---
_id: '483'
abstract:
- lang: eng
  text: We prove the universality for the eigenvalue gap statistics in the bulk of
    the spectrum for band matrices, in the regime where the band width is comparable
    with the dimension of the matrix, W ~ N. All previous results concerning universality
    of non-Gaussian random matrices are for mean-field models. By relying on a new
    mean-field reduction technique, we deduce universality from quantum unique ergodicity
    for band matrices.
author:
- first_name: Paul
  full_name: Bourgade, Paul
  last_name: Bourgade
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Horng
  full_name: Yau, Horng
  last_name: Yau
- first_name: Jun
  full_name: Yin, Jun
  last_name: Yin
citation:
  ama: Bourgade P, Erdös L, Yau H, Yin J. Universality for a class of random band
    matrices. <i>Advances in Theoretical and Mathematical Physics</i>. 2017;21(3):739-800.
    doi:<a href="https://doi.org/10.4310/ATMP.2017.v21.n3.a5">10.4310/ATMP.2017.v21.n3.a5</a>
  apa: Bourgade, P., Erdös, L., Yau, H., &#38; Yin, J. (2017). Universality for a
    class of random band matrices. <i>Advances in Theoretical and Mathematical Physics</i>.
    International Press. <a href="https://doi.org/10.4310/ATMP.2017.v21.n3.a5">https://doi.org/10.4310/ATMP.2017.v21.n3.a5</a>
  chicago: Bourgade, Paul, László Erdös, Horng Yau, and Jun Yin. “Universality for
    a Class of Random Band Matrices.” <i>Advances in Theoretical and Mathematical
    Physics</i>. International Press, 2017. <a href="https://doi.org/10.4310/ATMP.2017.v21.n3.a5">https://doi.org/10.4310/ATMP.2017.v21.n3.a5</a>.
  ieee: P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random
    band matrices,” <i>Advances in Theoretical and Mathematical Physics</i>, vol.
    21, no. 3. International Press, pp. 739–800, 2017.
  ista: Bourgade P, Erdös L, Yau H, Yin J. 2017. Universality for a class of random
    band matrices. Advances in Theoretical and Mathematical Physics. 21(3), 739–800.
  mla: Bourgade, Paul, et al. “Universality for a Class of Random Band Matrices.”
    <i>Advances in Theoretical and Mathematical Physics</i>, vol. 21, no. 3, International
    Press, 2017, pp. 739–800, doi:<a href="https://doi.org/10.4310/ATMP.2017.v21.n3.a5">10.4310/ATMP.2017.v21.n3.a5</a>.
  short: P. Bourgade, L. Erdös, H. Yau, J. Yin, Advances in Theoretical and Mathematical
    Physics 21 (2017) 739–800.
date_created: 2018-12-11T11:46:43Z
date_published: 2017-08-25T00:00:00Z
date_updated: 2021-01-12T08:00:57Z
day: '25'
department:
- _id: LaEr
doi: 10.4310/ATMP.2017.v21.n3.a5
ec_funded: 1
intvolume: '        21'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1602.02312
month: '08'
oa: 1
oa_version: Submitted Version
page: 739 - 800
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
  issn:
  - '10950761'
publication_status: published
publisher: International Press
publist_id: '7337'
quality_controlled: '1'
scopus_import: 1
status: public
title: Universality for a class of random band matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2017'
...
---
_id: '484'
abstract:
- lang: eng
  text: We consider the dynamics of a large quantum system of N identical bosons in
    3D interacting via a two-body potential of the form N3β-1w(Nβ(x - y)). For fixed
    0 = β &lt; 1/3 and large N, we obtain a norm approximation to the many-body evolution
    in the Nparticle Hilbert space. The leading order behaviour of the dynamics is
    determined by Hartree theory while the second order is given by Bogoliubov theory.
author:
- first_name: Phan
  full_name: Nam, Phan
  id: 404092F4-F248-11E8-B48F-1D18A9856A87
  last_name: Nam
- first_name: Marcin M
  full_name: Napiórkowski, Marcin M
  id: 4197AD04-F248-11E8-B48F-1D18A9856A87
  last_name: Napiórkowski
citation:
  ama: Nam P, Napiórkowski MM. Bogoliubov correction to the mean-field dynamics of
    interacting bosons. <i>Advances in Theoretical and Mathematical Physics</i>. 2017;21(3):683-738.
    doi:<a href="https://doi.org/10.4310/ATMP.2017.v21.n3.a4">10.4310/ATMP.2017.v21.n3.a4</a>
  apa: Nam, P., &#38; Napiórkowski, M. M. (2017). Bogoliubov correction to the mean-field
    dynamics of interacting bosons. <i>Advances in Theoretical and Mathematical Physics</i>.
    International Press. <a href="https://doi.org/10.4310/ATMP.2017.v21.n3.a4">https://doi.org/10.4310/ATMP.2017.v21.n3.a4</a>
  chicago: Nam, Phan, and Marcin M Napiórkowski. “Bogoliubov Correction to the Mean-Field
    Dynamics of Interacting Bosons.” <i>Advances in Theoretical and Mathematical Physics</i>.
    International Press, 2017. <a href="https://doi.org/10.4310/ATMP.2017.v21.n3.a4">https://doi.org/10.4310/ATMP.2017.v21.n3.a4</a>.
  ieee: P. Nam and M. M. Napiórkowski, “Bogoliubov correction to the mean-field dynamics
    of interacting bosons,” <i>Advances in Theoretical and Mathematical Physics</i>,
    vol. 21, no. 3. International Press, pp. 683–738, 2017.
  ista: Nam P, Napiórkowski MM. 2017. Bogoliubov correction to the mean-field dynamics
    of interacting bosons. Advances in Theoretical and Mathematical Physics. 21(3),
    683–738.
  mla: Nam, Phan, and Marcin M. Napiórkowski. “Bogoliubov Correction to the Mean-Field
    Dynamics of Interacting Bosons.” <i>Advances in Theoretical and Mathematical Physics</i>,
    vol. 21, no. 3, International Press, 2017, pp. 683–738, doi:<a href="https://doi.org/10.4310/ATMP.2017.v21.n3.a4">10.4310/ATMP.2017.v21.n3.a4</a>.
  short: P. Nam, M.M. Napiórkowski, Advances in Theoretical and Mathematical Physics
    21 (2017) 683–738.
date_created: 2018-12-11T11:46:43Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:00:58Z
day: '01'
department:
- _id: RoSe
doi: 10.4310/ATMP.2017.v21.n3.a4
ec_funded: 1
intvolume: '        21'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1509.04631
month: '01'
oa: 1
oa_version: Submitted Version
page: 683 - 738
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P27533_N27
  name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
  issn:
  - '10950761'
publication_status: published
publisher: International Press
publist_id: '7336'
quality_controlled: '1'
scopus_import: 1
status: public
title: Bogoliubov correction to the mean-field dynamics of interacting bosons
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2017'
...