---
OA_place: repository
OA_type: green
_id: '18656'
abstract:
- lang: eng
  text: "We consider the time evolution of the out-of-time-ordered correlator (OTOC)
    of two general observables \r\n and \r\n in a mean field chaotic quantum system
    described by a random Wigner matrix as its Hamiltonian. We rigorously identify
    three time regimes separated by the physically relevant scrambling and relaxation
    times. The main feature of our analysis is that we express the error terms in
    the optimal Schatten (tracial) norms of the observables, allowing us to track
    the exact dependence of the errors on their rank. In particular, for significantly
    overlapping observables with low rank the OTOC is shown to exhibit a significant
    local maximum at the scrambling time, a feature that may not have been noticed
    in the physics literature before. Our main tool is a novel multi-resolvent local
    law with Schatten norms that unifies and improves previous local laws involving
    either the much cruder operator norm (cf. [10]) or the Hilbert-Schmidt norm (cf.
    [11])."
acknowledgement: LE and JH were supported by the ERC Advanced Grant łRMTBeyondž No.
  101020331
article_processing_charge: No
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
citation:
  ama: Cipolloni G, Erdös L, Henheik SJ. Out-of-time-ordered correlators for Wigner
    matrices. <i>Advances in Theoretical and Mathematical Physics</i>. 2024;28(6):2025-2083.
    doi:<a href="https://doi.org/10.4310/ATMP.241031013250">10.4310/ATMP.241031013250</a>
  apa: Cipolloni, G., Erdös, L., &#38; Henheik, S. J. (2024). Out-of-time-ordered
    correlators for Wigner matrices. <i>Advances in Theoretical and Mathematical Physics</i>.
    International Press. <a href="https://doi.org/10.4310/ATMP.241031013250">https://doi.org/10.4310/ATMP.241031013250</a>
  chicago: Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Out-of-Time-Ordered
    Correlators for Wigner Matrices.” <i>Advances in Theoretical and Mathematical
    Physics</i>. International Press, 2024. <a href="https://doi.org/10.4310/ATMP.241031013250">https://doi.org/10.4310/ATMP.241031013250</a>.
  ieee: G. Cipolloni, L. Erdös, and S. J. Henheik, “Out-of-time-ordered correlators
    for Wigner matrices,” <i>Advances in Theoretical and Mathematical Physics</i>,
    vol. 28, no. 6. International Press, pp. 2025–2083, 2024.
  ista: Cipolloni G, Erdös L, Henheik SJ. 2024. Out-of-time-ordered correlators for
    Wigner matrices. Advances in Theoretical and Mathematical Physics. 28(6), 2025–2083.
  mla: Cipolloni, Giorgio, et al. “Out-of-Time-Ordered Correlators for Wigner Matrices.”
    <i>Advances in Theoretical and Mathematical Physics</i>, vol. 28, no. 6, International
    Press, 2024, pp. 2025–83, doi:<a href="https://doi.org/10.4310/ATMP.241031013250">10.4310/ATMP.241031013250</a>.
  short: G. Cipolloni, L. Erdös, S.J. Henheik, Advances in Theoretical and Mathematical
    Physics 28 (2024) 2025–2083.
corr_author: '1'
date_created: 2024-12-15T23:01:51Z
date_published: 2024-10-30T00:00:00Z
date_updated: 2026-04-07T12:37:10Z
day: '30'
department:
- _id: LaEr
doi: 10.4310/ATMP.241031013250
ec_funded: 1
external_id:
  arxiv:
  - '2402.17609'
intvolume: '        28'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2402.17609
month: '10'
oa: 1
oa_version: Preprint
page: 2025-2083
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
  eissn:
  - 1095-0753
  issn:
  - 1095-0761
publication_status: published
publisher: International Press
quality_controlled: '1'
related_material:
  record:
  - id: '19540'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Out-of-time-ordered correlators for Wigner matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2024'
...