[{"publication":"Communications on Pure and Applied Mathematics","day":"01","year":"2018","isi":1,"date_created":"2018-12-11T11:46:31Z","date_published":"2018-03-01T00:00:00Z","doi":"10.1002/cpa.21717","page":"577 - 614","acknowledgement":"We thank the referee for helpful suggestions that improved the presentation of the paper. We also acknowledge partial support by National Science Foundation Grant DMS-1363432 (R.L.F.), Austrian Science Fund (FWF) Project Nr. P 27533-N27 (P.T.N.), CONICYT (Chile) through CONICYT–PCHA/ Doctorado Nacional/2014, and Iniciativa Científica Milenio (Chile) through Millenium Nucleus RC–120002 “Física Matemática” (H.V.D.B.).\r\n","oa":1,"quality_controlled":"1","publisher":"Wiley-Blackwell","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Frank, Rupert, et al. “The Ionization Conjecture in Thomas–Fermi–Dirac–von Weizsäcker Theory.” Communications on Pure and Applied Mathematics, vol. 71, no. 3, Wiley-Blackwell, 2018, pp. 577–614, doi:10.1002/cpa.21717.","ama":"Frank R, Nam P, Van Den Bosch H. The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory. Communications on Pure and Applied Mathematics. 2018;71(3):577-614. doi:10.1002/cpa.21717","apa":"Frank, R., Nam, P., & Van Den Bosch, H. (2018). The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory. Communications on Pure and Applied Mathematics. Wiley-Blackwell. https://doi.org/10.1002/cpa.21717","short":"R. Frank, P. Nam, H. Van Den Bosch, Communications on Pure and Applied Mathematics 71 (2018) 577–614.","ieee":"R. Frank, P. Nam, and H. Van Den Bosch, “The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory,” Communications on Pure and Applied Mathematics, vol. 71, no. 3. Wiley-Blackwell, pp. 577–614, 2018.","chicago":"Frank, Rupert, Phan Nam, and Hanne Van Den Bosch. “The Ionization Conjecture in Thomas–Fermi–Dirac–von Weizsäcker Theory.” Communications on Pure and Applied Mathematics. Wiley-Blackwell, 2018. https://doi.org/10.1002/cpa.21717.","ista":"Frank R, Nam P, Van Den Bosch H. 2018. The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory. Communications on Pure and Applied Mathematics. 71(3), 577–614."},"title":"The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory","article_processing_charge":"No","external_id":{"isi":["000422675800004"],"arxiv":["1606.07355"]},"publist_id":"7377","author":[{"last_name":"Frank","full_name":"Frank, Rupert","first_name":"Rupert"},{"id":"404092F4-F248-11E8-B48F-1D18A9856A87","first_name":"Nam","last_name":"Phan Thanh","full_name":"Phan Thanh, Nam"},{"first_name":"Hanne","full_name":"Van Den Bosch, Hanne","last_name":"Van Den Bosch"}],"language":[{"iso":"eng"}],"publication_status":"published","volume":71,"issue":"3","oa_version":"Preprint","abstract":[{"text":"We prove that in Thomas–Fermi–Dirac–von Weizsäcker theory, a nucleus of charge Z > 0 can bind at most Z + C electrons, where C is a universal constant. This result is obtained through a comparison with Thomas-Fermi theory which, as a by-product, gives bounds on the screened nuclear potential and the radius of the minimizer. A key ingredient of the proof is a novel technique to control the particles in the exterior region, which also applies to the liquid drop model with a nuclear background potential.","lang":"eng"}],"intvolume":" 71","month":"03","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1606.07355"}],"date_updated":"2023-09-19T10:09:40Z","department":[{"_id":"RoSe"}],"_id":"446","status":"public","type":"journal_article","article_type":"original"},{"status":"public","type":"journal_article","_id":"484","department":[{"_id":"RoSe"}],"date_updated":"2021-01-12T08:00:58Z","intvolume":" 21","month":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1509.04631"}],"scopus_import":1,"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"We consider the dynamics of a large quantum system of N identical bosons in 3D interacting via a two-body potential of the form N3β-1w(Nβ(x - y)). For fixed 0 = β < 1/3 and large N, we obtain a norm approximation to the many-body evolution in the Nparticle Hilbert space. The leading order behaviour of the dynamics is determined by Hartree theory while the second order is given by Bogoliubov theory."