Heating of a semi-infinite Hooke chain

[2502.13346] Heating of a semi-infinite Hooke chain Skip to main content Search Submit Donate Log in Condensed Matter > Statistical Mechanics arXiv:2502.13346 (cond-mat) [Submitted on 19 Feb 2025 ( v1 ), last revised 4 Oct 2026 (this version, v4)] Title: Heating of a semi-infinite Hooke chain Authors: Sergei D. Liazhkov View PDF HTML (experimental) Abstract: We investigate unsteady ballistic heat transport in a semi-infinite Hooke chain with a free end subjected to an arbitrary heat source. We derive an exact integral representation for the kinetic temperature, together with a weak-dissipation lattice approximation and two continuum-type descriptions. The continualization of the discrete solution for the kinetic temperature in the weakly dissipative limit is obtained in two representations. The first is a symmetrical continuum solution based on an even extension of the source with respect to the boundary. The second is a discrete-continuum solution derived by applying a large-time asymptotic approximation to the fundamental solution at the fronts of the incident and reflected thermal waves in an instantaneously perturbed conservative semi-infinite chain. This solution retains a contribution from the interaction of the incident and reflected waves, which is absent in the symmetrical continuum solution. Analysis of sudden point heat supply indicates that, even in the non-dissipative chain, the discrete solution for the kinetic temperature exhibits pronounced large-time slowing near the free end, consistent with a local nonequilibrium plateau, whereas the symmetrical continuum representation predicts unbounded logarithmic growth. The results are expected to provide a benchmark for continuum models of heat transport in lattices with a free boundary. Subjects: Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2502.13346 [cond-mat.stat-mech] (or arXiv:2502.13346v4 [cond-mat.stat-mech] for this version) https://doi.org/10.48550/arXiv.2502.13346 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sergei Liazhkov [ view email ] [v1] Wed, 19 Feb 2025 00:20:40 UTC (736 KB) [v2] Mon, 20 Oct 2025 00:32:38 UTC (1,201 KB) [v3] Wed, 26 Aug 2026 20:58:35 UTC (550 KB) [v4] Sun, 4 Oct 2026 01:02:34 UTC (552 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.stat-mech < prev | next > new | recent | 2025-02 Change to browse by: cond-mat References & Citations 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? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) 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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