[{"ec_funded":1,"publication_identifier":{"issn":["1095-0761"]},"publication":"Advances in Theoretical and Mathematical Physics","status":"public","date_created":"2018-12-11T11:46:43Z","main_file_link":[{"url":"https://arxiv.org/abs/1509.04631","open_access":"1"}],"article_processing_charge":"No","author":[{"first_name":"Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87","last_name":"Nam","full_name":"Nam, Phan"},{"first_name":"Marcin M","id":"4197AD04-F248-11E8-B48F-1D18A9856A87","full_name":"Napiórkowski, Marcin M","last_name":"Napiórkowski"}],"intvolume":"        21","date_updated":"2025-09-18T09:52:14Z","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 &lt; 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."}],"title":"Bogoliubov correction to the mean-field dynamics of interacting bosons","day":"01","isi":1,"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"},{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"P27533_N27"}],"department":[{"_id":"RoSe"}],"external_id":{"isi":["000409382300004"],"arxiv":["1509.04631"]},"page":"683 - 738","year":"2017","quality_controlled":"1","oa":1,"issue":"3","date_published":"2017-01-01T00:00:00Z","publisher":"International Press","doi":"10.4310/ATMP.2017.v21.n3.a4","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"chicago":"Nam, Phan, and Marcin M Napiórkowski. “Bogoliubov Correction to the Mean-Field Dynamics of Interacting Bosons.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press, 2017. <a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a4\">https://doi.org/10.4310/ATMP.2017.v21.n3.a4</a>.","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.","mla":"Nam, Phan, and Marcin M. Napiórkowski. “Bogoliubov Correction to the Mean-Field Dynamics of Interacting Bosons.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 21, no. 3, International Press, 2017, pp. 683–738, doi:<a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a4\">10.4310/ATMP.2017.v21.n3.a4</a>.","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,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 21, no. 3. International Press, pp. 683–738, 2017.","apa":"Nam, P., &#38; Napiórkowski, M. M. (2017). Bogoliubov correction to the mean-field dynamics of interacting bosons. <i>Advances in Theoretical and Mathematical Physics</i>. International Press. <a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a4\">https://doi.org/10.4310/ATMP.2017.v21.n3.a4</a>","ama":"Nam P, Napiórkowski MM. Bogoliubov correction to the mean-field dynamics of interacting bosons. <i>Advances in Theoretical and Mathematical Physics</i>. 2017;21(3):683-738. doi:<a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a4\">10.4310/ATMP.2017.v21.n3.a4</a>"},"publication_status":"published","type":"journal_article","volume":21,"arxiv":1,"publist_id":"7336","month":"01","scopus_import":"1","_id":"484"},{"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","corr_author":"1","volume":145,"type":"journal_article","publication_status":"published","citation":{"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>.","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>.","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.","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>","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."},"scopus_import":"1","month":"01","arxiv":1,"publist_id":"7160","_id":"632","page":"2441 - 2454","external_id":{"arxiv":["1509.09045"],"isi":["000398833500014"]},"quality_controlled":"1","year":"2017","date_published":"2017-01-01T00:00:00Z","publisher":"American Mathematical Society","language":[{"iso":"eng"}],"doi":"10.1090/proc/13468","issue":"6","oa":1,"author":[{"first_name":"Mathieu","full_name":"Lewin, Mathieu","last_name":"Lewin"},{"first_name":"Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87","last_name":"Nam","full_name":"Nam, Phan"},{"first_name":"Nicolas","full_name":"Rougerie, Nicolas","last_name":"Rougerie"}],"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. "}],"oa_version":"Submitted Version","intvolume":"       145","date_updated":"2025-09-11T07:26:38Z","day":"01","title":"A note on 2D focusing many boson systems","department":[{"_id":"RoSe"}],"project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"isi":1,"ec_funded":1,"publication":"Proceedings of the American Mathematical Society","date_created":"2018-12-11T11:47:36Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1509.09045"}],"status":"public","article_processing_charge":"No"},{"external_id":{"isi":["000401270000004"],"arxiv":["1603.07368"]},"quality_controlled":"1","year":"2017","publisher":"Springer","language":[{"iso":"eng"}],"doi":"10.1007/s11040-017-9238-0","date_published":"2017-06-01T00:00:00Z","issue":"2","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","volume":20,"publication_status":"published","citation":{"ieee":"P. Nam and H. Van Den Bosch, “Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges,” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 20, no. 2. Springer, 2017.","ama":"Nam P, Van Den Bosch H. Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges. <i>Mathematical Physics, Analysis and Geometry</i>. 2017;20(2). doi:<a href=\"https://doi.org/10.1007/s11040-017-9238-0\">10.1007/s11040-017-9238-0</a>","apa":"Nam, P., &#38; Van Den Bosch, H. (2017). Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges. <i>Mathematical Physics, Analysis and Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s11040-017-9238-0\">https://doi.org/10.1007/s11040-017-9238-0</a>","short":"P. Nam, H. Van Den Bosch, Mathematical Physics, Analysis and Geometry 20 (2017).","mla":"Nam, Phan, and Hanne Van Den Bosch. “Nonexistence in Thomas Fermi-Dirac-von Weizsäcker Theory with Small Nuclear Charges.” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 20, no. 2, 6, Springer, 2017, doi:<a href=\"https://doi.org/10.1007/s11040-017-9238-0\">10.1007/s11040-017-9238-0</a>.","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.” <i>Mathematical Physics, Analysis and Geometry</i>. Springer, 2017. <a href=\"https://doi.org/10.1007/s11040-017-9238-0\">https://doi.org/10.1007/s11040-017-9238-0</a>."},"scopus_import":"1","month":"06","arxiv":1,"publist_id":"6300","_id":"1079","publication_identifier":{"issn":["1385-0172"]},"publication":"Mathematical Physics, Analysis and Geometry","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1603.07368"}],"date_created":"2018-12-11T11:50:02Z","status":"public","article_processing_charge":"No","author":[{"first_name":"Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87","full_name":"Nam, Phan","last_name":"Nam"},{"first_name":"Hanne","last_name":"Van Den Bosch","full_name":"Van Den Bosch, Hanne"}],"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"}],"article_number":"6","oa_version":"Submitted Version","intvolume":"        20","date_updated":"2025-06-04T08:11:50Z","day":"01","title":"Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges","department":[{"_id":"RoSe"}],"project":[{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","call_identifier":"FWF","_id":"25C878CE-B435-11E9-9278-68D0E5697425"}],"isi":1},{"department":[{"_id":"RoSe"}],"project":[{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"isi":1,"day":"01","title":"A lower bound for the BCS functional with boundary conditions at infinity","abstract":[{"lang":"eng","text":"We consider a many-body system of fermionic atoms interacting via a local pair potential and subject to an external potential within the framework of Bardeen-Cooper-Schrieffer (BCS) theory. We measure the free energy of the whole sample with respect to the free energy of a reference state which allows us to define a BCS functional with boundary conditions at infinity. Our main result is a lower bound for this energy functional in terms of expressions that typically appear in Ginzburg-Landau functionals.