Asymptotic analysis of a Fredholm determinant occurring in the description of the dynamical correlation functions of the Lieb--Liniger Bose gas

[2608.16727] Asymptotic analysis of a Fredholm determinant occurring in the description of the dynamical correlation functions of the Lieb--Liniger Bose gas Skip to main content Search Submit Donate Log in Mathematical Physics arXiv:2608.16727 (math-ph) [Submitted on 17 Aug 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Asymptotic analysis of a Fredholm determinant occurring in the description of the dynamical correlation functions of the Lieb--Liniger Bose gas Authors: Frank Göhmann , Karol K. Kozlowski , Mikhail D. Minin View PDF HTML (experimental) Abstract: We perform a large-$x$ asymptotic analysis of the Fredholm determinant of an integrable integral operator with generalized sine kernel, where $x$ controls the strength of the oscillations along the integration contour of the operator and will play the role of the distance variable in applications to the correlation functions of integrable quantum systems. Our generalized sine kernel involves a number of functional parameters that will allow us to adapt it to the analysis of the dynamical correlation functions of the Lieb--Liniger model at finite temperature and for all positive values of the coupling constant. It will also allow us to consider a class of equilibrium correlation functions that are governed by generalized Gibbs ensembles. Our work is based on the analysis of a matrix Riemann--Hilbert problem that is canonically connected with our integrable integral operator. Comments: 87 pages, typos corrected Subjects: Mathematical Physics (math-ph) ; Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th) Cite as: arXiv:2608.16727 [math-ph] (or arXiv:2608.16727v2 [math-ph] for this version) https://doi.org/10.48550/arXiv.2608.16727 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mikhail Minin [ view email ] [v1] Mon, 17 Aug 2026 15:41:16 UTC (1,565 KB) [v2] Fri, 28 Aug 2026 10:28:23 UTC (1,565 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math-ph < prev | next > new | recent | 2026-08 Change to browse by: cond-mat cond-mat.stat-mech hep-th math math.MP References & Citations INSPIRE HEP SciX 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 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)

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