--- _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' ...