One-parameter counterexamples to the refined Bessis-Moussa-Villani conjecture

Quantum Physics [Submitted on 20 Mar 2026] One-parameter counterexamples to the refined Bessis-Moussa-Villani conjecture Hyunho Cha 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: 6 pages 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 Submission history From: Hyunho Cha [view email] [v1] Fri, 20 Mar 2026 13:12:03 UTC (6 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)