{"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/bogolyubov-s-averaging-theorem-applied-to-the","title":"Bogolyubov's averaging theorem applied to the Kramers-Henneberger Hamiltonian","arxiv_id":"2107.01946","date":"2021-07-05","proceeding":null,"authors":["Elena Floriani","Jonathan Dubois","Cristel Chandre"],"abstract":"We apply Bogolyubov's averaging theorem to the motion of an electron of an atom driven by a linearly polarized laser field in the Kramers-Henneberger frame. We provide estimates of the differences between the original trajectories and the trajectories associated with the averaged system as a function of the parameters of the laser field and the region of phase space. We formulate a modified Bogolyubov averaging theorem based on the Hamiltonian properties of the system, and show that this version is better suited for these systems. From these estimates, we discuss the validity of the Kramers-Henneberger approximation.","url_abs":"https://arxiv.org/abs/2107.01946v1","url_pdf":"https://arxiv.org/pdf/2107.01946v1.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":"bogolyubov-s-averaging-theorem-applied-to-the","repo_url":"https://github.com/cchandre/KH","is_official":1,"mentioned_in_paper":1,"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}