}],"ec_funded":1,"volume":21,"issue":"3","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["10950761"]},"project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","call_identifier":"FWF","_id":"25C878CE-B435-11E9-9278-68D0E5697425"}],"title":"Bogoliubov correction to the mean-field dynamics of interacting bosons","publist_id":"7336","author":[{"id":"404092F4-F248-11E8-B48F-1D18A9856A87","first_name":"Phan","last_name":"Nam","full_name":"Nam, Phan"},{"id":"4197AD04-F248-11E8-B48F-1D18A9856A87","first_name":"Marcin M","last_name":"Napiórkowski","full_name":"Napiórkowski, Marcin M"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Nam, Phan, and Marcin M. Napiórkowski. “Bogoliubov Correction to the Mean-Field Dynamics of Interacting Bosons.” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3, International Press, 2017, pp. 683–738, doi:10.4310/ATMP.2017.v21.n3.a4.","short":"P. Nam, M.M. Napiórkowski, Advances in Theoretical and Mathematical Physics 21 (2017) 683–738.","ieee":"P. Nam and M. M. Napiórkowski, “Bogoliubov correction to the mean-field dynamics of interacting bosons,” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3. International Press, pp. 683–738, 2017.","apa":"Nam, P., & Napiórkowski, M. M. (2017). Bogoliubov correction to the mean-field dynamics of interacting bosons. Advances in Theoretical and Mathematical Physics. International Press. https://doi.org/10.4310/ATMP.2017.v21.n3.a4","ama":"Nam P, Napiórkowski MM. Bogoliubov correction to the mean-field dynamics of interacting bosons. Advances in Theoretical and Mathematical Physics. 2017;21(3):683-738. doi:10.4310/ATMP.2017.v21.n3.a4","chicago":"Nam, Phan, and Marcin M Napiórkowski. “Bogoliubov Correction to the Mean-Field Dynamics of Interacting Bosons.” Advances in Theoretical and Mathematical Physics. International Press, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a4.","ista":"Nam P, Napiórkowski MM. 2017. Bogoliubov correction to the mean-field dynamics of interacting bosons. Advances in Theoretical and Mathematical Physics. 21(3), 683–738."},"oa":1,"quality_controlled":"1","publisher":"International Press","date_created":"2018-12-11T11:46:43Z","date_published":"2017-01-01T00:00:00Z","doi":"10.4310/ATMP.2017.v21.n3.a4","page":"683 - 738","publication":"Advances in Theoretical and Mathematical Physics","day":"01","year":"2017"},{"issue":"6","volume":145,"ec_funded":1,"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":1,"main_file_link":[{"url":"https://arxiv.org/abs/1509.09045","open_access":"1"}],"month":"01","intvolume":" 145","abstract":[{"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. ","lang":"eng"}],"oa_version":"Submitted Version","department":[{"_id":"RoSe"}],"date_updated":"2021-01-12T08:07:03Z","type":"journal_article","status":"public","_id":"632","page":"2441 - 2454","doi":"10.1090/proc/13468","date_published":"2017-01-01T00:00:00Z","date_created":"2018-12-11T11:47:36Z","year":"2017","day":"01","publication":"Proceedings of the American Mathematical Society","quality_controlled":"1","publisher":"American Mathematical Society","oa":1,"publist_id":"7160","author":[{"last_name":"Lewin","full_name":"Lewin, Mathieu","first_name":"Mathieu"},{"last_name":"Nam","full_name":"Nam, Phan","first_name":"Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Nicolas","last_name":"Rougerie","full_name":"Rougerie, Nicolas"}],"title":"A note on 2D focusing many boson systems","citation":{"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.","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.","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. American Mathematical Society, pp. 2441–2454, 2017.","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","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."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}]},{"date_updated":"2023-09-20T11:53:35Z","department":[{"_id":"RoSe"}],"_id":"1079","status":"public","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["13850172"]},"issue":"2","volume":20,"oa_version":"Submitted Version","abstract":[{"text":"We study the ionization problem in the Thomas-Fermi-Dirac-von Weizsäcker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the number of electrons is large and the total nuclear charge is small. This nonexistence result also applies to external potentials decaying faster than the Coulomb potential. In the case of arbitrary nuclear charges, we obtain the nonexistence of stable minimizers and radial minimizers.","lang":"eng"}],"intvolume":" 20","month":"06","main_file_link":[{"url":"https://arxiv.org/abs/1603.07368","open_access":"1"}],"scopus_import":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"apa":"Nam, P., & Van Den Bosch, H. (2017). Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges. Mathematical Physics, Analysis and Geometry. Springer. https://doi.org/10.1007/s11040-017-9238-0","ama":"Nam P, Van Den Bosch H. Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges. Mathematical Physics, Analysis and Geometry. 2017;20(2). doi:10.1007/s11040-017-9238-0","short":"P. Nam, H. Van Den Bosch, Mathematical Physics, Analysis and Geometry 20 (2017).","ieee":"P. Nam and H. Van Den Bosch, “Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges,” Mathematical Physics, Analysis and Geometry, vol. 20, no. 2. Springer, 2017.","mla":"Nam, Phan, and Hanne Van Den Bosch. “Nonexistence in Thomas Fermi-Dirac-von Weizsäcker Theory with Small Nuclear Charges.” Mathematical Physics, Analysis and Geometry, vol. 20, no. 2, 6, Springer, 2017, doi:10.1007/s11040-017-9238-0.","ista":"Nam P, Van Den Bosch H. 2017. Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges. Mathematical Physics, Analysis and Geometry. 20(2), 6.","chicago":"Nam, Phan, and Hanne Van Den Bosch. “Nonexistence in Thomas Fermi-Dirac-von Weizsäcker Theory with Small Nuclear Charges.” Mathematical Physics, Analysis and Geometry. Springer, 2017. https://doi.org/10.1007/s11040-017-9238-0."},"title":"Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges","external_id":{"isi":["000401270000004"]},"article_processing_charge":"No","publist_id":"6300","author":[{"last_name":"Nam","full_name":"Nam, Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87","first_name":"Phan"},{"first_name":"Hanne","full_name":"Van Den Bosch, Hanne","last_name":"Van Den Bosch"}],"article_number":"6","project":[{"_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"P27533_N27","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems"}],"publication":"Mathematical Physics, Analysis and Geometry","day":"01","year":"2017","isi":1,"date_created":"2018-12-11T11:50:02Z","date_published":"2017-06-01T00:00:00Z","doi":"10.1007/s11040-017-9238-0","oa":1,"publisher":"Springer","quality_controlled":"1"},{"year":"2017","isi":1,"publication":"Journal de Mathématiques Pures et Appliquées","day":"01","page":"662 - 688","date_created":"2018-12-11T11:48:15Z","doi":"10.1016/j.matpur.2017.05.013","date_published":"2017-11-01T00:00:00Z","oa":1,"quality_controlled":"1","publisher":"Elsevier","citation":{"chicago":"Nam, Phan, and Marcin M Napiórkowski. “A Note on the Validity of Bogoliubov Correction to Mean Field Dynamics.” Journal de Mathématiques Pures et Appliquées. Elsevier, 2017. https://doi.org/10.1016/j.matpur.2017.05.013.","ista":"Nam P, Napiórkowski MM. 2017. A note on the validity of Bogoliubov correction to mean field dynamics. Journal de Mathématiques Pures et Appliquées. 108(5), 662–688.","mla":"Nam, Phan, and Marcin M. Napiórkowski. “A Note on the Validity of Bogoliubov Correction to Mean Field Dynamics.” Journal de Mathématiques Pures et Appliquées, vol. 108, no. 5, Elsevier, 2017, pp. 662–88, doi:10.1016/j.matpur.2017.05.013.","short":"P. Nam, M.M. Napiórkowski, Journal de Mathématiques Pures et Appliquées 108 (2017) 662–688.","ieee":"P. Nam and M. M. Napiórkowski, “A note on the validity of Bogoliubov correction to mean field dynamics,” Journal de Mathématiques Pures et Appliquées, vol. 108, no. 5. Elsevier, pp. 662–688, 2017.","ama":"Nam P, Napiórkowski MM. A note on the validity of Bogoliubov correction to mean field dynamics. Journal de Mathématiques Pures et Appliquées. 2017;108(5):662-688. doi:10.1016/j.matpur.2017.05.013","apa":"Nam, P., & Napiórkowski, M. M. (2017). A note on the validity of Bogoliubov correction to mean field dynamics. Journal de Mathématiques Pures et Appliquées. Elsevier. https://doi.org/10.1016/j.matpur.2017.05.013"},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","external_id":{"isi":["000414113600003"]},"article_processing_charge":"No","publist_id":"6928","author":[{"last_name":"Nam","full_name":"Nam, Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87","first_name":"Phan"},{"full_name":"Napiórkowski, Marcin M","last_name":"Napiórkowski","first_name":"Marcin M","id":"4197AD04-F248-11E8-B48F-1D18A9856A87"}],"title":"A note on the validity of Bogoliubov correction to mean field dynamics","project":[{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"publication_status":"published","publication_identifier":{"issn":["00217824"]},"language":[{"iso":"eng"}],"volume":108,"issue":"5","abstract":[{"text":"We study the norm approximation to the Schrödinger dynamics of N bosons in with an interaction potential of the form . Assuming that in the initial state the particles outside of the condensate form a quasi-free state with finite kinetic energy, we show that in the large N limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation for all . The range of β is expected to be optimal for this large class of initial states.","lang":"eng"}],"oa_version":"Submitted Version","main_file_link":[{"url":"https://arxiv.org/abs/1604.05240","open_access":"1"}],"scopus_import":"1","intvolume":" 108","month":"11","date_updated":"2023-09-27T12:52:07Z","department":[{"_id":"RoSe"}],"_id":"739","type":"journal_article","status":"public"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1503.07061"}],"scopus_import":1,"intvolume":" 9","month":"03","abstract":[{"text":"We study the ground state of a dilute Bose gas in a scaling limit where the Gross-Pitaevskii functional emerges. This is a repulsive nonlinear Schrödinger functional whose quartic term is proportional to the scattering length of the interparticle interaction potential. We propose a new derivation of this limit problem, with a method that bypasses some of the technical difficulties that previous derivations had to face. The new method is based on a combination of Dyson\\'s lemma, the quantum de Finetti theorem and a second moment estimate for ground states of the effective Dyson Hamiltonian. It applies equally well to the case where magnetic fields or rotation are present.","lang":"eng"}],"oa_version":"Preprint","ec_funded":1,"volume":9,"issue":"2","publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","status":"public","_id":"1143","department":[{"_id":"RoSe"}],"date_updated":"2021-01-12T06:48:36Z","oa":1,"quality_controlled":"1","publisher":"Mathematical Sciences Publishers","page":"459 - 485","date_created":"2018-12-11T11:50:23Z","doi":"10.2140/apde.2016.9.459","date_published":"2016-03-24T00:00:00Z","year":"2016","publication":"Analysis and PDE","day":"24","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"publist_id":"6215","author":[{"first_name":"Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87","last_name":"Nam","full_name":"Nam, Phan"},{"first_name":"Nicolas","last_name":"Rougerie","full_name":"Rougerie, Nicolas"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"title":"Ground states of large bosonic systems: The gross Pitaevskii limit revisited","citation":{"ieee":"P. Nam, N. Rougerie, and R. Seiringer, “Ground states of large bosonic systems: The gross Pitaevskii limit revisited,” Analysis and PDE, vol. 9, no. 2. Mathematical Sciences Publishers, pp. 459–485, 2016.","short":"P. Nam, N. Rougerie, R. Seiringer, Analysis and PDE 9 (2016) 459–485.","apa":"Nam, P., Rougerie, N., & Seiringer, R. (2016). Ground states of large bosonic systems: The gross Pitaevskii limit revisited. Analysis and PDE. Mathematical Sciences Publishers. https://doi.org/10.2140/apde.2016.9.459","ama":"Nam P, Rougerie N, Seiringer R. Ground states of large bosonic systems: The gross Pitaevskii limit revisited. Analysis and PDE. 2016;9(2):459-485. doi:10.2140/apde.2016.9.459","mla":"Nam, Phan, et al. “Ground States of Large Bosonic Systems: The Gross Pitaevskii Limit Revisited.” Analysis and PDE, vol. 9, no. 2, Mathematical Sciences Publishers, 2016, pp. 459–85, doi:10.2140/apde.2016.9.459.","ista":"Nam P, Rougerie N, Seiringer R. 2016. Ground states of large bosonic systems: The gross Pitaevskii limit revisited. Analysis and PDE. 9(2), 459–485.","chicago":"Nam, Phan, Nicolas Rougerie, and Robert Seiringer. “Ground States of Large Bosonic Systems: The Gross Pitaevskii Limit Revisited.” Analysis and PDE. Mathematical Sciences Publishers, 2016. https://doi.org/10.2140/apde.2016.9.459."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"publist_id":"6054","author":[{"last_name":"Frank","full_name":"Frank, Rupert","first_name":"Rupert"},{"first_name":"Rowan","last_name":"Killip","full_name":"Killip, Rowan"},{"id":"404092F4-F248-11E8-B48F-1D18A9856A87","first_name":"Phan","last_name":"Nam","full_name":"Nam, Phan"}],"title":"Nonexistence of large nuclei in the liquid drop model","citation":{"ieee":"R. Frank, R. Killip, and P. Nam, “Nonexistence of large nuclei in the liquid drop model,” Letters in Mathematical Physics, vol. 106, no. 8. Springer, pp. 1033–1036, 2016.","short":"R. Frank, R. Killip, P. Nam, Letters in Mathematical Physics 106 (2016) 1033–1036.","apa":"Frank, R., Killip, R., & Nam, P. (2016). Nonexistence of large nuclei in the liquid drop model. Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-016-0860-8","ama":"Frank R, Killip R, Nam P. Nonexistence of large nuclei in the liquid drop model. Letters in Mathematical Physics. 