\r\n"}],"oa_version":"Submitted Version","article_number":"081901","intvolume":"        58","date_updated":"2025-06-04T08:19:58Z","author":[{"full_name":"Deuchert, Andreas","last_name":"Deuchert","orcid":"0000-0003-3146-6746","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","first_name":"Andreas"}],"article_processing_charge":"No","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1703.04616"}],"date_created":"2018-12-11T11:49:10Z","status":"public","publication":" Journal of Mathematical Physics","publication_identifier":{"issn":["0022-2488"]},"ec_funded":1,"_id":"912","scopus_import":"1","month":"08","publist_id":"6531","arxiv":1,"corr_author":"1","type":"journal_article","volume":58,"publication_status":"published","citation":{"short":"A. Deuchert,  Journal of Mathematical Physics 58 (2017).","mla":"Deuchert, Andreas. “A Lower Bound for the BCS Functional with Boundary Conditions at Infinity.” <i> Journal of Mathematical Physics</i>, vol. 58, no. 8, 081901, AIP Publishing, 2017, doi:<a href=\"https://doi.org/10.1063/1.4996580\">10.1063/1.4996580</a>.","chicago":"Deuchert, Andreas. “A Lower Bound for the BCS Functional with Boundary Conditions at Infinity.” <i> Journal of Mathematical Physics</i>. AIP Publishing, 2017. <a href=\"https://doi.org/10.1063/1.4996580\">https://doi.org/10.1063/1.4996580</a>.","ista":"Deuchert A. 2017. A lower bound for the BCS functional with boundary conditions at infinity.  Journal of Mathematical Physics. 58(8), 081901.","ieee":"A. Deuchert, “A lower bound for the BCS functional with boundary conditions at infinity,” <i> Journal of Mathematical Physics</i>, vol. 58, no. 8. AIP Publishing, 2017.","apa":"Deuchert, A. (2017). A lower bound for the BCS functional with boundary conditions at infinity. <i> Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/1.4996580\">https://doi.org/10.1063/1.4996580</a>","ama":"Deuchert A. A lower bound for the BCS functional with boundary conditions at infinity. <i> Journal of Mathematical Physics</i>. 2017;58(8). doi:<a href=\"https://doi.org/10.1063/1.4996580\">10.1063/1.4996580</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"date_published":"2017-08-01T00:00:00Z","publisher":"AIP Publishing","doi":"10.1063/1.4996580","issue":"8","oa":1,"quality_controlled":"1","year":"2017","external_id":{"arxiv":["1703.04616"],"isi":["000409197200015"]}},{"date_created":"2018-12-11T11:48:15Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1604.05240"}],"status":"public","article_processing_charge":"No","publication_identifier":{"issn":["0021-7824"]},"publication":"Journal de Mathématiques Pures et Appliquées","day":"01","title":"A note on the validity of Bogoliubov correction to mean field dynamics","department":[{"_id":"RoSe"}],"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"}],"isi":1,"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"}],"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","date_updated":"2025-06-04T09:41:48Z","intvolume":"       108","doi":"10.1016/j.matpur.2017.05.013","language":[{"iso":"eng"}],"publisher":"Elsevier","date_published":"2017-11-01T00:00:00Z","issue":"5","oa":1,"page":"662 - 688","external_id":{"arxiv":["1604.05240"],"isi":["000414113600003"]},"quality_controlled":"1","year":"2017","scopus_import":"1","month":"11","publist_id":"6928","arxiv":1,"_id":"739","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","volume":108,"type":"journal_article","publication_status":"published","citation":{"ieee":"P. Nam and M. M. Napiórkowski, “A note on the validity of Bogoliubov correction to mean field dynamics,” <i>Journal de Mathématiques Pures et Appliquées</i>, vol. 108, no. 5. Elsevier, pp. 662–688, 2017.","apa":"Nam, P., &#38; Napiórkowski, M. M. (2017). A note on the validity of Bogoliubov correction to mean field dynamics. <i>Journal de Mathématiques Pures et Appliquées</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.matpur.2017.05.013\">https://doi.org/10.1016/j.matpur.2017.05.013</a>","ama":"Nam P, Napiórkowski MM. A note on the validity of Bogoliubov correction to mean field dynamics. <i>Journal de Mathématiques Pures et Appliquées</i>. 2017;108(5):662-688. doi:<a href=\"https://doi.org/10.1016/j.matpur.2017.05.013\">10.1016/j.matpur.2017.05.013</a>","short":"P. Nam, M.M. Napiórkowski, Journal de Mathématiques Pures et Appliquées 108 (2017) 662–688.","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.” <i>Journal de Mathématiques Pures et Appliquées</i>, vol. 108, no. 5, Elsevier, 2017, pp. 662–88, doi:<a href=\"https://doi.org/10.1016/j.matpur.2017.05.013\">10.1016/j.matpur.2017.05.013</a>.","chicago":"Nam, Phan, and Marcin M Napiórkowski. “A Note on the Validity of Bogoliubov Correction to Mean Field Dynamics.” <i>Journal de Mathématiques Pures et Appliquées</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.matpur.2017.05.013\">https://doi.org/10.1016/j.matpur.2017.05.013</a>."}},{"date_created":"2018-12-11T11:48:15Z","status":"public","file_date_updated":"2020-07-14T12:47:57Z","article_processing_charge":"No","pubrep_id":"880","publication_identifier":{"issn":["0010-3616"]},"ec_funded":1,"related_material":{"record":[{"id":"52","relation":"dissertation_contains","status":"public"}]},"publication":"Communications in Mathematical Physics","ddc":["539"],"day":"01","title":"Stability of a fermionic N+1 particle system with point interactions","department":[{"_id":"RoSe"}],"project":[{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems"}],"isi":1,"has_accepted_license":"1","author":[{"id":"2B5FC9A4-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas","full_name":"Moser, Thomas","last_name":"Moser"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","last_name":"Seiringer","full_name":"Seiringer, Robert"}],"abstract":[{"lang":"eng","text":"We prove that a system of N fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical m*. The value of m* is independent of N and turns out to be less than 1. This fact has important implications for the stability of the unitary Fermi gas. We also characterize the domain of the Hamiltonian of this model, and establish the validity of the Tan relations for all wave functions in the domain."}],"oa_version":"Published Version","date_updated":"2026-04-08T14:12:30Z","intvolume":"       356","doi":"10.1007/s00220-017-2980-0","language":[{"iso":"eng"}],"date_published":"2017-11-01T00:00:00Z","publisher":"Springer","issue":"1","file":[{"creator":"system","relation":"main_file","date_created":"2018-12-12T10:10:50Z","content_type":"application/pdf","date_updated":"2020-07-14T12:47:57Z","file_size":952639,"file_id":"4841","file_name":"IST-2017-880-v1+1_s00220-017-2980-0.pdf","checksum":"0fd9435400f91e9b3c5346319a2d24e3","access_level":"open_access"}],"oa":1,"page":"329 - 355","external_id":{"isi":["000409821300010"]},"quality_controlled":"1","year":"2017","scopus_import":"1","month":"11","publist_id":"6926","_id":"741","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","volume":356,"type":"journal_article","publication_status":"published","citation":{"ama":"Moser T, Seiringer R. Stability of a fermionic N+1 particle system with point interactions. <i>Communications in Mathematical Physics</i>. 2017;356(1):329-355. doi:<a href=\"https://doi.org/10.1007/s00220-017-2980-0\">10.1007/s00220-017-2980-0</a>","apa":"Moser, T., &#38; Seiringer, R. (2017). Stability of a fermionic N+1 particle system with point interactions. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-017-2980-0\">https://doi.org/10.1007/s00220-017-2980-0</a>","ieee":"T. Moser and R. Seiringer, “Stability of a fermionic N+1 particle system with point interactions,” <i>Communications in Mathematical Physics</i>, vol. 356, no. 1. Springer, pp. 329–355, 2017.","mla":"Moser, Thomas, and Robert Seiringer. “Stability of a Fermionic N+1 Particle System with Point Interactions.” <i>Communications in Mathematical Physics</i>, vol. 356, no. 1, Springer, 2017, pp. 329–55, doi:<a href=\"https://doi.org/10.1007/s00220-017-2980-0\">10.1007/s00220-017-2980-0</a>.","ista":"Moser T, Seiringer R. 2017. Stability of a fermionic N+1 particle system with point interactions. Communications in Mathematical Physics. 356(1), 329–355.","chicago":"Moser, Thomas, and Robert Seiringer. “Stability of a Fermionic N+1 Particle System with Point Interactions.” <i>Communications in Mathematical Physics</i>. Springer, 2017. <a href=\"https://doi.org/10.1007/s00220-017-2980-0\">https://doi.org/10.1007/s00220-017-2980-0</a>.","short":"T. Moser, R. Seiringer, Communications in Mathematical Physics 356 (2017) 329–355."