--- _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' ...