One-parameter counterexamples to the refined Bessis-Moussa-Villani conjecture
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Quantum Physics arXiv:2603.19927 (quant-ph) [Submitted on 20 Mar 2026] Title:One-parameter counterexamples to the refined Bessis-Moussa-Villani conjecture Authors:Hyunho Cha View a PDF of the paper titled One-parameter counterexamples to the refined Bessis-Moussa-Villani conjecture, by Hyunho Cha View PDF HTML (experimental) Abstract:The Bessis-Moussa-Villani (BMV) conjecture, originating in quantum statistical mechanics, was proved by Stahl after an influential reformulation by Lieb and Seiringer. A later refinement asks whether the normalized average over all words with $n$ letters $A$ and $m$ letters $B$ is always bounded above by $\mathrm{tr}(A^nB^m)$ and below by $\mathrm{tr}\exp(n\log A+m\log B)$. We study a specific one-parameter family $(A_x, B_x)$ and derive exact closed formulas for both sides of the first inequality when $(n,m)=(5,5)$. In particular, $x=10^{-3}$ gives a counterexample. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.19927 [quant-ph] (or arXiv:2603.19927v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.19927 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Hyunho Cha [view email] [v1] Fri, 20 Mar 2026 13:12:03 UTC (6 KB) Full-text links: Access Paper: View a PDF of the paper titled One-parameter counterexamples to the refined Bessis-Moussa-Villani conjecture, by Hyunho ChaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)