{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/matrix-valued-boltzmann-equation-for-the","title":"Matrix-valued Boltzmann Equation for the Hubbard Chain","arxiv_id":"1207.6926","date":"2012-07-30","proceeding":null,"authors":["Martin L. R. Fürst","Christian B. Mendl","Herbert Spohn"],"abstract":"We study, both analytically and numerically, the Boltzmann transport equation for the Hubbard chain with nearest neighbor hopping and spatially homogeneous initial condition. The time-dependent Wigner function is matrix-valued because of spin. The H-theorem holds. The nearest neighbor chain is integrable which, on the kinetic level, is reflected by infinitely many additional conservation laws and linked to the fact that there are also non-thermal stationary states. We characterize all stationary solutions. Numerically, we observe an exponentially fast convergence to stationarity and investigate the convergence rate in dependence on the initial conditions.","url_abs":"https://arxiv.org/abs/1207.6926v2","url_pdf":"https://arxiv.org/pdf/1207.6926v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"matrix-valued-boltzmann-equation-for-the","repo_url":"https://github.com/cmendl/matrix-quantum-boltzmann-1D","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}