{"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/reservoir-induced-stabilisation-of-a","title":"Reservoir-induced stabilisation of a periodically driven classical spin chain: local vs. global relaxation","arxiv_id":"2208.08998","date":"2022-08-18","proceeding":null,"authors":["Thomas Veness","Kay Brandner"],"abstract":"Floquet theory is an indispensable tool for analysing periodically-driven quantum many-body systems. Although it does not universally extend to classical systems, some of its methodologies can be adopted in the presence of well-separated timescales. Here we use these tools to investigate the stroboscopic behaviours of a classical spin chain that is driven by a periodic magnetic field and coupled to a thermal reservoir. We detail and expand our previous work: we investigate the significance of higher-order corrections to the classical Floquet-Magnus expansion in both the high- and low-frequency regimes; explicitly probe the evolution the dynamics of the reservoir; and further explore how the driven system synchronises with the applied field at low frequencies. In line with our earlier results, we find that the high-frequency regime is characterised by a local Floquet-Gibbs ensemble with the reservoir acting as a nearly-reversible heatsink. At low frequencies, the driven system rapidly enters a synchronised state, which can only be fully described in a global picture accounting for the concurrent relaxation of the reservoir in a fictitious magnetic field arising from the drive. We highlight how the evolving nature of the reservoir may still be incorporated in a local picture by introducing an effective temperature. Finally, we argue that dissipative equations of motion for periodically-driven many-body systems, at least at intermediate frequencies, must generically be non-Markovian.","url_abs":"https://arxiv.org/abs/2208.08998v1","url_pdf":"https://arxiv.org/pdf/2208.08998v1.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":"reservoir-induced-stabilisation-of-a","repo_url":"https://github.com/tveness/spinchain-papers","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}