[{"doi":"10.1090/tran/6537","citation":{"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>.","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.","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>.","short":"M. Lewin, P. Nam, N. Rougerie, Transactions of the American Mathematical Society 368 (2016) 6131–6157.","ama":"Lewin M, Nam P, Rougerie N. The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases. <i>Transactions of the American Mathematical Society</i>. 2016;368(9):6131-6157. doi:<a href=\"https://doi.org/10.1090/tran/6537\">10.1090/tran/6537</a>"},"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"}],"article_processing_charge":"No","department":[{"_id":"RoSe"}],"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.","external_id":{"arxiv":["1405.3220"],"isi":["000370726100004"]},"publisher":"American Mathematical Society","_id":"1491","date_updated":"2025-09-18T11:15:32Z","title":"The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases","oa_version":"Submitted Version","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1405.3220"}],"scopus_import":"1","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","month":"01","publication":"Transactions of the American Mathematical Society","publication_status":"published","arxiv":1,"fulldoi":"https://doi.org/10.1090/tran/6537","publist_id":"5692","issue":"9","type":"journal_article","intvolume":"       368","year":"2016","status":"public","oa":1,"date_published":"2016-01-01T00:00:00Z","date_created":"2018-12-11T11:52:20Z","page":"6131 - 6157","day":"01","author":[{"last_name":"Lewin","first_name":"Mathieu","full_name":"Lewin, Mathieu"},{"last_name":"Nam","id":"404092F4-F248-11E8-B48F-1D18A9856A87","full_name":"Nam, Phan","first_name":"Phan"},{"last_name":"Rougerie","first_name":"Nicolas","full_name":"Rougerie, Nicolas"}],"isi":1,"quality_controlled":"1","volume":368},{"title":"A new method and a new scaling for deriving fermionic mean-field dynamics","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","external_id":{"isi":["000374267300003"]},"_id":"1493","publisher":"Springer","date_updated":"2025-09-18T11:12:46Z","ddc":["510","530"],"has_accepted_license":"1","department":[{"_id":"RoSe"}],"corr_author":"1","file_date_updated":"2020-07-14T12:44:58Z","doi":"10.1007/s11040-016-9204-2","citation":{"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>","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>.","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>","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>.","short":"S.P. Petrat, P. Pickl, Mathematical Physics, Analysis and Geometry 19 (2016).","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.","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."},"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_processing_charge":"Yes (via OA deal)","article_number":"3","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"scopus_import":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","language":[{"iso":"eng"}],"month":"03","oa_version":"Published Version","oa":1,"date_published":"2016-03-01T00:00:00Z","date_created":"2018-12-11T11:52:20Z","issue":"1","type":"journal_article","intvolume":"        19","status":"public","year":"2016","publist_id":"5690","publication":"Mathematical Physics, Analysis and Geometry","tmp":{"image":"/images/cc_by.png","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"},"publication_status":"published","fulldoi":"https://doi.org/10.1007/s11040-016-9204-2","volume":19,"quality_controlled":"1","file":[{"relation":"main_file","date_updated":"2020-07-14T12:44:58Z","checksum":"eb5d2145ef0d377c4f78bf06e18f4529","file_name":"IST-2016-514-v1+1_s11040-016-9204-2.pdf","date_created":"2018-12-12T10:16:55Z","access_level":"open_access","creator":"system","file_size":911310,"file_id":"5246","content_type":"application/pdf"}],"pubrep_id":"514","day":"01","author":[{"orcid":"0000-0002-9166-5889","last_name":"Petrat","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","first_name":"Sören P","full_name":"Petrat, Sören P"},{"last_name":"Pickl","full_name":"Pickl, Peter","first_name":"Peter"}],"isi":1,"ec_funded":1},{"publication":"Journal of Functional Analysis","fulldoi":"https://doi.org/10.1016/j.jfa.2015.12.007","arxiv":1,"publication_status":"published","publist_id":"5626","type":"journal_article","issue":"11","year":"2016","status":"public","intvolume":"       270","date_published":"2016-06-01T00:00:00Z","oa":1,"date_created":"2018-12-11T11:52:38Z","page":"4340 - 4368","ec_funded":1,"day":"01","isi":1,"author":[{"id":"404092F4-F248-11E8-B48F-1D18A9856A87","last_name":"Nam","full_name":"Nam, Phan","first_name":"Phan"},{"id":"4197AD04-F248-11E8-B48F-1D18A9856A87","last_name":"Napiórkowski","first_name":"Marcin