}},{"month":"12","scopus_import":"1","arxiv":1,"publist_id":"6401","_id":"997","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","type":"journal_article","volume":119,"citation":{"short":"E. Yakaboylu, A. Deuchert, M. Lemeshko, Physical Review Letters 119 (2017).","chicago":"Yakaboylu, Enderalp, Andreas Deuchert, and Mikhail Lemeshko. “Emergence of Non-Abelian Magnetic Monopoles in a Quantum Impurity Problem.” <i>Physical Review Letters</i>. American Physical Society, 2017. <a href=\"https://doi.org/10.1103/PhysRevLett.119.235301\">https://doi.org/10.1103/PhysRevLett.119.235301</a>.","mla":"Yakaboylu, Enderalp, et al. “Emergence of Non-Abelian Magnetic Monopoles in a Quantum Impurity Problem.” <i>Physical Review Letters</i>, vol. 119, no. 23, 235301, American Physical Society, 2017, doi:<a href=\"https://doi.org/10.1103/PhysRevLett.119.235301\">10.1103/PhysRevLett.119.235301</a>.","ista":"Yakaboylu E, Deuchert A, Lemeshko M. 2017. Emergence of non-abelian magnetic monopoles in a quantum impurity problem. Physical Review Letters. 119(23), 235301.","ama":"Yakaboylu E, Deuchert A, Lemeshko M. Emergence of non-abelian magnetic monopoles in a quantum impurity problem. <i>Physical Review Letters</i>. 2017;119(23). doi:<a href=\"https://doi.org/10.1103/PhysRevLett.119.235301\">10.1103/PhysRevLett.119.235301</a>","apa":"Yakaboylu, E., Deuchert, A., &#38; Lemeshko, M. (2017). Emergence of non-abelian magnetic monopoles in a quantum impurity problem. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevLett.119.235301\">https://doi.org/10.1103/PhysRevLett.119.235301</a>","ieee":"E. Yakaboylu, A. Deuchert, and M. Lemeshko, “Emergence of non-abelian magnetic monopoles in a quantum impurity problem,” <i>Physical Review Letters</i>, vol. 119, no. 23. American Physical Society, 2017."},"publication_status":"published","issue":"23","date_published":"2017-12-06T00:00:00Z","publisher":"American Physical Society","doi":"10.1103/PhysRevLett.119.235301","language":[{"iso":"eng"}],"oa":1,"article_type":"original","external_id":{"isi":["000417132100007"],"arxiv":["1705.05162"]},"year":"2017","quality_controlled":"1","day":"06","title":"Emergence of non-abelian magnetic monopoles in a quantum impurity problem","project":[{"name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734"},{"name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"_id":"26031614-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"P29902","name":"Quantum rotations in the presence of a many-body environment"}],"department":[{"_id":"MiLe"},{"_id":"RoSe"}],"isi":1,"author":[{"id":"38CB71F6-F248-11E8-B48F-1D18A9856A87","first_name":"Enderalp","orcid":"0000-0001-5973-0874","last_name":"Yakaboylu","full_name":"Yakaboylu, Enderalp"},{"full_name":"Deuchert, Andreas","last_name":"Deuchert","orcid":"0000-0003-3146-6746","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","first_name":"Andreas"},{"orcid":"0000-0002-6990-7802","first_name":"Mikhail","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","full_name":"Lemeshko, Mikhail","last_name":"Lemeshko"}],"abstract":[{"text":"Recently it was shown that molecules rotating in superfluid helium can be described in terms of the angulon quasiparticles (Phys. Rev. Lett. 118, 095301 (2017)). Here we demonstrate that in the experimentally realized regime the angulon can be seen as a point charge on a 2-sphere interacting with a gauge field of a non-abelian magnetic monopole. Unlike in several other settings, the gauge fields of the angulon problem emerge in the real coordinate space, as opposed to the momentum space or some effective parameter space. Furthermore, we find a topological transition associated with making the monopole abelian, which takes place in the vicinity of the previously reported angulon instabilities. These results pave the way for studying topological phenomena in experiments on molecules trapped in superfluid helium nanodroplets, as well as on other realizations of orbital impurity problems.","lang":"eng"}],"intvolume":"       119","date_updated":"2025-04-14T07:26:54Z","article_number":"235301","oa_version":"Preprint","status":"public","date_created":"2018-12-11T11:49:36Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.05162"}],"article_processing_charge":"No","publication_identifier":{"issn":["0031-9007"]},"ec_funded":1,"publication":"Physical Review Letters"},{"publist_id":"6215","arxiv":1,"scopus_import":"1","month":"03","_id":"1143","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"apa":"Nam, P., Rougerie, N., &#38; Seiringer, R. (2016). Ground states of large bosonic systems: The gross Pitaevskii limit revisited. <i>Analysis and PDE</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/apde.2016.9.459\">https://doi.org/10.2140/apde.2016.9.459</a>","ama":"Nam P, Rougerie N, Seiringer R. Ground states of large bosonic systems: The gross Pitaevskii limit revisited. <i>Analysis and PDE</i>. 2016;9(2):459-485. doi:<a href=\"https://doi.org/10.2140/apde.2016.9.459\">10.2140/apde.2016.9.459</a>","ieee":"P. Nam, N. Rougerie, and R. Seiringer, “Ground states of large bosonic systems: The gross Pitaevskii limit revisited,” <i>Analysis and PDE</i>, vol. 9, no. 2. Mathematical Sciences Publishers, pp. 459–485, 2016.","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.","mla":"Nam, Phan, et al. “Ground States of Large Bosonic Systems: The Gross Pitaevskii Limit Revisited.” <i>Analysis and PDE</i>, vol. 9, no. 2, Mathematical Sciences Publishers, 2016, pp. 459–85, doi:<a href=\"https://doi.org/10.2140/apde.2016.9.459\">10.2140/apde.2016.9.459</a>.","chicago":"Nam, Phan, Nicolas Rougerie, and Robert Seiringer. “Ground States of Large Bosonic Systems: The Gross Pitaevskii Limit Revisited.” <i>Analysis and PDE</i>. Mathematical Sciences Publishers, 2016. <a href=\"https://doi.org/10.2140/apde.2016.9.459\">https://doi.org/10.2140/apde.2016.9.459</a>.","short":"P. Nam, N. Rougerie, R. Seiringer, Analysis and PDE 9 (2016) 459–485."},"publication_status":"published","volume":9,"type":"journal_article","oa":1,"issue":"2","date_published":"2016-03-24T00:00:00Z","publisher":"Mathematical Sciences Publishers","doi":"10.2140/apde.2016.9.459","language":[{"iso":"eng"}],"external_id":{"isi":["000378287000006"],"arxiv":["1503.07061"]},"page":"459 - 485","year":"2016","quality_controlled":"1","title":"Ground states of large bosonic systems: The gross Pitaevskii limit revisited","day":"24","isi":1,"project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"department":[{"_id":"RoSe"}],"author":[{"id":"404092F4-F248-11E8-B48F-1D18A9856A87","first_name":"Phan","full_name":"Nam, Phan","last_name":"Nam"},{"full_name":"Rougerie, Nicolas","last_name":"Rougerie","first_name":"Nicolas"},{"orcid":"0000-0002-6781-0521","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"intvolume":"         9","date_updated":"2025-09-22T14:10:16Z","oa_version":"Preprint","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"}],"status":"public","main_file_link":[{"url":"https://arxiv.org/abs/1503.07061","open_access":"1"}],"date_created":"2018-12-11T11:50:23Z","article_processing_charge":"No","ec_funded":1,"publication":"Analysis and PDE"},{"pubrep_id":"702","publication":"Mathematical Physics, Analysis and Geometry","acknowledgement":"Partial financial support from the DFG grant GRK 1838, as well as the Austrian Science Fund (FWF), project Nr. P 27533-N27 (R.S.), is gratefully acknowledged.","date_created":"2018-12-11T11:50:59Z","file_date_updated":"2020-07-14T12:44:42Z","status":"public","article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Gerhard","full_name":"Bräunlich, Gerhard","last_name":"Bräunlich"},{"first_name":"Christian","last_name":"Hainzl","full_name":"Hainzl, Christian"},{"full_name":"Seiringer, Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"abstract":[{"lang":"eng","text":"We consider the Bogolubov–Hartree–Fock functional for a fermionic many-body system with two-body interactions. For suitable interaction potentials that have a strong enough attractive tail in order to allow for two-body bound states, but are otherwise sufficiently repulsive to guarantee stability of the system, we show that in the low-density limit the ground state of this model consists of a Bose–Einstein condensate of fermion pairs. The latter can be described by means of the Gross–Pitaevskii energy functional."