-like Hamiltonian as a probe for quantized prey-predator dynamics, by Alex E. Bernardini and Orfeu Bertolami View PDF HTML (experimental) Abstract:Phase-space features of a reduced version of the Toda-like Hamiltonian, $\mathcal{H}(x,\,k)$, written in a form constrained by the condition $\partial^2 \mathcal{H} / \partial x \partial k = 0$, with $x$ and $k$ as canonically conjugate variables, are analyzed in terms of Wigner currents. For Wigner currents convoluted with either thermodynamic or Gaussian ensembles, the underlying Hamiltonian dynamics admits analytic corrections due to quantum distortions over the classical phase-space pattern, computed and interpreted through quantifiers of quantumness and stationarity. Notably, while emulating the Lotka-Volterra (LV) dynamics that describe ecological competition systems, the Toda-like classical dynamics allows for analytical solutions with computable periods corresponding to closed phase-space orbits of isotropic prey-predator population distributions. The essential conditions for understanding how classical and quantum evolution can coexist are provided at different scales of quantumness, driven by the associated convoluting ensemble parameter. In the case of Gaussian statistical ensembles, the exact profile of the quantum distortions over classical prey-predator phase-space trajectories is obtained non-perturbatively. Our results indicate that, besides the classical stability admitted by LV models, the Toda-like patterns also exhibit quantum stability. Therefore, this can be regarded as the first step as a predictive theoretical framework towards more robust descriptions of quantum patterns in competitive microscopic biosystems. Comments: Subjects: Quantum Physics (quant-ph); Exactly Solvable and Integrable Systems (nlin.SI); Populations and Evolution (q-bio.PE) Cite as: arXiv:2603.09071 [quant-ph] (or arXiv:2603.09071v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.09071 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Alex Bernardini Dr. [view email] [v1] Tue, 10 Mar 2026 01:29:17 UTC (2,641 KB) Full-text links: Access Paper: View a PDF of the paper titled Toda-like Hamiltonian as a probe for quantized prey-predator dynamics, by Alex E. Bernardini and Orfeu BertolamiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: nlin nlin.SI q-bio q-bio.PE 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?)