[2608.14436] A semiclassical limit of reduced Hartree-Fock theory at positive temperature Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematical Physics arXiv:2608.14436 (math-ph) [Submitted on 14 Aug 2026] Title: A semiclassical limit of reduced Hartree-Fock theory at positive temperature Authors: Dominic Shillingford View a PDF of the paper titled A semiclassical limit of reduced Hartree-Fock theory at positive temperature, by Dominic Shillingford View PDF HTML (experimental) Abstract: It is established that the reduced Hartree-Fock grand potential at positive temperature converges in the semiclassical limit to a Thomas-Fermi grand potential. In particular, a density-potential dual representation of the limiting functional is proposed for a general class of fermionic entropy functions. The corresponding dual problem has no duality gap and admits a maximizer. The resulting grand potential converges to the established zero-temperature grand potential as the temperature tends to zero and, for the Fermi-Dirac entropy, agrees with the standard positive-temperature Thomas-Fermi free-energy functional. The proof also establishes a semiclassical trace formula that is uniform over locally precompact families of potentials subject to a common confinement condition. Comments: 28 pages Subjects: Mathematical Physics (math-ph) ; Analysis of PDEs (math.AP); Spectral Theory (math.SP) MSC classes: 81Q20 (Primary) 82B10, 81V70 (Secondary) Cite as: arXiv:2608.14436 [math-ph] (or arXiv:2608.14436v1 [math-ph] for this version) https://doi.org/10.48550/arXiv.2608.14436 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Dominic Shillingford [ view email ] [v1] Fri, 14 Aug 2026 16:18:17 UTC (29 KB) Full-text links: Access Paper: View a PDF of the paper titled A semiclassical limit of reduced Hartree-Fock theory at positive temperature, by Dominic Shillingford View PDF HTML (experimental) TeX Source view license Current browse context: math-ph < prev | next > new | recent | 2026-08 Change to browse by: math math.AP math.MP math.SP References & Citations NASA ADS Google 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from