}],"article_number":"13","oa_version":"Published Version","intvolume":"        19","date_updated":"2025-09-22T09:02:01Z","ddc":["510","539"],"day":"01","title":"Bogolubov–Hartree–Fock theory for strongly interacting fermions in the low density limit","department":[{"_id":"RoSe"}],"project":[{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","call_identifier":"FWF","grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425"}],"isi":1,"has_accepted_license":"1","external_id":{"isi":["000377379300001"]},"quality_controlled":"1","year":"2016","language":[{"iso":"eng"}],"doi":"10.1007/s11040-016-9209-x","publisher":"Springer","date_published":"2016-06-01T00:00:00Z","issue":"2","file":[{"date_created":"2018-12-12T10:09:13Z","relation":"main_file","creator":"system","file_name":"IST-2016-702-v1+1_s11040-016-9209-x.pdf","checksum":"9954f685cc25c58d7f1712c67b47ad8d","access_level":"open_access","file_id":"4736","file_size":506242,"content_type":"application/pdf","date_updated":"2020-07-14T12:44:42Z"}],"oa":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","corr_author":"1","volume":19,"type":"journal_article","publication_status":"published","citation":{"ama":"Bräunlich G, Hainzl C, Seiringer R. Bogolubov–Hartree–Fock theory for strongly interacting fermions in the low density limit. <i>Mathematical Physics, Analysis and Geometry</i>. 2016;19(2). doi:<a href=\"https://doi.org/10.1007/s11040-016-9209-x\">10.1007/s11040-016-9209-x</a>","apa":"Bräunlich, G., Hainzl, C., &#38; Seiringer, R. (2016). Bogolubov–Hartree–Fock theory for strongly interacting fermions in the low density limit. <i>Mathematical Physics, Analysis and Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s11040-016-9209-x\">https://doi.org/10.1007/s11040-016-9209-x</a>","ieee":"G. Bräunlich, C. Hainzl, and R. Seiringer, “Bogolubov–Hartree–Fock theory for strongly interacting fermions in the low density limit,” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 19, no. 2. Springer, 2016.","chicago":"Bräunlich, Gerhard, Christian Hainzl, and Robert Seiringer. “Bogolubov–Hartree–Fock Theory for Strongly Interacting Fermions in the Low Density Limit.” <i>Mathematical Physics, Analysis and Geometry</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s11040-016-9209-x\">https://doi.org/10.1007/s11040-016-9209-x</a>.","mla":"Bräunlich, Gerhard, et al. “Bogolubov–Hartree–Fock Theory for Strongly Interacting Fermions in the Low Density Limit.” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 19, no. 2, 13, Springer, 2016, doi:<a href=\"https://doi.org/10.1007/s11040-016-9209-x\">10.1007/s11040-016-9209-x</a>.","ista":"Bräunlich G, Hainzl C, Seiringer R. 2016. Bogolubov–Hartree–Fock theory for strongly interacting fermions in the low density limit. Mathematical Physics, Analysis and Geometry. 19(2), 13.","short":"G. Bräunlich, C. Hainzl, R. Seiringer, Mathematical Physics, Analysis and Geometry 19 (2016)."},"scopus_import":"1","month":"06","publist_id":"6066","_id":"1259","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"}},{"department":[{"_id":"RoSe"}],"project":[{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","call_identifier":"FWF","grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"has_accepted_license":"1","isi":1,"ddc":["510","539"],"day":"01","title":"Nonexistence of large nuclei in the liquid drop model","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","intvolume":"       106","date_updated":"2025-09-22T08:49:29Z","author":[{"first_name":"Rupert","last_name":"Frank","full_name":"Frank, Rupert"},{"full_name":"Killip, Rowan","last_name":"Killip","first_name":"Rowan"},{"full_name":"Nam, Phan","last_name":"Nam","id":"404092F4-F248-11E8-B48F-1D18A9856A87","first_name":"Phan"}],"article_processing_charge":"No","acknowledgement":"Open access funding provided by Institute of Science and Technology Austria.\r\n","date_created":"2018-12-11T11:51:02Z","status":"public","file_date_updated":"2020-07-14T12:44:42Z","publication":"Letters in Mathematical Physics","pubrep_id":"698","_id":"1267","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"scopus_import":"1","month":"08","publist_id":"6054","corr_author":"1","type":"journal_article","volume":106,"publication_status":"published","citation":{"short":"R. Frank, R. Killip, P. Nam, Letters in Mathematical Physics 106 (2016) 1033–1036.","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.” <i>Letters in Mathematical Physics</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s11005-016-0860-8\">https://doi.org/10.1007/s11005-016-0860-8</a>.","mla":"Frank, Rupert, et al. “Nonexistence of Large Nuclei in the Liquid Drop Model.” <i>Letters in Mathematical Physics</i>, vol. 106, no. 8, Springer, 2016, pp. 1033–36, doi:<a href=\"https://doi.org/10.1007/s11005-016-0860-8\">10.1007/s11005-016-0860-8</a>.","ama":"Frank R, Killip R, Nam P. Nonexistence of large nuclei in the liquid drop model. <i>Letters in Mathematical Physics</i>. 2016;106(8):1033-1036. doi:<a href=\"https://doi.org/10.1007/s11005-016-0860-8\">10.1007/s11005-016-0860-8</a>","apa":"Frank, R., Killip, R., &#38; Nam, P. (2016). Nonexistence of large nuclei in the liquid drop model. <i>Letters in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s11005-016-0860-8\">https://doi.org/10.1007/s11005-016-0860-8</a>","ieee":"R. Frank, R. Killip, and P. Nam, “Nonexistence of large nuclei in the liquid drop model,” <i>Letters in Mathematical Physics</i>, vol. 106, no. 8. Springer, pp. 1033–1036, 2016."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"Springer","date_published":"2016-08-01T00:00:00Z","doi":"10.1007/s11005-016-0860-8","language":[{"iso":"eng"}],"issue":"8","file":[{"file_id":"4863","file_name":"IST-2016-698-v1+1_s11005-016-0860-8.pdf","checksum":"d740a6a226e0f5f864f40e3e269d3cc0","access_level":"open_access","content_type":"application/pdf","date_updated":"2020-07-14T12:44:42Z","file_size":349464,"date_created":"2018-12-12T10:11:09Z","relation":"main_file","creator":"system"}],"oa":1,"quality_controlled":"1","year":"2016","page":"1033 - 1036","external_id":{"isi":["000379609000001"]}},{"_id":"1291","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"publist_id":"6025","month":"11","scopus_import":"1","citation":{"chicago":"Giuliani, Alessandro, and Robert Seiringer. “Periodic Striped Ground States in Ising Models with Competing Interactions.” <i>Communications in Mathematical Physics</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s00220-016-2665-0\">https://doi.org/10.1007/s00220-016-2665-0</a>.","mla":"Giuliani, Alessandro, and Robert Seiringer. “Periodic Striped Ground States in Ising Models with Competing Interactions.” <i>Communications in Mathematical Physics</i>, vol. 347, no. 3, Springer, 2016, pp. 983–1007, doi:<a href=\"https://doi.org/10.1007/s00220-016-2665-0\">10.1007/s00220-016-2665-0</a>.","ista":"Giuliani A, Seiringer R. 2016. Periodic striped ground states in Ising models with competing interactions. Communications in Mathematical Physics. 347(3), 983–1007.","short":"A. Giuliani, R. Seiringer, Communications in Mathematical Physics 347 (2016) 983–1007.","apa":"Giuliani, A., &#38; Seiringer, R. (2016). Periodic striped ground states in Ising models with competing interactions. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-016-2665-0\">https://doi.org/10.1007/s00220-016-2665-0</a>","ama":"Giuliani A, Seiringer R. Periodic striped ground states in Ising models with competing interactions. <i>Communications in Mathematical Physics</i>. 2016;347(3):983-1007. doi:<a href=\"https://doi.org/10.1007/s00220-016-2665-0\">10.1007/s00220-016-2665-0</a>","ieee":"A. Giuliani and R. Seiringer, “Periodic striped ground states in Ising models with competing interactions,” <i>Communications in Mathematical Physics</i>, vol. 347, no. 3. Springer, pp. 983–1007, 2016."},"publication_status":"published","volume":347,"type":"journal_article","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"file":[{"relation":"main_file","creator":"system","date_created":"2018-12-12T10:09:02Z","date_updated":"2020-07-14T12:44:42Z","content_type":"application/pdf","file_size":794983,"file_id":"4725","access_level":"open_access","checksum":"3c6e08c048fc462e312788be72874bb1","file_name":"IST-2016-688-v1+1_s00220-016-2665-0.pdf"}],"issue":"3","date_published":"2016-11-01T00:00:00Z","publisher":"Springer","doi":"10.1007/s00220-016-2665-0","language":[{"iso":"eng"}],"year":"2016","quality_controlled":"1","external_id":{"isi":["000385162900010"]},"page":"983 - 1007","has_accepted_license":"1","isi":1,"project":[{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","call_identifier":"FWF","_id":"25C878CE-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"department":[{"_id":"RoSe"}],"title":"Periodic striped ground states in Ising models with competing interactions","day":"01","ddc":["510","530"],"date_updated":"2025-09-22T08:30:16Z","intvolume":"       347","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than d + 1, with d the space dimension, this happens for all values of J smaller than a critical value Jc(p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for p &gt; 2d and J in a left neighborhood of Jc(p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes (d = 2) or slabs (d = 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity."}],"author":[{"last_name":"Giuliani","full_name":"Giuliani, Alessandro","first_name":"Alessandro"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"}],"article_processing_charge":"No","file_date_updated":"2020-07-14T12:44:42Z","status":"public","date_created":"2018-12-11T11:51:11Z","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The\r\nresearch leading to these results has received funding from the European Research Council under the European\r\nUnion’s Seventh Framework Programme ERC Starting Grant CoMBoS (Grant Agreement No. 239694), from\r\nthe Italian PRIN National Grant Geometric and analytic theory of Hamiltonian systems in finite and infinite\r\ndimensions, and the Austrian Science Fund (FWF), project Nr. P 27533-N27. Part of this work was completed\r\nduring a stay at the Erwin Schrödinger Institute for Mathematical Physics in Vienna (ESI program 2015\r\n“Quantum many-body systems, random matrices, and disorder”), whose hospitality and financial support is\r\ngratefully acknowledged.","publication":"Communications in Mathematical Physics","pubrep_id":"688"},{"external_id":{"isi":["000378844700002"]},"page":"913 - 923","year":"2016","quality_controlled":"1","oa":1,"file":[{"date_updated":"2020-07-14T12:44:53Z","content_type":"application/pdf","file_size":458968,"file_id":"5181","checksum":"fb404923d8ca9a1faeb949561f26cbea","access_level":"open_access","file_name":"IST-2016-591-v1+1_s11005-016-0847-5.pdf","relation":"main_file","creator":"system","date_created":"2018-12-12T10:15:57Z"}],"issue":"7","publisher":"Springer","doi":"10.1007/s11005-016-0847-5","date_published":"2016-07-01T00:00:00Z","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"short":"R. Frank, C. Hainzl, B. Schlein, R. Seiringer, Letters in Mathematical Physics 106 (2016) 913–923.","ista":"Frank R, Hainzl C, Schlein B, Seiringer R. 2016. Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations. Letters in Mathematical Physics. 106(7), 913–923.","mla":"Frank, Rupert, et al. “Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations.” <i>Letters in Mathematical Physics</i>, vol. 106, no. 7, Springer, 2016, pp. 913–23, doi:<a href=\"https://doi.org/10.1007/s11005-016-0847-5\">10.1007/s11005-016-0847-5</a>.","chicago":"Frank, Rupert, Christian Hainzl, Benjamin Schlein, and Robert Seiringer. “Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations.” <i>Letters in Mathematical Physics</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s11005-016-0847-5\">https://doi.org/10.1007/s11005-016-0847-5</a>.","ama":"Frank R, Hainzl C, Schlein B, Seiringer R. Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations. <i>Letters in Mathematical Physics</i>. 2016;106(7):913-923. doi:<a href=\"https://doi.org/10.1007/s11005-016-0847-5\">10.1007/s11005-016-0847-5</a>","apa":"Frank, R., Hainzl, C., Schlein, B., &#38; Seiringer, R. (2016). Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations. <i>Letters in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s11005-016-0847-5\">https://doi.org/10.1007/s11005-016-0847-5</a>","ieee":"R. Frank, C. Hainzl, B. Schlein, and R. Seiringer, “Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations,” <i>Letters in Mathematical Physics</i>, vol. 106, no. 7. Springer, pp. 913–923, 2016."},"publication_status":"published","corr_author":"1","type":"journal_article","volume":106,"publist_id":"5785","month":"07","scopus_import":"1","_id":"1422","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"pubrep_id":"591","publication":"Letters in Mathematical Physics","status":"public","file_date_updated":"2020-07-14T12:44:53Z","date_created":"2018-12-11T11:51:56Z","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Frank, Rupert","last_name":"Frank","first_name":"Rupert"},{"full_name":"Hainzl, Christian","last_name":"Hainzl","first_name":"Christian"},{"full_name":"Schlein, Benjamin","last_name":"Schlein","first_name":"Benjamin"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","last_name":"Seiringer","full_name":"Seiringer, Robert"}],"intvolume":"       106","date_updated":"2025-09-18T14:20:53Z","oa_version":"Published Version","abstract":[{"text":"We study the time-dependent Bogoliubov–de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we show that the magnitude of the order parameter stays approximately constant in time and, in particular, does not follow a time-dependent Ginzburg–Landau equation, which is often employed as a phenomenological description and predicts a decay of the order parameter in time. The full non-linear structure of the equations is necessary to understand this behavior.","lang":"eng"}],"title":"Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations","day":"01","ddc":["510","530"],"isi":1,"has_accepted_license":"1","project":[{"grant_number":"P27533_N27","call_identifier":"FWF","_id":"25C878CE-B435-11E9-9278-68D0E5697425","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"department":[{"_id":"RoSe"}]},{"year":"2016","quality_controlled":"1","external_id":{"isi":["000402374100016"]},"issue":"1","publisher":"IOP Publishing","date_published":"2016-03-07T00:00:00Z","language":[{"iso":"eng"}],"doi":"10.1088/1742-6596/691/1/012016","oa":1,"file":[{"content_type":"application/pdf","date_updated":"2020-07-14T12:44:53Z","file_size":1434688,"file_id":"4847","file_name":"IST-2016-585-v1+1_JPCS_691_1_012016.pdf","checksum":"109db801749072c3f6c8f1a1848700fa","access_level":"open_access","relation":"main_file","creator":"system","date_created":"2018-12-12T10:10:55Z"}],"volume":691,"type":"conference","citation":{"short":"M. Könenberg, T. Moser, R. Seiringer, J. Yngvason, in:, Journal of Physics: Conference Series, IOP Publishing, 2016.","mla":"Könenberg, Martin, et al. “Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential.” <i>Journal of Physics: Conference Series</i>, vol. 691, no. 1, 012016, IOP Publishing, 2016, doi:<a href=\"https://doi.org/10.1088/1742-6596/691/1/012016\">10.1088/1742-6596/691/1/012016</a>.","chicago":"Könenberg, Martin, Thomas Moser, Robert Seiringer, and Jakob Yngvason. “Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential.” In <i>Journal of Physics: Conference Series</i>, Vol. 691. IOP Publishing, 2016. <a href=\"https://doi.org/10.1088/1742-6596/691/1/012016\">https://doi.org/10.1088/1742-6596/691/1/012016</a>.","ista":"Könenberg M, Moser T, Seiringer R, Yngvason J. 2016. Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential. Journal of Physics: Conference Series. 24th International Laser Physics Workshop (LPHYS’15) vol. 691, 012016.","ama":"Könenberg M, Moser T, Seiringer R, Yngvason J. Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential. In: <i>Journal of Physics: Conference Series</i>. Vol 691. IOP Publishing; 2016. doi:<a href=\"https://doi.org/10.1088/1742-6596/691/1/012016\">10.1088/1742-6596/691/1/012016</a>","apa":"Könenberg, M., Moser, T., Seiringer, R., &#38; Yngvason, J. (2016). Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential. In <i>Journal of Physics: Conference Series</i> (Vol. 691). Shanghai, China: IOP Publishing. <a href=\"https://doi.org/10.1088/1742-6596/691/1/012016\">https://doi.org/10.1088/1742-6596/691/1/012016</a>","ieee":"M. Könenberg, T. Moser, R. Seiringer, and J. Yngvason, “Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential,” in <i>Journal of Physics: Conference Series</i>, Shanghai, China, 2016, vol. 691, no. 1."