---
_id: '14343'
abstract:
- lang: eng
  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.
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."
article_number: e74
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Giorgio
  full_name: Cipolloni, Giorgio
  id: 42198EFA-F248-11E8-B48F-1D18A9856A87
  last_name: Cipolloni
  orcid: 0000-0002-4901-7992
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Sven Joscha
  full_name: Henheik, Sven Joscha
  id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
  last_name: Henheik
  orcid: 0000-0003-1106-327X
- first_name: Oleksii
  full_name: Kolupaiev, Oleksii
  id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61
  last_name: Kolupaiev
citation:
  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>
  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>
  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>.
  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.
  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.
  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>.
  short: G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Forum of Mathematics,
    Sigma 11 (2023).
date_created: 2023-09-17T22:01:09Z
date_published: 2023-08-23T00:00:00Z
date_updated: 2023-12-13T12:24:23Z
day: '23'
ddc:
- '510'
department:
- _id: LaEr
- _id: GradSch
doi: 10.1017/fms.2023.70
ec_funded: 1
external_id:
  arxiv:
  - '2301.05181'
  isi:
  - '001051980200001'
file:
- access_level: open_access
  checksum: eb747420e6a88a7796fa934151957676
  content_type: application/pdf
  creator: dernst
  date_created: 2023-09-20T11:09:35Z
  date_updated: 2023-09-20T11:09:35Z
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  file_name: 2023_ForumMathematics_Cipolloni.pdf
  file_size: 852652
  relation: main_file
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file_date_updated: 2023-09-20T11:09:35Z
has_accepted_license: '1'
intvolume: '        11'
isi: 1
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Forum of Mathematics, Sigma
publication_identifier:
  eissn:
  - 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Gaussian fluctuations in the equipartition principle for Wigner matrices
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)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2023'
...