{"issue":"9","date_published":"2016-01-01T00:00:00Z","publication_status":"published","abstract":[{"text":"We study the ground state of a trapped Bose gas, starting from the full many-body Schrödinger Hamiltonian, and derive the non-linear Schrödinger energy functional in the limit of a large particle number, when the interaction potential converges slowly to a Dirac delta function. Our method is based on quantitative estimates on the discrepancy between the full many-body energy and its mean-field approximation using Hartree states. These are proved using finite dimensional localization and a quantitative version of the quantum de Finetti theorem. Our approach covers the case of attractive interactions in the regime of stability. In particular, our main new result is a derivation of the 2D attractive non-linear Schrödinger ground state.","lang":"eng"}],"main_file_link":[{"url":"http://arxiv.org/abs/1405.3220","open_access":"1"}],"department":[{"_id":"RoSe"}],"day":"01","type":"journal_article","date_updated":"2021-01-12T06:51:07Z","month":"01","status":"public","title":"The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases","quality_controlled":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-11T11:52:20Z","oa_version":"Submitted Version","oa":1,"scopus_import":1,"publisher":"American Mathematical Society","citation":{"short":"M. Lewin, P. Nam, N. Rougerie, Transactions of the American Mathematical Society 368 (2016) 6131–6157.","ama":"Lewin M, Nam P, Rougerie N. The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases. <i>Transactions of the American Mathematical Society</i>. 2016;368(9):6131-6157. doi:<a href=\"https://doi.org/10.1090/tran/6537\">10.1090/tran/6537</a>","chicago":"Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “The Mean-Field Approximation and the Non-Linear Schrödinger Functional for Trapped Bose Gases.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2016. <a href=\"https://doi.org/10.1090/tran/6537\">https://doi.org/10.1090/tran/6537</a>.","apa":"Lewin, M., Nam, P., &#38; Rougerie, N. (2016). The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/6537\">https://doi.org/10.1090/tran/6537</a>","ista":"Lewin M, Nam P, Rougerie N. 2016. The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases. Transactions of the American Mathematical Society. 368(9), 6131–6157.","ieee":"M. Lewin, P. Nam, and N. Rougerie, “The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases,” <i>Transactions of the American Mathematical Society</i>, vol. 368, no. 9. American Mathematical Society, pp. 6131–6157, 2016.","mla":"Lewin, Mathieu, et al. “The Mean-Field Approximation and the Non-Linear Schrödinger Functional for Trapped Bose Gases.” <i>Transactions of the American Mathematical Society</i>, vol. 368, no. 9, American Mathematical Society, 2016, pp. 6131–57, doi:<a href=\"https://doi.org/10.1090/tran/6537\">10.1090/tran/6537</a>."},"_id":"1491","language":[{"iso":"eng"}],"author":[{"first_name":"Mathieu","last_name":"Lewin","full_name":"Lewin, Mathieu"},{"id":"404092F4-F248-11E8-B48F-1D18A9856A87","full_name":"Nam, Phan","last_name":"Nam","first_name":"Phan"},{"last_name":"Rougerie","first_name":"Nicolas","full_name":"Rougerie, Nicolas"}],"publication":"Transactions of the American Mathematical Society","page":"6131 - 6157","doi":"10.1090/tran/6537","acknowledgement":"The authors acknowledge financial support from the European Research Council (FP7/2007-2013 Grant Agreement MNIQS 258023) and the ANR (Mathostaq project, ANR-13-JS01-0005-01). The second and third authors have benefited from the hospitality of the Institute for Mathematical Science of the National University of Singapore.","publist_id":"5692","volume":368,"intvolume":"       368","year":"2016"}