},"publication_status":"published","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"1428","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"month":"03","scopus_import":"1","publist_id":"5770","publication":"Journal of Physics: Conference Series","pubrep_id":"585","conference":{"end_date":"2015-08-25","name":"24th International Laser Physics Workshop (LPHYS'15)","start_date":"2015-08-21","location":"Shanghai, China"},"article_processing_charge":"No","status":"public","file_date_updated":"2020-07-14T12:44:53Z","date_created":"2018-12-11T11:51:58Z","abstract":[{"text":"We report on a mathematically rigorous analysis of the superfluid properties of a Bose- Einstein condensate in the many-body ground state of a one-dimensional model of interacting bosons in a random potential.","lang":"eng"}],"intvolume":"       691","date_updated":"2025-09-18T14:04:23Z","oa_version":"Published Version","article_number":"012016","author":[{"full_name":"Könenberg, Martin","last_name":"Könenberg","first_name":"Martin"},{"full_name":"Moser, Thomas","last_name":"Moser","first_name":"Thomas","id":"2B5FC9A4-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Seiringer, Robert","last_name":"Seiringer"},{"last_name":"Yngvason","full_name":"Yngvason, Jakob","first_name":"Jakob"}],"project":[{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"P27533_N27"}],"department":[{"_id":"RoSe"}],"isi":1,"has_accepted_license":"1","day":"07","ddc":["510","530"],"title":"Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential"},{"author":[{"first_name":"Volker","full_name":"Bach, Volker","last_name":"Bach"},{"last_name":"Breteaux","full_name":"Breteaux, Sébastien","first_name":"Sébastien"},{"first_name":"Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9166-5889","last_name":"Petrat","full_name":"Petrat, Sören P"},{"first_name":"Peter","last_name":"Pickl","full_name":"Pickl, Peter"},{"full_name":"Tzaneteas, Tim","last_name":"Tzaneteas","first_name":"Tim"}],"date_updated":"2025-09-18T12:31:28Z","intvolume":"       105","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We study the time evolution of a system of N spinless fermions in R3 which interact through a pair potential, e.g., the Coulomb potential. We compare the dynamics given by the solution to Schrödinger's equation with the time-dependent Hartree-Fock approximation, and we give an estimate for the accuracy of this approximation in terms of the kinetic energy of the system. This leads, in turn, to bounds in terms of the initial total energy of the system."}],"title":"Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction","day":"01","ddc":["510","530"],"isi":1,"has_accepted_license":"1","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"department":[{"_id":"RoSe"}],"ec_funded":1,"pubrep_id":"581","publication":"Journal de Mathématiques Pures et Appliquées","file_date_updated":"2020-07-14T12:44:54Z","status":"public","date_created":"2018-12-11T11:52:00Z","article_processing_charge":"No","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"chicago":"Bach, Volker, Sébastien Breteaux, Sören P Petrat, Peter Pickl, and Tim Tzaneteas. “Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Interaction.” <i>Journal de Mathématiques Pures et Appliquées</i>. Elsevier, 2016. <a href=\"https://doi.org/10.1016/j.matpur.2015.09.003\">https://doi.org/10.1016/j.matpur.2015.09.003</a>.","ista":"Bach V, Breteaux S, Petrat SP, Pickl P, Tzaneteas T. 2016. Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction. Journal de Mathématiques Pures et Appliquées. 105(1), 1–30.","mla":"Bach, Volker, et al. “Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Interaction.” <i>Journal de Mathématiques Pures et Appliquées</i>, vol. 105, no. 1, Elsevier, 2016, pp. 1–30, doi:<a href=\"https://doi.org/10.1016/j.matpur.2015.09.003\">10.1016/j.matpur.2015.09.003</a>.","short":"V. Bach, S. Breteaux, S.P. Petrat, P. Pickl, T. Tzaneteas, Journal de Mathématiques Pures et Appliquées 105 (2016) 1–30.","ieee":"V. Bach, S. Breteaux, S. P. Petrat, P. Pickl, and T. Tzaneteas, “Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction,” <i>Journal de Mathématiques Pures et Appliquées</i>, vol. 105, no. 1. Elsevier, pp. 1–30, 2016.","ama":"Bach V, Breteaux S, Petrat SP, Pickl P, Tzaneteas T. Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction. <i>Journal de Mathématiques Pures et Appliquées</i>. 2016;105(1):1-30. doi:<a href=\"https://doi.org/10.1016/j.matpur.2015.09.003\">10.1016/j.matpur.2015.09.003</a>","apa":"Bach, V., Breteaux, S., Petrat, S. P., Pickl, P., &#38; Tzaneteas, T. (2016). Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction. <i>Journal de Mathématiques Pures et Appliquées</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.matpur.2015.09.003\">https://doi.org/10.1016/j.matpur.2015.09.003</a>"},"publication_status":"published","volume":105,"type":"journal_article","publist_id":"5763","month":"01","scopus_import":"1","tmp":{"short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"_id":"1436","external_id":{"isi":["000366773900001"]},"page":"1 - 30","year":"2016","quality_controlled":"1","oa":1,"file":[{"date_created":"2018-12-12T10:10:36Z","creator":"system","relation":"main_file","file_name":"IST-2016-581-v1+1_1-s2.0-S0021782415001191-main.pdf","access_level":"open_access","checksum":"c5afe1f6935bc7f2b546adbde1d31a35","file_id":"4825","file_size":658491,"content_type":"application/pdf","date_updated":"2020-07-14T12:44:54Z"}],"issue":"1","date_published":"2016-01-01T00:00:00Z","publisher":"Elsevier","doi":"10.1016/j.matpur.2015.09.003","language":[{"iso":"eng"}]},{"publist_id":"5716","month":"02","scopus_import":"1","_id":"1478","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"ieee":"R. Seiringer and S. Warzel, “Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas,” <i>New Journal of Physics</i>, vol. 18, no. 3. IOP Publishing, 2016.","apa":"Seiringer, R., &#38; Warzel, S. (2016). Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas. <i>New Journal of Physics</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1367-2630/18/3/035002\">https://doi.org/10.1088/1367-2630/18/3/035002</a>","ama":"Seiringer R, Warzel S. Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas. <i>New Journal of Physics</i>. 2016;18(3). doi:<a href=\"https://doi.org/10.1088/1367-2630/18/3/035002\">10.1088/1367-2630/18/3/035002</a>","chicago":"Seiringer, Robert, and Simone Warzel. “Decay of Correlations and Absence of Superfluidity in the Disordered Tonks-Girardeau Gas.” <i>New Journal of Physics</i>. IOP Publishing, 2016. <a href=\"https://doi.org/10.1088/1367-2630/18/3/035002\">https://doi.org/10.1088/1367-2630/18/3/035002</a>.","ista":"Seiringer R, Warzel S. 2016. Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas. New Journal of Physics. 18(3), 035002.","mla":"Seiringer, Robert, and Simone Warzel. “Decay of Correlations and Absence of Superfluidity in the Disordered Tonks-Girardeau Gas.” <i>New Journal of Physics</i>, vol. 18, no. 3, 035002, IOP Publishing, 2016, doi:<a href=\"https://doi.org/10.1088/1367-2630/18/3/035002\">10.1088/1367-2630/18/3/035002</a>.","short":"R. Seiringer, S. Warzel, New Journal of Physics 18 (2016)."},"publication_status":"published","type":"journal_article","volume":18,"oa":1,"file":[{"date_created":"2018-12-12T10:17:22Z","creator":"system","relation":"main_file","file_id":"5276","file_name":"IST-2016-579-v1+1_njp_18_3_035002.pdf","checksum":"4f959eabc19d2a2f518318a450a4d424","access_level":"open_access","content_type":"application/pdf","date_updated":"2020-07-14T12:44:56Z","file_size":965607}],"issue":"3","publisher":"IOP Publishing","language":[{"iso":"eng"}],"date_published":"2016-02-29T00:00:00Z","doi":"10.1088/1367-2630/18/3/035002","external_id":{"isi":["000373728100001"]},"year":"2016","quality_controlled":"1","title":"Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas","day":"29","ddc":["510","530"],"isi":1,"has_accepted_license":"1","project":[{"call_identifier":"FWF","grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems"}],"department":[{"_id":"RoSe"}],"author":[{"last_name":"Seiringer","full_name":"Seiringer, Robert","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"},{"first_name":"Simone","last_name":"Warzel","full_name":"Warzel, Simone"}],"intvolume":"        18","date_updated":"2025-09-18T11:37:58Z","oa_version":"Published Version","article_number":"035002","abstract":[{"text":"We consider the Tonks-Girardeau gas subject to a random external potential. If the disorder is such that the underlying one-particle Hamiltonian displays localization (which is known to be generically the case), we show that there is exponential decay of correlations in the many-body eigenstates. Moreover, there is no Bose-Einstein condensation and no superfluidity, even at zero temperature.","lang":"eng"}],"status":"public","file_date_updated":"2020-07-14T12:44:56Z","date_created":"2018-12-11T11:52:15Z","article_processing_charge":"No","pubrep_id":"579","publication":"New Journal of Physics"},{"oa":1,"issue":"2","publisher":"American Institute of Physics","doi":"10.1063/1.4941723","date_published":"2016-02-24T00:00:00Z","language":[{"iso":"eng"}],"external_id":{"isi":["000371620000001"],"arxiv":["1511.01995"]},"year":"2016","quality_controlled":"1","arxiv":1,"publist_id":"5701","month":"02","scopus_import":"1","_id":"1486","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"short":"C. Hainzl, R. Seiringer, Journal of Mathematical Physics 57 (2016).","ista":"Hainzl C, Seiringer R. 2016. The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties. Journal of Mathematical Physics. 