{"date_created":"2018-12-11T11:47:36Z","publication_status":"published","month":"01","page":"2441 - 2454","date_published":"2017-01-01T00:00:00Z","oa":1,"publisher":"American Mathematical Society","publication":"Proceedings of the American Mathematical Society","author":[{"full_name":"Lewin, Mathieu","first_name":"Mathieu","last_name":"Lewin"},{"id":"404092F4-F248-11E8-B48F-1D18A9856A87","last_name":"Nam","first_name":"Phan","full_name":"Nam, Phan"},{"last_name":"Rougerie","first_name":"Nicolas","full_name":"Rougerie, Nicolas"}],"issue":"6","type":"journal_article","title":"A note on 2D focusing many boson systems","year":"2017","department":[{"_id":"RoSe"}],"oa_version":"Submitted Version","intvolume":" 145","day":"01","scopus_import":1,"language":[{"iso":"eng"}],"status":"public","publist_id":"7160","main_file_link":[{"url":"https://arxiv.org/abs/1509.09045","open_access":"1"}],"doi":"10.1090/proc/13468","ec_funded":1,"_id":"632","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"date_updated":"2020-08-11T10:10:34Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","volume":145,"citation":{"chicago":"Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “A Note on 2D Focusing Many Boson Systems.” *Proceedings of the American Mathematical Society* 145, no. 6 (2017): 2441–54. https://doi.org/10.1090/proc/13468.","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*, *145*(6), 2441–2454. https://doi.org/10.1090/proc/13468","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.","short":"M. Lewin, P. Nam, N. Rougerie, Proceedings of the American Mathematical Society 145 (2017) 2441–2454.","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, pp. 2441–2454, 2017.","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."},"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. "}]}