{"related_material":{"record":[{"status":"for_moderation","id":"17164","relation":"dissertation_contains"}]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2310.06677"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"LaEr"}],"ec_funded":1,"language":[{"iso":"eng"}],"author":[{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László"},{"full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik"},{"first_name":"Jana","full_name":"Reker, Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","last_name":"Reker"},{"full_name":"Riabov, Volodymyr","first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","last_name":"Riabov"}],"day":"23","year":"2023","date_published":"2023-12-23T00:00:00Z","article_processing_charge":"No","date_updated":"2024-06-27T09:48:37Z","publication":"arXiv","date_created":"2024-06-26T08:56:52Z","abstract":[{"lang":"eng","text":"We prove that a class of weakly perturbed Hamiltonians of the form $H_λ= H_0 + λW$, with $W$ being a Wigner matrix, exhibits prethermalization. That is, the time evolution generated by $H_λ$ relaxes to its ultimate thermal state via an intermediate prethermal state with a lifetime of order $λ^{-2}$. Moreover, we obtain a general relaxation formula, expressing the perturbed dynamics via the unperturbed dynamics and the ultimate thermal state. The proof relies on a two-resolvent law for the deformed Wigner matrix $H_λ$."}],"status":"public","oa_version":"Preprint","type":"preprint","citation":{"ieee":"L. Erdös, S. J. Henheik, J. Reker, and V. Riabov, “Prethermalization for deformed Wigner Matrices,” <i>arXiv</i>. .","mla":"Erdös, László, et al. “Prethermalization for Deformed Wigner Matrices.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2310.06677\">10.48550/arXiv.2310.06677</a>.","chicago":"Erdös, László, Sven Joscha Henheik, Jana Reker, and Volodymyr Riabov. “Prethermalization for Deformed Wigner Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2310.06677\">https://doi.org/10.48550/arXiv.2310.06677</a>.","ista":"Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner Matrices. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2310.06677\">10.48550/arXiv.2310.06677</a>.","ama":"Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner Matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2310.06677\">10.48550/arXiv.2310.06677</a>","apa":"Erdös, L., Henheik, S. J., Reker, J., &#38; Riabov, V. (n.d.). Prethermalization for deformed Wigner Matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2310.06677\">https://doi.org/10.48550/arXiv.2310.06677</a>","short":"L. Erdös, S.J. Henheik, J. Reker, V. Riabov, ArXiv (n.d.)."},"doi":"10.48550/arXiv.2310.06677","_id":"17174","month":"12","title":"Prethermalization for deformed Wigner Matrices","external_id":{"arxiv":["2310.06677"]},"publication_status":"submitted","oa":1,"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020"}]}