57(2), 021101.","mla":"Hainzl, Christian, and Robert Seiringer. “The Bardeen–Cooper–Schrieffer Functional of Superconductivity and Its Mathematical Properties.” <i>Journal of Mathematical Physics</i>, vol. 57, no. 2, 021101, American Institute of Physics, 2016, doi:<a href=\"https://doi.org/10.1063/1.4941723\">10.1063/1.4941723</a>.","chicago":"Hainzl, Christian, and Robert Seiringer. “The Bardeen–Cooper–Schrieffer Functional of Superconductivity and Its Mathematical Properties.” <i>Journal of Mathematical Physics</i>. American Institute of Physics, 2016. <a href=\"https://doi.org/10.1063/1.4941723\">https://doi.org/10.1063/1.4941723</a>.","apa":"Hainzl, C., &#38; Seiringer, R. (2016). The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties. <i>Journal of Mathematical Physics</i>. American Institute of Physics. <a href=\"https://doi.org/10.1063/1.4941723\">https://doi.org/10.1063/1.4941723</a>","ama":"Hainzl C, Seiringer R. The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties. <i>Journal of Mathematical Physics</i>. 2016;57(2). doi:<a href=\"https://doi.org/10.1063/1.4941723\">10.1063/1.4941723</a>","ieee":"C. Hainzl and R. Seiringer, “The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties,” <i>Journal of Mathematical Physics</i>, vol. 57, no. 2. American Institute of Physics, 2016."},"publication_status":"published","type":"journal_article","volume":57,"status":"public","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1511.01995"}],"date_created":"2018-12-11T11:52:18Z","article_processing_charge":"No","publication":"Journal of Mathematical Physics","title":"The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties","day":"24","isi":1,"department":[{"_id":"RoSe"}],"author":[{"first_name":"Christian","last_name":"Hainzl","full_name":"Hainzl, Christian"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"}],"date_updated":"2025-09-18T11:31:30Z","intvolume":"        57","oa_version":"Preprint","article_number":"021101","abstract":[{"text":"We review recent results concerning the mathematical properties of the Bardeen-Cooper-Schrieffer (BCS) functional of superconductivity, which were obtained in a series of papers, partly in collaboration with R. Frank, E. Hamza, S. Naboko, and J. P. Solovej. Our discussion includes, in particular, an investigation of the critical temperature for a general class of interaction potentials, as well as a study of its dependence on external fields. We shall explain how the Ginzburg-Landau model can be derived from the BCS theory in a suitable parameter regime.","lang":"eng"}]},{"issue":"9","language":[{"iso":"eng"}],"doi":"10.1090/tran/6537","publisher":"American Mathematical Society","date_published":"2016-01-01T00:00:00Z","oa":1,"year":"2016","quality_controlled":"1","page":"6131 - 6157","external_id":{"arxiv":["1405.3220"],"isi":["000370726100004"]},"_id":"1491","scopus_import":"1","month":"01","publist_id":"5692","arxiv":1,"type":"journal_article","volume":368,"citation":{"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>","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>","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.","short":"M. Lewin, P. Nam, N. Rougerie, Transactions of the American Mathematical Society 368 (2016) 6131–6157.","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>.","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.” <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>."},"publication_status":"published","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_processing_charge":"No","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.","status":"public","date_created":"2018-12-11T11:52:20Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1405.3220"}],"publication":"Transactions of the American Mathematical Society","department":[{"_id":"RoSe"}],"isi":1,"day":"01","title":"The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases","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"}],"intvolume":"       368","date_updated":"2025-09-18T11:15:32Z","oa_version":"Submitted Version","author":[{"first_name":"Mathieu","last_name":"Lewin","full_name":"Lewin, Mathieu"},{"full_name":"Nam, Phan","last_name":"Nam","id":"404092F4-F248-11E8-B48F-1D18A9856A87","first_name":"Phan"},{"last_name":"Rougerie","full_name":"Rougerie, Nicolas","first_name":"Nicolas"}]},{"ddc":["510","530"],"day":"01","title":"A new method and a new scaling for deriving fermionic mean-field dynamics","department":[{"_id":"RoSe"}],"project":[{"grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"has_accepted_license":"1","isi":1,"author":[{"full_name":"Petrat, Sören P","last_name":"Petrat","orcid":"0000-0002-9166-5889","first_name":"Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Peter","full_name":"Pickl, Peter","last_name":"Pickl"}],"abstract":[{"lang":"eng","text":"We introduce a new method for deriving the time-dependent Hartree or Hartree-Fock equations as an effective mean-field dynamics from the microscopic Schrödinger equation for fermionic many-particle systems in quantum mechanics. The method is an adaption of the method used in Pickl (Lett. Math. Phys. 97 (2) 151–164 2011) for bosonic systems to fermionic systems. It is based on a Gronwall type estimate for a suitable measure of distance between the microscopic solution and an antisymmetrized product state. We use this method to treat a new mean-field limit for fermions with long-range interactions in a large volume. Some of our results hold for singular attractive or repulsive interactions. We can also treat Coulomb interaction assuming either a mild singularity cutoff or certain regularity conditions on the solutions to the Hartree(-Fock) equations. In the considered limit, the kinetic and interaction energy are of the same order, while the average force is subleading. For some interactions, we prove that the Hartree(-Fock) dynamics is a more accurate approximation than a simpler dynamics that one would expect from the subleading force. With our method we also treat the mean-field limit coupled to a semiclassical limit, which was discussed in the literature before, and we recover some of the previous results. All results hold for initial data close (but not necessarily equal) to antisymmetrized product states and we always provide explicit rates of convergence."}],"article_number":"3","oa_version":"Published Version","date_updated":"2025-09-18T11:12:46Z","intvolume":"        19","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","date_created":"2018-12-11T11:52:20Z","file_date_updated":"2020-07-14T12:44:58Z","status":"public","article_processing_charge":"Yes (via OA deal)","pubrep_id":"514","ec_funded":1,"publication":"Mathematical Physics, Analysis and Geometry","scopus_import":"1","month":"03","publist_id":"5690","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"_id":"1493","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","volume":19,"corr_author":"1","type":"journal_article","publication_status":"published","citation":{"ieee":"S. P. Petrat and P. Pickl, “A new method and a new scaling for deriving fermionic mean-field dynamics,” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 19, no. 1. Springer, 2016.","ama":"Petrat SP, Pickl P. A new method and a new scaling for deriving fermionic mean-field dynamics. <i>Mathematical Physics, Analysis and Geometry</i>. 