2016;106(8):1033-1036. doi:10.1007/s11005-016-0860-8","mla":"Frank, Rupert, et al. “Nonexistence of Large Nuclei in the Liquid Drop Model.” Letters in Mathematical Physics, vol. 106, no. 8, Springer, 2016, pp. 1033–36, doi:10.1007/s11005-016-0860-8.","ista":"Frank R, Killip R, Nam P. 2016. Nonexistence of large nuclei in the liquid drop model. Letters in Mathematical Physics. 106(8), 1033–1036.","chicago":"Frank, Rupert, Rowan Killip, and Phan Nam. “Nonexistence of Large Nuclei in the Liquid Drop Model.” Letters in Mathematical Physics. Springer, 2016. https://doi.org/10.1007/s11005-016-0860-8."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"page":"1033 - 1036","doi":"10.1007/s11005-016-0860-8","date_published":"2016-08-01T00:00:00Z","date_created":"2018-12-11T11:51:02Z","has_accepted_license":"1","year":"2016","day":"01","publication":"Letters in Mathematical Physics","publisher":"Springer","quality_controlled":"1","oa":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology Austria.\r\n","file_date_updated":"2020-07-14T12:44:42Z","department":[{"_id":"RoSe"}],"date_updated":"2021-01-12T06:49:30Z","ddc":["510","539"],"type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","pubrep_id":"698","_id":"1267","issue":"8","volume":106,"publication_status":"published","file":[{"creator":"system","file_size":349464,"date_updated":"2020-07-14T12:44:42Z","file_name":"IST-2016-698-v1+1_s11005-016-0860-8.pdf","date_created":"2018-12-12T10:11:09Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"4863","checksum":"d740a6a226e0f5f864f40e3e269d3cc0"}],"language":[{"iso":"eng"}],"scopus_import":1,"month":"08","intvolume":" 106","abstract":[{"lang":"eng","text":"We give a simplified proof of the nonexistence of large nuclei in the liquid drop model and provide an explicit bound. Our bound is within a factor of 2.3 of the conjectured value and seems to be the first quantitative result."}],"oa_version":"Published Version"},{"_id":"1491","status":"public","type":"journal_article","date_updated":"2021-01-12T06:51:07Z","department":[{"_id":"RoSe"}],"oa_version":"Submitted Version","abstract":[{"lang":"eng","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."}],"intvolume":" 368","month":"01","main_file_link":[{"url":"http://arxiv.org/abs/1405.3220","open_access":"1"}],"scopus_import":1,"language":[{"iso":"eng"}],"publication_status":"published","volume":368,"issue":"9","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"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.","chicago":"Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “The Mean-Field Approximation and the Non-Linear Schrödinger Functional for Trapped Bose Gases.” Transactions of the American Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/tran/6537.","ieee":"M. Lewin, P. Nam, and N. Rougerie, “The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases,” Transactions of the American Mathematical Society, vol. 368, no. 9. American Mathematical Society, pp. 6131–6157, 2016.","short":"M. Lewin, P. Nam, N. Rougerie, Transactions of the American Mathematical Society 368 (2016) 6131–6157.","apa":"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. American Mathematical Society. https://doi.org/10.1090/tran/6537","ama":"Lewin M, Nam P, Rougerie N. The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases. Transactions of the American Mathematical Society. 2016;368(9):6131-6157. doi:10.1090/tran/6537","mla":"Lewin, Mathieu, et al. “The Mean-Field Approximation and the Non-Linear Schrödinger Functional for Trapped Bose Gases.” Transactions of the American Mathematical Society, vol. 368, no. 9, American Mathematical Society, 2016, pp. 6131–57, doi:10.1090/tran/6537."},"title":"The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases","publist_id":"5692","author":[{"first_name":"Mathieu","last_name":"Lewin","full_name":"Lewin, 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"}],"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.","oa":1,"publisher":"American Mathematical Society","quality_controlled":"1","publication":"Transactions of the American Mathematical Society","day":"01","year":"2016","date_created":"2018-12-11T11:52:20Z","doi":"10.1090/tran/6537","date_published":"2016-01-01T00:00:00Z","page":"6131 - 6157"},{"project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"grant_number":"P27533_N27","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Nam, Phan, et al. “Diagonalization of Bosonic Quadratic Hamiltonians by Bogoliubov Transformations.” Journal of Functional Analysis, vol. 270, no. 11, Academic Press, 2016, pp. 4340–68, doi:10.1016/j.jfa.2015.12.007.","ama":"Nam P, Napiórkowski MM, Solovej J. Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations. Journal of Functional Analysis. 2016;270(11):4340-4368. doi:10.1016/j.jfa.2015.12.007","apa":"Nam, P., Napiórkowski, M. M., & Solovej, J. (2016). Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations. Journal of Functional Analysis. Academic Press. https://doi.org/10.1016/j.jfa.2015.12.007","ieee":"P. Nam, M. M. Napiórkowski, and J. Solovej, “Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations,” Journal of Functional Analysis, vol. 270, no. 11. Academic Press, pp. 4340–4368, 2016.","short":"P. Nam, M.M. Napiórkowski, J. Solovej, Journal of Functional Analysis 270 (2016) 4340–4368.","chicago":"Nam, Phan, Marcin M Napiórkowski, and Jan Solovej. “Diagonalization of Bosonic Quadratic Hamiltonians by Bogoliubov Transformations.” Journal of Functional Analysis. Academic Press, 2016. https://doi.org/10.1016/j.jfa.2015.12.007.","ista":"Nam P, Napiórkowski MM, Solovej J. 2016. Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations. Journal of Functional Analysis. 270(11), 4340–4368."},"title":"Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations","author":[{"id":"404092F4-F248-11E8-B48F-1D18A9856A87","first_name":"Phan","last_name":"Nam","full_name":"Nam, Phan"},{"last_name":"Napiórkowski","full_name":"Napiórkowski, Marcin M","id":"4197AD04-F248-11E8-B48F-1D18A9856A87","first_name":"Marcin M"},{"last_name":"Solovej","full_name":"Solovej, Jan","first_name":"Jan"}],"publist_id":"5626","acknowledgement":"We thank Jan Dereziński for several inspiring discussions and useful remarks. We thank the referee for helpful comments. J.P.S. thanks the Erwin Schrödinger Institute for the hospitality during the thematic programme “Quantum many-body systems, random matrices, and disorder”. We gratefully acknowledge the financial supports by the European Union's Seventh Framework Programme under the ERC Advanced Grant ERC-2012-AdG 321029 (J.P.S.) and the REA grant agreement No. 291734 (P.T.N.), as well as the support of the National Science Center (NCN) grant No. 2012/07/N/ST1/03185 and the Austrian Science Fund (FWF) project No. P 27533-N27 (M.N.).","publisher":"Academic Press","quality_controlled":"1","oa":1,"day":"01","publication":"Journal of Functional Analysis","year":"2016","doi":"10.1016/j.jfa.2015.12.007","date_published":"2016-06-01T00:00:00Z","date_created":"2018-12-11T11:52:38Z","page":"4340 - 4368","_id":"1545","status":"public","type":"journal_article","date_updated":"2021-01-12T06:51:30Z","department":[{"_id":"RoSe"}],"oa_version":"Submitted Version","abstract":[{"text":"We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our sufficient conditions are optimal in the sense that they become necessary when the relevant one-body operators commute.","lang":"eng"}],"month":"06","intvolume":" 270","scopus_import":1,"main_file_link":[{"url":"http://arxiv.org/abs/1508.07321","open_access":"1"}],"language":[{"iso":"eng"}],"publication_status":"published","issue":"11","volume":270,"ec_funded":1},{"_id":"1622","status":"public","type":"journal_article","date_updated":"2021-01-12T06:52:04Z","department":[{"_id":"RoSe"}],"oa_version":"Submitted Version","abstract":[{"text":"We prove analogues of the Lieb–Thirring and Hardy–Lieb–Thirring inequalities for many-body quantum systems with fractional kinetic operators and homogeneous interaction potentials, where no anti-symmetry on the wave functions is assumed. These many-body inequalities imply interesting one-body interpolation inequalities, and we show that the corresponding one- and many-body inequalities are actually equivalent in certain cases.","lang":"eng"}],"month":"03","intvolume":" 219","scopus_import":1,"main_file_link":[{"url":"http://arxiv.org/abs/1501.04570","open_access":"1"}],"language":[{"iso":"eng"}],"publication_status":"published","volume":219,"issue":"3","ec_funded":1,"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Lundholm, Douglas, et al. “Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems.” Archive for Rational Mechanics and Analysis, vol. 219, no. 3, Springer, 2016, pp. 1343–82, doi:10.1007/s00205-015-0923-5.","short":"D. Lundholm, P. Nam, F. Portmann, Archive for Rational Mechanics and Analysis 219 (2016) 1343–1382.","ieee":"D. Lundholm, P. Nam, and F. Portmann, “Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems,” Archive for Rational Mechanics and Analysis, vol. 219, no. 3. Springer, pp. 1343–1382, 2016.","ama":"Lundholm D, Nam P, Portmann F. Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems. Archive for Rational Mechanics and Analysis. 2016;219(3):1343-1382. doi:10.1007/s00205-015-0923-5","apa":"Lundholm, D., Nam, P., & Portmann, F. (2016). Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems. Archive for Rational Mechanics and Analysis. Springer. https://doi.org/10.1007/s00205-015-0923-5","chicago":"Lundholm, Douglas, Phan Nam, and Fabian Portmann. “Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems.” Archive for Rational Mechanics and Analysis. Springer, 2016. https://doi.org/10.1007/s00205-015-0923-5.","ista":"Lundholm D, Nam P, Portmann F. 2016. Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems. Archive for Rational Mechanics and Analysis. 219(3), 1343–1382."},"title":"Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems","publist_id":"5542","author":[{"first_name":"Douglas","last_name":"Lundholm","full_name":"Lundholm, Douglas"},{"first_name":"Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87","last_name":"Nam","full_name":"Nam, Phan"},{"last_name":"Portmann","full_name":"Portmann, Fabian","first_name":"Fabian"}],"acknowledgement":"We thank Jan Philip Solovej, Robert Seiringer and Vladimir Maz’ya for helpful discussions, as well as Rupert Frank\r\nand the anonymous referee for useful comments. Part of this work has been carried out during a visit at the Institut Mittag-Leffler (Stockholm). D.L. acknowledges financial support by the grant KAW 2010.0063 from the Knut and Alice Wallenberg Foundation and the Swedish Research Council grant no. 2013-4734. P.T.N. is supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 291734. F.P. acknowledges support from the ERC project no. 321029 “The\r\nmathematics of the structure of matter”.","quality_controlled":"1","publisher":"Springer","oa":1,"day":"01","publication":"Archive for Rational Mechanics and Analysis","year":"2016","doi":"10.1007/s00205-015-0923-5","date_published":"2016-03-01T00:00:00Z","date_created":"2018-12-11T11:53:05Z","page":"1343 - 1382"},{"year":"2015","publication_status":"published","day":"01","language":[{"iso":"eng"}],"publication":"Archive for Rational Mechanics and Analysis","page":"381 - 417","date_published":"2015-02-01T00:00:00Z","doi":"10.1007/s00205-014-0781-6","volume":215,"issue":"2","date_created":"2018-12-11T11:55:37Z","abstract":[{"lang":"eng","text":"We study the spectrum of a large system of N identical bosons interacting via a two-body potential with strength 1/N. In this mean-field regime, Bogoliubov's theory predicts that the spectrum of the N-particle Hamiltonian can be approximated by that of an effective quadratic Hamiltonian acting on Fock space, which describes the fluctuations around a condensed state. Recently, Bogoliubov's theory has been justified rigorously in the case that the low-energy eigenvectors of the N-particle Hamiltonian display complete condensation in the unique minimizer of the corresponding Hartree functional. In this paper, we shall justify Bogoliubov's theory for the high-energy part of the spectrum of the N-particle Hamiltonian corresponding to (non-linear) excited states of the Hartree functional. Moreover, we shall extend the existing results on the excitation spectrum to the case of non-uniqueness and/or degeneracy of the Hartree minimizer. In particular, the latter covers the case of rotating Bose gases, when the rotation speed is large enough to break the symmetry and to produce multiple quantized vortices in the Hartree minimizer. "}],"oa_version":"Preprint","quality_controlled":"1","scopus_import":1,"publisher":"Springer","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1402.1153"}],"oa":1,"month":"02","intvolume":" 215","citation":{"ista":"Nam P, Seiringer R. 2015. Collective excitations of Bose gases in the mean-field regime. Archive for Rational Mechanics and Analysis. 215(2), 381–417.","chicago":"Nam, Phan, and Robert Seiringer. “Collective Excitations of Bose Gases in the Mean-Field Regime.” Archive for Rational Mechanics and Analysis. Springer, 2015. https://doi.org/10.1007/s00205-014-0781-6.","apa":"Nam, P., & Seiringer, R. (2015). Collective excitations of Bose gases in the mean-field regime. Archive for Rational Mechanics and Analysis. Springer. https://doi.org/10.1007/s00205-014-0781-6","ama":"Nam P, Seiringer R. Collective excitations of Bose gases in the mean-field regime. Archive for Rational Mechanics and Analysis. 