--- _id: '632' abstract: - lang: eng text: 'We consider a 2D quantum system of N bosons in a trapping potential |x|s, interacting via a pair potential of the form N2β−1 w(Nβ x). We show that for all 0 < β < (s + 1)/(s + 2), the leading order behavior of ground states of the many-body system is described in the large N limit by the corresponding cubic nonlinear Schrödinger energy functional. Our result covers the focusing case (w < 0) where even the stability of the many-body system is not obvious. This answers an open question mentioned by X. Chen and J. Holmer for harmonic traps (s = 2). Together with the BBGKY hierarchy approach used by these authors, our result implies the convergence of the many-body quantum dynamics to the focusing NLS equation with harmonic trap for all 0 < β < 3/4. ' author: - first_name: Mathieu full_name: Lewin, Mathieu last_name: Lewin - first_name: Phan full_name: Nam, Phan id: 404092F4-F248-11E8-B48F-1D18A9856A87 last_name: Nam - first_name: Nicolas full_name: Rougerie, Nicolas last_name: Rougerie citation: ama: Lewin M, Nam P, Rougerie N. A note on 2D focusing many boson systems. Proceedings of the American Mathematical Society. 2017;145(6):2441-2454. doi:10.1090/proc/13468 apa: Lewin, M., Nam, P., & Rougerie, N. (2017). A note on 2D focusing many boson systems. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/13468 chicago: Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “A Note on 2D Focusing Many Boson Systems.” Proceedings of the American Mathematical Society. American Mathematical Society, 2017. https://doi.org/10.1090/proc/13468. ieee: M. Lewin, P. Nam, and N. Rougerie, “A note on 2D focusing many boson systems,” Proceedings of the American Mathematical Society, vol. 145, no. 6. American Mathematical Society, pp. 2441–2454, 2017. ista: Lewin M, Nam P, Rougerie N. 2017. A note on 2D focusing many boson systems. Proceedings of the American Mathematical Society. 145(6), 2441–2454. mla: Lewin, Mathieu, et al. “A Note on 2D Focusing Many Boson Systems.” Proceedings of the American Mathematical Society, vol. 145, no. 6, American Mathematical Society, 2017, pp. 2441–54, doi:10.1090/proc/13468. short: M. Lewin, P. Nam, N. Rougerie, Proceedings of the American Mathematical Society 145 (2017) 2441–2454. date_created: 2018-12-11T11:47:36Z date_published: 2017-01-01T00:00:00Z date_updated: 2021-01-12T08:07:03Z day: '01' department: - _id: RoSe doi: 10.1090/proc/13468 ec_funded: 1 intvolume: ' 145' issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1509.09045 month: '01' oa: 1 oa_version: Submitted Version page: 2441 - 2454 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Proceedings of the American Mathematical Society publication_status: published publisher: American Mathematical Society publist_id: '7160' quality_controlled: '1' scopus_import: 1 status: public title: A note on 2D focusing many boson systems type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 145 year: '2017' ...