M","full_name":"Napiórkowski, Marcin M"},{"last_name":"Solovej","first_name":"Jan","full_name":"Solovej, Jan"}],"quality_controlled":"1","volume":270,"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"}],"citation":{"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>","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>.","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>","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>.","short":"P. Nam, M.M. Napiórkowski, J. Solovej, Journal of Functional Analysis 270 (2016) 4340–4368.","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."},"doi":"10.1016/j.jfa.2015.12.007","article_processing_charge":"No","department":[{"_id":"RoSe"}],"corr_author":"1","external_id":{"isi":["000375241700011"],"arxiv":["1508.07321"]},"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.).","date_updated":"2025-09-18T11:04:09Z","_id":"1545","publisher":"Academic Press","title":"Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations","oa_version":"Submitted Version","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1508.07321"}],"scopus_import":"1","language":[{"iso":"eng"}],"month":"06","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","call_identifier":"FWF"}]},{"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.","external_id":{"isi":["000369965600006"],"arxiv":["1410.2352"]},"publisher":"Springer","_id":"1620","date_updated":"2025-09-18T10:57:14Z","title":"The external field dependence of the BCS critical temperature","citation":{"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.","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.","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>.","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>","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>.","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>"},"doi":"10.1007/s00220-015-2526-2","abstract":[{"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.","lang":"eng"}],"article_processing_charge":"No","department":[{"_id":"RoSe"}],"oa_version":"Submitted Version","main_file_link":[{"url":"http://arxiv.org/abs/1410.2352","open_access":"1"}],"scopus_import":"1","language":[{"iso":"eng"}],"month":"02","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","issue":"1","type":"journal_article","intvolume":"       342","year":"2016","status":"public","oa":1,"date_published":"2016-02-01T00:00:00Z","date_created":"2018-12-11T11:53:04Z","publication":"Communications in Mathematical Physics","arxiv":1,"publication_status":"published","fulldoi":"https://doi.org/10.1007/s00220-015-2526-2","publist_id":"5546","quality_controlled":"1","volume":342,"page":"189 - 216","day":"01","author":[{"first_name":"Rupert","full_name":"Frank, Rupert","last_name":"Frank"},{"first_name":"Christian","full_name":"Hainzl, Christian","last_name":"Hainzl"},{"full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Solovej","first_name":"Jan","full_name":"Solovej, Jan"}],"isi":1},{"project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"language":[{"iso":"eng"}],"month":"03","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","scopus_import":"1","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1501.04570"}],"oa_version":"Submitted Version","title":"Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems","_id":"1622","publisher":"Springer","date_updated":"2025-09-18T10:52:35Z","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”.","external_id":{"isi":["000368535400010"],"arxiv":["1501.04570"]},"corr_author":"1","department":[{"_id":"RoSe"}],"article_processing_charge":"No","doi":"10.1007/s00205-015-0923-5","citation":{"apa":"Lundholm, D., Nam, P., &#38; Portmann, F. (2016). Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems. <i>Archive for Rational Mechanics and Analysis</i>. Springer. <a href=\"https://doi.org/10.1007/s00205-015-0923-5\">https://doi.org/10.1007/s00205-015-0923-5</a>","mla":"Lundholm, Douglas, et al. “Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 219, no. 3, Springer, 2016, pp. 1343–82, doi:<a href=\"https://doi.org/10.1007/s00205-015-0923-5\">10.1007/s00205-015-0923-5</a>.","ama":"Lundholm D, Nam P, Portmann F. Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems. <i>Archive for Rational Mechanics and Analysis</i>. 