{"month":"01","day":"01","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","_id":"632","page":"2441 - 2454","ec_funded":1,"language":[{"iso":"eng"}],"date_updated":"2021-01-12T08:07:03Z","publication_status":"published","publist_id":"7160","main_file_link":[{"url":"https://arxiv.org/abs/1509.09045","open_access":"1"}],"publisher":"American Mathematical Society","intvolume":"       145","author":[{"last_name":"Lewin","full_name":"Lewin, Mathieu","first_name":"Mathieu"},{"first_name":"Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87","full_name":"Nam, Phan","last_name":"Nam"},{"first_name":"Nicolas","full_name":"Rougerie, Nicolas","last_name":"Rougerie"}],"date_created":"2018-12-11T11:47:36Z","oa":1,"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 &lt; β &lt; (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 &lt; 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 &lt; β &lt; 3/4. "}],"title":"A note on 2D focusing many boson systems","doi":"10.1090/proc/13468","department":[{"_id":"RoSe"}],"scopus_import":1,"issue":"6","status":"public","oa_version":"Submitted Version","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"publication":"Proceedings of the American Mathematical Society","type":"journal_article","date_published":"2017-01-01T00:00:00Z","citation":{"short":"M. Lewin, P. Nam, N. Rougerie, Proceedings of the American Mathematical Society 145 (2017) 2441–2454.","mla":"Lewin, Mathieu, et al. “A Note on 2D Focusing Many Boson Systems.” <i>Proceedings of the American Mathematical Society</i>, vol. 145, no. 6, American Mathematical Society, 2017, pp. 2441–54, doi:<a href=\"https://doi.org/10.1090/proc/13468\">10.1090/proc/13468</a>.","chicago":"Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “A Note on 2D Focusing Many Boson Systems.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2017. <a href=\"https://doi.org/10.1090/proc/13468\">https://doi.org/10.1090/proc/13468</a>.","ieee":"M. Lewin, P. Nam, and N. Rougerie, “A note on 2D focusing many boson systems,” <i>Proceedings of the American Mathematical Society</i>, 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.","ama":"Lewin M, Nam P, Rougerie N. A note on 2D focusing many boson systems. <i>Proceedings of the American Mathematical Society</i>. 2017;145(6):2441-2454. doi:<a href=\"https://doi.org/10.1090/proc/13468\">10.1090/proc/13468</a>","apa":"Lewin, M., Nam, P., &#38; Rougerie, N. (2017). A note on 2D focusing many boson systems. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/13468\">https://doi.org/10.1090/proc/13468</a>"},"volume":145,"year":"2017"}