2016;19(1). doi:<a href=\"https://doi.org/10.1007/s11040-016-9204-2\">10.1007/s11040-016-9204-2</a>","apa":"Petrat, S. P., &#38; Pickl, P. (2016). A new method and a new scaling for deriving fermionic mean-field dynamics. <i>Mathematical Physics, Analysis and Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s11040-016-9204-2\">https://doi.org/10.1007/s11040-016-9204-2</a>","chicago":"Petrat, Sören P, and Peter Pickl. “A New Method and a New Scaling for Deriving Fermionic Mean-Field Dynamics.” <i>Mathematical Physics, Analysis and Geometry</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s11040-016-9204-2\">https://doi.org/10.1007/s11040-016-9204-2</a>.","mla":"Petrat, Sören P., and Peter Pickl. “A New Method and a New Scaling for Deriving Fermionic Mean-Field Dynamics.” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 19, no. 1, 3, Springer, 2016, doi:<a href=\"https://doi.org/10.1007/s11040-016-9204-2\">10.1007/s11040-016-9204-2</a>.","ista":"Petrat SP, Pickl P. 2016. A new method and a new scaling for deriving fermionic mean-field dynamics. Mathematical Physics, Analysis and Geometry. 19(1), 3.","short":"S.P. Petrat, P. Pickl, Mathematical Physics, Analysis and Geometry 19 (2016)."},"publisher":"Springer","doi":"10.1007/s11040-016-9204-2","language":[{"iso":"eng"}],"date_published":"2016-03-01T00:00:00Z","issue":"1","file":[{"date_created":"2018-12-12T10:16:55Z","relation":"main_file","creator":"system","file_id":"5246","file_name":"IST-2016-514-v1+1_s11040-016-9204-2.pdf","access_level":"open_access","checksum":"eb5d2145ef0d377c4f78bf06e18f4529","content_type":"application/pdf","date_updated":"2020-07-14T12:44:58Z","file_size":911310}],"oa":1,"external_id":{"isi":["000374267300003"]},"quality_controlled":"1","year":"2016"},{"year":"2016","quality_controlled":"1","page":"4340 - 4368","external_id":{"arxiv":["1508.07321"],"isi":["000375241700011"]},"issue":"11","publisher":"Academic Press","language":[{"iso":"eng"}],"date_published":"2016-06-01T00:00:00Z","doi":"10.1016/j.jfa.2015.12.007","oa":1,"type":"journal_article","corr_author":"1","volume":270,"citation":{"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.” <i>Journal of Functional Analysis</i>. Academic Press, 2016. <a href=\"https://doi.org/10.1016/j.jfa.2015.12.007\">https://doi.org/10.1016/j.jfa.2015.12.007</a>.","mla":"Nam, Phan, et al. “Diagonalization of Bosonic Quadratic Hamiltonians by Bogoliubov Transformations.” <i>Journal of Functional Analysis</i>, vol. 270, no. 11, Academic Press, 2016, pp. 4340–68, doi:<a href=\"https://doi.org/10.1016/j.jfa.2015.12.007\">10.1016/j.jfa.2015.12.007</a>.","ista":"Nam P, Napiórkowski MM, Solovej J. 2016. Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations. Journal of Functional Analysis. 270(11), 4340–4368.","ieee":"P. Nam, M. M. Napiórkowski, and J. Solovej, “Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations,” <i>Journal of Functional Analysis</i>, vol. 270, no. 11. Academic Press, pp. 4340–4368, 2016.","apa":"Nam, P., Napiórkowski, M. M., &#38; Solovej, J. (2016). Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations. <i>Journal of Functional Analysis</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.jfa.2015.12.007\">https://doi.org/10.1016/j.jfa.2015.12.007</a>","ama":"Nam P, Napiórkowski MM, Solovej J. Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations. <i>Journal of Functional Analysis</i>. 2016;270(11):4340-4368. doi:<a href=\"https://doi.org/10.1016/j.jfa.2015.12.007\">10.1016/j.jfa.2015.12.007</a>"},"publication_status":"published","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"1545","scopus_import":"1","month":"06","arxiv":1,"publist_id":"5626","publication":"Journal of Functional Analysis","ec_funded":1,"article_processing_charge":"No","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.).","status":"public","main_file_link":[{"url":"http://arxiv.org/abs/1508.07321","open_access":"1"}],"date_created":"2018-12-11T11:52:38Z","abstract":[{"lang":"eng","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."}],"intvolume":"       270","date_updated":"2025-09-18T11:04:09Z","oa_version":"Submitted Version","author":[{"first_name":"Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87","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"},{"first_name":"Jan","last_name":"Solovej","full_name":"Solovej, Jan"}],"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"},{"_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"P27533_N27","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems"}],"department":[{"_id":"RoSe"}],"isi":1,"day":"01","title":"Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations"},{"publisher":"Springer","date_published":"2016-02-01T00:00:00Z","doi":"10.1007/s00220-015-2526-2","language":[{"iso":"eng"}],"issue":"1","oa":1,"page":"189 - 216","external_id":{"arxiv":["1410.2352"],"isi":["000369965600006"]},"quality_controlled":"1","year":"2016","scopus_import":"1","month":"02","arxiv":1,"publist_id":"5546","_id":"1620","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","volume":342,"type":"journal_article","publication_status":"published","citation":{"mla":"Frank, Rupert, et al. “The External Field Dependence of the BCS Critical Temperature.” <i>Communications in Mathematical Physics</i>, vol. 342, no. 1, Springer, 2016, pp. 189–216, doi:<a href=\"https://doi.org/10.1007/s00220-015-2526-2\">10.1007/s00220-015-2526-2</a>.","chicago":"Frank, Rupert, Christian Hainzl, Robert Seiringer, and Jan Solovej. “The External Field Dependence of the BCS Critical Temperature.” <i>Communications in Mathematical Physics</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s00220-015-2526-2\">https://doi.org/10.1007/s00220-015-2526-2</a>.","ista":"Frank R, Hainzl C, Seiringer R, Solovej J. 2016. The external field dependence of the BCS critical temperature. Communications in Mathematical Physics. 342(1), 189–216.","short":"R. Frank, C. Hainzl, R. Seiringer, J. Solovej, Communications in Mathematical Physics 342 (2016) 189–216.","apa":"Frank, R., Hainzl, C., Seiringer, R., &#38; Solovej, J. (2016). The external field dependence of the BCS critical temperature. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-015-2526-2\">https://doi.org/10.1007/s00220-015-2526-2</a>","ama":"Frank R, Hainzl C, Seiringer R, Solovej J. The external field dependence of the BCS critical temperature. <i>Communications in Mathematical Physics</i>. 2016;342(1):189-216. doi:<a href=\"https://doi.org/10.1007/s00220-015-2526-2\">10.1007/s00220-015-2526-2</a>","ieee":"R. Frank, C. Hainzl, R. Seiringer, and J. Solovej, “The external field dependence of the BCS critical temperature,” <i>Communications in Mathematical Physics</i>, vol. 342, no. 1. Springer, pp. 189–216, 2016."},"acknowledgement":"The authors are grateful to I. M. Sigal for useful discussions. Financial support from the US National Science Foundation through Grants PHY-1347399 and DMS-1363432 (R.L.F.), from the Danish council for independent research and from ERC Advanced Grant 321029 (J.P.S.) is acknowledged.","main_file_link":[{"url":"http://arxiv.org/abs/1410.2352","open_access":"1"}],"date_created":"2018-12-11T11:53:04Z","status":"public","article_processing_charge":"No","publication":"Communications in Mathematical Physics","day":"01","title":"The external field dependence of the BCS critical temperature","department":[{"_id":"RoSe"}],"isi":1,"author":[{"last_name":"Frank","full_name":"Frank, Rupert","first_name":"Rupert"},{"last_name":"Hainzl","full_name":"Hainzl, Christian","first_name":"Christian"},{"full_name":"Seiringer, Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"},{"first_name":"Jan","last_name":"Solovej","full_name":"Solovej, Jan"}],"abstract":[{"lang":"eng","text":"We consider the Bardeen–Cooper–Schrieffer free energy functional for particles interacting via a two-body potential on a microscopic scale and in the presence of weak external fields varying on a macroscopic scale. We study the influence of the external fields on the critical temperature. We show that in the limit where the ratio between the microscopic and macroscopic scale tends to zero, the next to leading order of the critical temperature is determined by the lowest eigenvalue of the linearization of the Ginzburg–Landau equation."}],"oa_version":"Submitted Version","intvolume":"       342","date_updated":"2025-09-18T10:57:14Z"}]