2016;219(3):1343-1382. doi:<a href=\"https://doi.org/10.1007/s00205-015-0923-5\">10.1007/s00205-015-0923-5</a>","chicago":"Lundholm, Douglas, Phan Nam, and Fabian Portmann. “Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems.” <i>Archive for Rational Mechanics and Analysis</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s00205-015-0923-5\">https://doi.org/10.1007/s00205-015-0923-5</a>.","short":"D. Lundholm, P. Nam, F. Portmann, Archive for Rational Mechanics and Analysis 219 (2016) 1343–1382.","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.","ieee":"D. Lundholm, P. Nam, and F. Portmann, “Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 219, no. 3. Springer, pp. 1343–1382, 2016."},"abstract":[{"lang":"eng","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."}],"volume":219,"quality_controlled":"1","author":[{"last_name":"Lundholm","full_name":"Lundholm, Douglas","first_name":"Douglas"},{"id":"404092F4-F248-11E8-B48F-1D18A9856A87","last_name":"Nam","first_name":"Phan","full_name":"Nam, Phan"},{"first_name":"Fabian","full_name":"Portmann, Fabian","last_name":"Portmann"}],"isi":1,"day":"01","ec_funded":1,"page":"1343 - 1382","date_created":"2018-12-11T11:53:05Z","oa":1,"date_published":"2016-03-01T00:00:00Z","intvolume":"       219","year":"2016","status":"public","issue":"3","type":"journal_article","publist_id":"5542","arxiv":1,"publication_status":"published","fulldoi":"https://doi.org/10.1007/s00205-015-0923-5","publication":"Archive for Rational Mechanics and Analysis"},{"publisher":"AIP Publishing","_id":"1486","date_updated":"2026-08-12T13:59:20Z","external_id":{"arxiv":["1511.01995"],"isi":["000371620000001"]},"title":"The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties","article_processing_charge":"No","doi":"10.1063/1.4941723","citation":{"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, AIP Publishing, 2016, doi:<a href=\"https://doi.org/10.1063/1.4941723\">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>. AIP Publishing. <a href=\"https://doi.org/10.1063/1.4941723\">https://doi.org/10.1063/1.4941723</a>","short":"C. Hainzl, R. Seiringer, Journal of Mathematical Physics 57 (2016).","chicago":"Hainzl, Christian, and Robert Seiringer. “The Bardeen–Cooper–Schrieffer Functional of Superconductivity and Its Mathematical Properties.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2016. <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. AIP Publishing, 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."},"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"}],"department":[{"_id":"RoSe"}],"article_number":"021101","main_file_link":[{"url":"http://arxiv.org/abs/1511.01995","open_access":"1"}],"oa_version":"Preprint","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"02","scopus_import":"1","intvolume":"        57","status":"public","year":"2016","issue":"2","type":"journal_article","date_created":"2018-12-11T11:52:18Z","oa":1,"date_published":"2016-02-24T00:00:00Z","arxiv":1,"publication_status":"published","fulldoi":"https://doi.org/10.1063/1.4941723","publication":"Journal of Mathematical Physics","publist_id":"5701","quality_controlled":"1","volume":57,"author":[{"last_name":"Hainzl","first_name":"Christian","full_name":"Hainzl, Christian"},{"first_name":"Robert","full_name":"Seiringer, Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"}],"isi":1,"day":"24"},{"language":[{"iso":"eng"}],"month":"02","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","scopus_import":"1","main_file_link":[{"url":"http://arxiv.org/abs/1402.1153","open_access":"1"}],"oa_version":"Preprint","corr_author":"1","department":[{"_id":"RoSe"}],"article_processing_charge":"No","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. "}],"doi":"10.1007/s00205-014-0781-6","citation":{"ama":"Nam P, Seiringer R. Collective excitations of Bose gases in the mean-field regime. <i>Archive for Rational Mechanics and Analysis</i>. 2015;215(2):381-417. doi:<a href=\"https://doi.org/10.1007/s00205-014-0781-6\">10.1007/s00205-014-0781-6</a>","chicago":"Nam, Phan, and Robert Seiringer. “Collective Excitations of Bose Gases in the Mean-Field Regime.” <i>Archive for Rational Mechanics and Analysis</i>. Springer, 2015. <a href=\"https://doi.org/10.1007/s00205-014-0781-6\">https://doi.org/10.1007/s00205-014-0781-6</a>.","short":"P. Nam, R. Seiringer, Archive for Rational Mechanics and Analysis 215 (2015) 381–417.","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.","ieee":"P. Nam and R. Seiringer, “Collective excitations of Bose gases in the mean-field regime,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 215, no. 2. Springer, pp. 381–417, 2015.","apa":"Nam, P., &#38; Seiringer, R. (2015). Collective excitations of Bose gases in the mean-field regime. <i>Archive for Rational Mechanics and Analysis</i>. Springer. <a href=\"https://doi.org/10.1007/s00205-014-0781-6\">https://doi.org/10.1007/s00205-014-0781-6</a>","mla":"Nam, Phan, and Robert Seiringer. “Collective Excitations of Bose Gases in the Mean-Field Regime.