2015;215(2):381-417. doi:10.1007/s00205-014-0781-6","short":"P. Nam, R. Seiringer, Archive for Rational Mechanics and Analysis 215 (2015) 381–417.","ieee":"P. Nam and R. Seiringer, “Collective excitations of Bose gases in the mean-field regime,” Archive for Rational Mechanics and Analysis, vol. 215, no. 2. Springer, pp. 381–417, 2015.","mla":"Nam, Phan, and Robert Seiringer. “Collective Excitations of Bose Gases in the Mean-Field Regime.” Archive for Rational Mechanics and Analysis, vol. 215, no. 2, Springer, 2015, pp. 381–417, doi:10.1007/s00205-014-0781-6."},"date_updated":"2021-01-12T06:55:13Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87","full_name":"Nam, Phan","last_name":"Nam"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521"}],"publist_id":"4951","title":"Collective excitations of Bose gases in the mean-field regime","department":[{"_id":"RoSe"}],"_id":"2085","type":"journal_article","status":"public"},{"oa":1,"publisher":"Ecole Polytechnique","quality_controlled":"1","publication":"Journal de l'Ecole Polytechnique - Mathematiques","day":"01","year":"2015","has_accepted_license":"1","date_created":"2018-12-11T11:46:40Z","date_published":"2015-01-01T00:00:00Z","doi":"10.5802/jep.18","page":"65 - 115","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Lewin, Mathieu, et al. “Derivation of Nonlinear Gibbs Measures from Many-Body Quantum Mechanics.” Journal de l’Ecole Polytechnique - Mathematiques, vol. 2, Ecole Polytechnique, 2015, pp. 65–115, doi:10.5802/jep.18.","short":"M. Lewin, P. Nam, N. Rougerie, Journal de l’Ecole Polytechnique - Mathematiques 2 (2015) 65–115.","ieee":"M. Lewin, P. Nam, and N. Rougerie, “Derivation of nonlinear gibbs measures from many-body quantum mechanics,” Journal de l’Ecole Polytechnique - Mathematiques, vol. 2. Ecole Polytechnique, pp. 65–115, 2015.","apa":"Lewin, M., Nam, P., & Rougerie, N. (2015). Derivation of nonlinear gibbs measures from many-body quantum mechanics. Journal de l’Ecole Polytechnique - Mathematiques. Ecole Polytechnique. https://doi.org/10.5802/jep.18","ama":"Lewin M, Nam P, Rougerie N. Derivation of nonlinear gibbs measures from many-body quantum mechanics. Journal de l’Ecole Polytechnique - Mathematiques. 2015;2:65-115. doi:10.5802/jep.18","chicago":"Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “Derivation of Nonlinear Gibbs Measures from Many-Body Quantum Mechanics.” Journal de l’Ecole Polytechnique - Mathematiques. Ecole Polytechnique, 2015. https://doi.org/10.5802/jep.18.","ista":"Lewin M, Nam P, Rougerie N. 2015. Derivation of nonlinear gibbs measures from many-body quantum mechanics. Journal de l’Ecole Polytechnique - Mathematiques. 2, 65–115."},"title":"Derivation of nonlinear gibbs measures from many-body quantum mechanics","publist_id":"7344","author":[{"full_name":"Lewin, Mathieu","last_name":"Lewin","first_name":"Mathieu"},{"last_name":"Phan Thanh","full_name":"Phan Thanh, Nam","first_name":"Nam","id":"404092F4-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Rougerie","full_name":"Rougerie, Nicolas","first_name":"Nicolas"}],"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We prove that nonlinear Gibbs measures can be obtained from the corresponding many-body, grand-canonical, quantum Gibbs states, in a mean-field limit where the temperature T diverges and the interaction strength behaves as 1/T. We proceed by characterizing the interacting Gibbs state as minimizing a functional counting the free-energy relatively to the non-interacting case. We then perform an infinite-dimensional analogue of phase-space semiclassical analysis, using fine properties of the quantum relative entropy, the link between quantum de Finetti measures and upper/lower symbols in a coherent state basis, as well as Berezin-Lieb type inequalities. Our results cover the measure built on the defocusing nonlinear Schrödinger functional on a finite interval, as well as smoother interactions in dimensions d 2."}],"intvolume":" 2","month":"01","scopus_import":1,"language":[{"iso":"eng"}],"file":[{"file_id":"4974","checksum":"a40eb4016717ddc9927154798a4c164a","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2018-12-12T10:12:53Z","file_name":"IST-2018-951-v1+1_2015_Thanh-Nam_Derivation_of.pdf","date_updated":"2020-07-14T12:46:35Z","file_size":1084254,"creator":"system"}],"publication_status":"published","ec_funded":1,"license":"https://creativecommons.org/licenses/by-nd/4.0/","volume":2,"_id":"473","pubrep_id":"951","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","short":"CC BY-ND (4.0)"},"type":"journal_article","ddc":["539"],"date_updated":"2021-01-12T08:00:52Z","department":[{"_id":"RoSe"}],"file_date_updated":"2020-07-14T12:46:35Z"}]