{"month":"10","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"doi":"10.1007/s00220-021-04239-z","abstract":[{"lang":"eng","text":"We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020)."}],"ddc":["510"],"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","isi":1,"has_accepted_license":"1","_id":"10221","status":"public","oa_version":"Published Version","volume":388,"license":"https://creativecommons.org/licenses/by/4.0/","publication":"Communications in Mathematical Physics","file":[{"creator":"cchlebak","checksum":"a2c7b6f5d23b5453cd70d1261272283b","file_id":"10715","success":1,"content_type":"application/pdf","file_name":"2021_CommunMathPhys_Cipolloni.pdf","date_updated":"2022-02-02T10:19:55Z","file_size":841426,"relation":"main_file","access_level":"open_access","date_created":"2022-02-02T10:19:55Z"}],"issue":"2","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00220-021-04239-z\">https://doi.org/10.1007/s00220-021-04239-z</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Eigenstate thermalization hypothesis for Wigner matrices. <i>Communications in Mathematical Physics</i>. 2021;388(2):1005–1048. doi:<a href=\"https://doi.org/10.1007/s00220-021-04239-z\">10.1007/s00220-021-04239-z</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2021). Eigenstate thermalization hypothesis for Wigner matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-021-04239-z\">https://doi.org/10.1007/s00220-021-04239-z</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Eigenstate thermalization hypothesis for Wigner matrices,” <i>Communications in Mathematical Physics</i>, vol. 388, no. 2. Springer Nature, pp. 1005–1048, 2021.","mla":"Cipolloni, Giorgio, et al. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” <i>Communications in Mathematical Physics</i>, vol. 388, no. 2, Springer Nature, 2021, pp. 1005–1048, doi:<a href=\"https://doi.org/10.1007/s00220-021-04239-z\">10.1007/s00220-021-04239-z</a>."},"day":"29","title":"Eigenstate thermalization hypothesis for Wigner matrices","intvolume":"       388","scopus_import":"1","author":[{"orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","first_name":"Giorgio"},{"orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J"}],"date_created":"2021-11-07T23:01:25Z","article_processing_charge":"Yes (via OA deal)","type":"journal_article","page":"1005–1048","publisher":"Springer Nature","publication_status":"published","department":[{"_id":"LaEr"}],"date_updated":"2023-08-14T10:29:49Z","year":"2021","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file_date_updated":"2022-02-02T10:19:55Z","date_published":"2021-10-29T00:00:00Z","external_id":{"isi":["000712232700001"],"arxiv":["2012.13215"]},"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"language":[{"iso":"eng"}],"quality_controlled":"1","oa":1,"article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"}