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 215, no. 2, Springer, 2015, pp. 381–417, doi:<a href=\"https://doi.org/10.1007/s00205-014-0781-6\">10.1007/s00205-014-0781-6</a>."},"title":"Collective excitations of Bose gases in the mean-field regime","date_updated":"2025-09-23T08:17:14Z","publisher":"Springer","_id":"2085","external_id":{"isi":["000347150400002"],"arxiv":["1402.1153"]},"isi":1,"author":[{"full_name":"Nam, Phan","first_name":"Phan","last_name":"Nam","id":"404092F4-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Seiringer, Robert","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer"}],"day":"01","page":"381 - 417","volume":215,"quality_controlled":"1","publist_id":"4951","fulldoi":"https://doi.org/10.1007/s00205-014-0781-6","publication_status":"published","arxiv":1,"publication":"Archive for Rational Mechanics and Analysis","date_created":"2018-12-11T11:55:37Z","date_published":"2015-02-01T00:00:00Z","oa":1,"year":"2015","status":"public","intvolume":"       215","type":"journal_article","issue":"2"},{"fulldoi":"https://doi.org/10.1007/s00220-015-2402-0","arxiv":1,"publication_status":"published","publication":"Communications in Mathematical Physics","publist_id":"5599","status":"public","year":"2015","intvolume":"       339","type":"journal_article","issue":"1","date_created":"2018-12-11T11:52:47Z","date_published":"2015-06-23T00:00:00Z","oa":1,"page":"279 - 307","isi":1,"author":[{"full_name":"Correggi, Michele","first_name":"Michele","last_name":"Correggi"},{"full_name":"Giuliani, Alessandro","first_name":"Alessandro","last_name":"Giuliani"},{"first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521"}],"day":"23","quality_controlled":"1","volume":339,"article_processing_charge":"No","abstract":[{"text":"We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins S ≥ 1/2. We rigorously prove the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial contribution to the free energy at low temperatures. Our proof comes with explicit, constructive upper and lower bounds on the error term. It uses in an essential way the bosonic formulation of the model in terms of the Holstein-Primakoff representation. In this language, the model describes interacting bosons with a hard-core on-site repulsion and a nearest-neighbor attraction. This attractive interaction makes the lower bound on the free energy particularly tricky: the key idea there is to prove a differential inequality for the two-particle density, which is thereby shown to be smaller than the probability density of a suitably weighted two-particle random process on the lattice.\r\n","lang":"eng"}],"citation":{"ista":"Correggi M, Giuliani A, Seiringer R. 2015. Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet. Communications in Mathematical Physics. 339(1), 279–307.","ieee":"M. Correggi, A. Giuliani, and R. Seiringer, “Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet,” <i>Communications in Mathematical Physics</i>, vol. 339, no. 1. Springer, pp. 279–307, 2015.","ama":"Correggi M, Giuliani A, Seiringer R. Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet. <i>Communications in Mathematical Physics</i>. 2015;339(1):279-307. doi:<a href=\"https://doi.org/10.1007/s00220-015-2402-0\">10.1007/s00220-015-2402-0</a>","short":"M. Correggi, A. Giuliani, R. Seiringer, Communications in Mathematical Physics 339 (2015) 279–307.","chicago":"Correggi, Michele, Alessandro Giuliani, and Robert Seiringer. “Validity of the Spin-Wave Approximation for the Free Energy of the Heisenberg Ferromagnet.” <i>Communications in Mathematical Physics</i>. Springer, 2015. <a href=\"https://doi.org/10.1007/s00220-015-2402-0\">https://doi.org/10.1007/s00220-015-2402-0</a>.","apa":"Correggi, M., Giuliani, A., &#38; Seiringer, R. (2015). Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-015-2402-0\">https://doi.org/10.1007/s00220-015-2402-0</a>","mla":"Correggi, Michele, et al. “Validity of the Spin-Wave Approximation for the Free Energy of the Heisenberg Ferromagnet.” <i>Communications in Mathematical Physics</i>, vol. 339, no. 1, Springer, 2015, pp. 279–307, doi:<a href=\"https://doi.org/10.1007/s00220-015-2402-0\">10.1007/s00220-015-2402-0</a>."