---
_id: '473'
abstract:
- lang: eng
text: We prove that nonlinear Gibbs measures can be obtained from the corresponding
many-body, grand-canonical, quantum Gibbs states, in a mean-field limit where
the temperature T diverges and the interaction strength behaves as 1/T. We proceed
by characterizing the interacting Gibbs state as minimizing a functional counting
the free-energy relatively to the non-interacting case. We then perform an infinite-dimensional
analogue of phase-space semiclassical analysis, using fine properties of the quantum
relative entropy, the link between quantum de Finetti measures and upper/lower
symbols in a coherent state basis, as well as Berezin-Lieb type inequalities.
Our results cover the measure built on the defocusing nonlinear Schrödinger functional
on a finite interval, as well as smoother interactions in dimensions d 2.
author:
- first_name: Mathieu
full_name: Lewin, Mathieu
last_name: Lewin
- first_name: Nam
full_name: Phan Thanh, Nam
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Phan Thanh
- first_name: Nicolas
full_name: Rougerie, Nicolas
last_name: Rougerie
citation:
ama: Lewin M, Nam P, Rougerie N. Derivation of nonlinear gibbs measures from many-body
quantum mechanics. Journal de l’Ecole Polytechnique - Mathematiques. 2015;2:65-115.
doi:10.5802/jep.18
apa: Lewin, M., Nam, P., & Rougerie, N. (2015). Derivation of nonlinear gibbs
measures from many-body quantum mechanics. Journal de l’Ecole Polytechnique
- Mathematiques. Ecole Polytechnique. https://doi.org/10.5802/jep.18
chicago: Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “Derivation of Nonlinear
Gibbs Measures from Many-Body Quantum Mechanics.” Journal de l’Ecole Polytechnique
- Mathematiques. Ecole Polytechnique, 2015. https://doi.org/10.5802/jep.18.
ieee: M. Lewin, P. Nam, and N. Rougerie, “Derivation of nonlinear gibbs measures
from many-body quantum mechanics,” Journal de l’Ecole Polytechnique - Mathematiques,
vol. 2. Ecole Polytechnique, pp. 65–115, 2015.
ista: Lewin M, Nam P, Rougerie N. 2015. Derivation of nonlinear gibbs measures from
many-body quantum mechanics. Journal de l’Ecole Polytechnique - Mathematiques.
2, 65–115.
mla: Lewin, Mathieu, et al. “Derivation of Nonlinear Gibbs Measures from Many-Body
Quantum Mechanics.” Journal de l’Ecole Polytechnique - Mathematiques, vol.
2, Ecole Polytechnique, 2015, pp. 65–115, doi:10.5802/jep.18.
short: M. Lewin, P. Nam, N. Rougerie, Journal de l’Ecole Polytechnique - Mathematiques
2 (2015) 65–115.
date_created: 2018-12-11T11:46:40Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2021-01-12T08:00:52Z
day: '01'
ddc:
- '539'
department:
- _id: RoSe
doi: 10.5802/jep.18
ec_funded: 1
file:
- access_level: open_access
checksum: a40eb4016717ddc9927154798a4c164a
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:12:53Z
date_updated: 2020-07-14T12:46:35Z
file_id: '4974'
file_name: IST-2018-951-v1+1_2015_Thanh-Nam_Derivation_of.pdf
file_size: 1084254
relation: main_file
file_date_updated: 2020-07-14T12:46:35Z
has_accepted_license: '1'
intvolume: ' 2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nd/4.0/
month: '01'
oa: 1
oa_version: Published Version
page: 65 - 115
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Journal de l'Ecole Polytechnique - Mathematiques
publication_status: published
publisher: Ecole Polytechnique
publist_id: '7344'
pubrep_id: '951'
quality_controlled: '1'
scopus_import: 1
status: public
title: Derivation of nonlinear gibbs measures from many-body quantum mechanics
tmp:
image: /image/cc_by_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode
name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)
short: CC BY-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2
year: '2015'
...