[{"doi":"10.1090/proc/13468","date_updated":"2020-01-16T12:38:00Z","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","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.","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.","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","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.","short":"M. Lewin, P. Nam, N. Rougerie, Proceedings of the American Mathematical Society 145 (2017) 2441–2454."},"volume":145,"creator":{"id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","login":"apreinsp"},"date_published":"2017-01-01T00:00:00Z","year":"2017","page":"2441 - 2454","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. "}],"date_created":"2018-12-11T11:47:36Z","oa":1,"month":"01","_id":"632","quality_controlled":"1","day":"01","_version":16,"publist_id":"7160","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publisher":"American Mathematical Society","intvolume":" 145","project":[{"call_identifier":"FP7","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1509.09045"}],"status":"public","publication":"Proceedings of the American Mathematical Society","department":[{"_id":"RoSe","tree":[{"_id":"ResearchGroups"},{"_id":"IST"}]}],"publication_status":"published","type":"journal_article","issue":"6","title":"A note on 2D focusing many boson systems","language":[{"iso":"eng"}],"author":[{"full_name":"Lewin, Mathieu","first_name":"Mathieu","last_name":"Lewin"},{"full_name":"Nam, Phan","last_name":"Nam","first_name":"Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Nicolas","last_name":"Rougerie","full_name":"Rougerie, Nicolas"}],"oa_version":"Submitted Version"}]