{"author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0003-1106-327X","last_name":"Henheik","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha"},{"first_name":"Oleksii","last_name":"Kolupaiev","full_name":"Kolupaiev, Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61"}],"day":"23","language":[{"iso":"eng"}],"year":"2023","oa":1,"abstract":[{"text":"The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices. As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation.","lang":"eng"}],"isi":1,"scopus_import":"1","volume":11,"date_published":"2023-08-23T00:00:00Z","quality_controlled":"1","article_number":"e74","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"has_accepted_license":"1","publication_identifier":{"eissn":["2050-5094"]},"ddc":["510"],"citation":{"mla":"Cipolloni, Giorgio, et al. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 11, e74, Cambridge University Press, 2023, doi:<a href=\"https://doi.org/10.1017/fms.2023.70\">10.1017/fms.2023.70</a>.","ista":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2023. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 11, e74.","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Gaussian fluctuations in the equipartition principle for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 11. Cambridge University Press, 2023.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Forum of Mathematics, Sigma 11 (2023).","ama":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Gaussian fluctuations in the equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2023;11. doi:<a href=\"https://doi.org/10.1017/fms.2023.70\">10.1017/fms.2023.70</a>","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/fms.2023.70\">https://doi.org/10.1017/fms.2023.70</a>.","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2023). Gaussian fluctuations in the equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2023.70\">https://doi.org/10.1017/fms.2023.70</a>"},"title":"Gaussian fluctuations in the equipartition principle for Wigner matrices","intvolume":"        11","article_processing_charge":"Yes","publication":"Forum of Mathematics, Sigma","external_id":{"isi":["001051980200001"],"arxiv":["2301.05181"]},"license":"https://creativecommons.org/licenses/by/4.0/","publisher":"Cambridge University Press","publication_status":"published","date_created":"2023-09-17T22:01:09Z","month":"08","_id":"14343","file":[{"success":1,"date_updated":"2023-09-20T11:09:35Z","access_level":"open_access","creator":"dernst","file_size":852652,"date_created":"2023-09-20T11:09:35Z","file_name":"2023_ForumMathematics_Cipolloni.pdf","checksum":"eb747420e6a88a7796fa934151957676","content_type":"application/pdf","file_id":"14352","relation":"main_file"}],"article_type":"original","status":"public","date_updated":"2023-12-13T12:24:23Z","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020"}],"oa_version":"Published Version","department":[{"_id":"LaEr"},{"_id":"GradSch"}],"doi":"10.1017/fms.2023.70","ec_funded":1,"acknowledgement":"G.C. and L.E. gratefully acknowledge many discussions with Dominik Schröder at the preliminary stage of this project, especially his essential contribution to identify the correct generalisation of traceless observables to the deformed Wigner ensembles.\r\nL.E. and J.H. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331.","file_date_updated":"2023-09-20T11:09:35Z"}