{"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/kinetic-blockings-in-long-range-interacting","title":"Kinetic blockings in long-range interacting inhomogeneous systems","arxiv_id":"2306.04613","date":"2023-06-07","proceeding":null,"authors":["Jean-Baptiste Fouvry","Mathieu Roule"],"abstract":"Long-range interacting systems unavoidably relax through Poisson shot noise fluctuations generated by their finite number of particles, $N$. When driven by two-body correlations, i.e. ${1/N}$ effects, this long-term evolution is described by the inhomogeneous Balescu-Lenard equation. Yet, in one-dimensional systems with a monotonic frequency profile and only subject to 1:1 resonances, this kinetic equation exactly vanishes: this is a first-order full kinetic blocking. These systems' long-term evolution is then driven by three-body correlations, i.e. ${1/N^2}$ effects. In the limit of dynamically hot systems, this is described by the inhomogeneous ${1/N^2}$ Landau equation. We investigate numerically the long-term evolution of systems for which this second kinetic equation also exactly vanishes: this a second-order bare kinetic blocking. We demonstrate that these systems relax through the \"leaking\" contributions of dressed three-body interactions that are neglected in the inhomogeneous ${1/N^2}$ Landau equation. Finally, we argue that these never-vanishing contributions prevent four-body correlations, i.e. ${1/N^{3}}$ effects, from ever being the main driver of relaxation.","url_abs":"https://arxiv.org/abs/2306.04613v1","url_pdf":"https://arxiv.org/pdf/2306.04613v1.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":"kinetic-blockings-in-long-range-interacting","repo_url":"https://github.com/jbfouvry/landau-n3","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}