---
_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 < 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. Advances in Theoretical and Mathematical Physics. 2017;21(3):683-738.
doi:10.4310/ATMP.2017.v21.n3.a4
apa: Nam, P., & Napiórkowski, M. M. (2017). Bogoliubov correction to the mean-field
dynamics of interacting bosons. Advances in Theoretical and Mathematical Physics.
International Press. https://doi.org/10.4310/ATMP.2017.v21.n3.a4
chicago: Nam, Phan, and Marcin M Napiórkowski. “Bogoliubov Correction to the Mean-Field
Dynamics of Interacting Bosons.” Advances in Theoretical and Mathematical Physics.
International Press, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a4.
ieee: P. Nam and M. M. Napiórkowski, “Bogoliubov correction to the mean-field dynamics
of interacting bosons,” Advances in Theoretical and Mathematical Physics,
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.” Advances in Theoretical and Mathematical Physics,
vol. 21, no. 3, International Press, 2017, pp. 683–738, doi:10.4310/ATMP.2017.v21.n3.a4.
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'
...
---
_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. Advances in Theoretical and Mathematical Physics. 2017;21(3):739-800.
doi:10.4310/ATMP.2017.v21.n3.a5
apa: Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2017). Universality for a
class of random band matrices. Advances in Theoretical and Mathematical Physics.
International Press. https://doi.org/10.4310/ATMP.2017.v21.n3.a5
chicago: Bourgade, Paul, László Erdös, Horng Yau, and Jun Yin. “Universality for
a Class of Random Band Matrices.” Advances in Theoretical and Mathematical
Physics. International Press, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a5.
ieee: P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random
band matrices,” Advances in Theoretical and Mathematical Physics, 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.”
Advances in Theoretical and Mathematical Physics, vol. 21, no. 3, International
Press, 2017, pp. 739–800, doi:10.4310/ATMP.2017.v21.n3.a5.
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'
...