},"doi":"10.1007/s00220-015-2402-0","department":[{"_id":"RoSe"}],"date_updated":"2025-09-29T11:04:37Z","publisher":"Springer","_id":"1572","external_id":{"arxiv":["1312.7873"],"isi":["000357582800010"]},"title":"Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1312.7873"}],"oa_version":"Preprint","month":"06","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","scopus_import":"1"},{"year":"2015","status":"public","intvolume":"        68","type":"journal_article","issue":"10","date_created":"2018-12-11T11:52:48Z","date_published":"2015-10-01T00:00:00Z","oa":1,"fulldoi":"https://doi.org/10.1002/cpa.21552","arxiv":1,"publication_status":"published","publication":"Communications on Pure and Applied Mathematics","publist_id":"5598","quality_controlled":"1","volume":68,"page":"1845 - 1884","isi":1,"author":[{"first_name":"Thomas","full_name":"Chen, Thomas","last_name":"Chen"},{"last_name":"Hainzl","full_name":"Hainzl, Christian","first_name":"Christian"},{"last_name":"Pavlović","first_name":"Nataša","full_name":"Pavlović, Nataša"},{"full_name":"Seiringer, Robert","first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"day":"01","date_updated":"2025-09-29T10:59:59Z","publisher":"Wiley","_id":"1573","external_id":{"isi":["000359670800004"],"arxiv":["1307.3168"]},"title":"Unconditional uniqueness for the cubic gross pitaevskii hierarchy via quantum de finetti","article_processing_charge":"No","abstract":[{"lang":"eng","text":"We present a new, simpler proof of the unconditional uniqueness of solutions to the cubic Gross-Pitaevskii hierarchy in ℝ3. One of the main tools in our analysis is the quantum de Finetti theorem. Our uniqueness result is equivalent to the one established in the celebrated works of Erdos, Schlein, and Yau."}],"doi":"10.1002/cpa.21552","citation":{"mla":"Chen, Thomas, et al. “Unconditional Uniqueness for the Cubic Gross Pitaevskii Hierarchy via Quantum de Finetti.” <i>Communications on Pure and Applied Mathematics</i>, vol. 68, no. 10, Wiley, 2015, pp. 1845–84, doi:<a href=\"https://doi.org/10.1002/cpa.21552\">10.1002/cpa.21552</a>.","apa":"Chen, T., Hainzl, C., Pavlović, N., &#38; Seiringer, R. (2015). Unconditional uniqueness for the cubic gross pitaevskii hierarchy via quantum de finetti. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.21552\">https://doi.org/10.1002/cpa.21552</a>","ieee":"T. Chen, C. Hainzl, N. Pavlović, and R. Seiringer, “Unconditional uniqueness for the cubic gross pitaevskii hierarchy via quantum de finetti,” <i>Communications on Pure and Applied Mathematics</i>, vol. 68, no. 10. Wiley, pp. 1845–1884, 2015.","ista":"Chen T, Hainzl C, Pavlović N, Seiringer R. 2015. Unconditional uniqueness for the cubic gross pitaevskii hierarchy via quantum de finetti. Communications on Pure and Applied Mathematics. 68(10), 1845–1884.","chicago":"Chen, Thomas, Christian Hainzl, Nataša Pavlović, and Robert Seiringer. “Unconditional Uniqueness for the Cubic Gross Pitaevskii Hierarchy via Quantum de Finetti.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2015. <a href=\"https://doi.org/10.1002/cpa.21552\">https://doi.org/10.1002/cpa.21552</a>.","short":"T. Chen, C. Hainzl, N. Pavlović, R. Seiringer, Communications on Pure and Applied Mathematics 68 (2015) 1845–1884.","ama":"Chen T, Hainzl C, Pavlović N, Seiringer R. Unconditional uniqueness for the cubic gross pitaevskii hierarchy via quantum de finetti. <i>Communications on Pure and Applied Mathematics</i>. 2015;68(10):1845-1884. doi:<a href=\"https://doi.org/10.1002/cpa.21552\">10.1002/cpa.21552</a>"},"department":[{"_id":"RoSe"}],"project":[{"name":"NSERC Postdoctoral fellowship","_id":"26450934-B435-11E9-9278-68D0E5697425"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1307.3168"}],"oa_version":"Preprint","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","month":"10","scopus_import":"1"},{"year":"2015","status":"public","intvolume":"       105","type":"journal_article","issue":"10","date_created":"2018-12-11T11:53:34Z","date_published":"2015-08-05T00:00:00Z","oa":1,"fulldoi":"https://doi.org/10.1007/s11005-015-0787-5","publication_status":"published","arxiv":1,"tmp":{"image":"/images/cc_by_nc.png","short":"CC BY-NC (4.0)","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode"},"publication":"Letters in Mathematical Physics","publist_id":"5432","file":[{"checksum":"fd7307282a314cc1fbbaef77b187516b","date_updated":"2020-07-14T12:45:13Z","relation":"main_file","access_level":"open_access","date_created":"2019-01-15T14:42:07Z","file_name":"2015_LettersMathPhys_Deuchert.pdf","file_size":484967,"creator":"dernst","file_id":"5836","content_type":"application/pdf"}],"quality_controlled":"1","volume":105,"page":"1449 - 1466","license":"https://creativecommons.org/licenses/by-nc/4.0/","isi":1,"author":[{"orcid":"0000-0003-3146-6746","last_name":"Deuchert","first_name":"Andreas","full_name":"Deuchert, Andreas"},{"first_name":"Christian","full_name":"Hainzl, Christian","last_name":"Hainzl"},{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","full_name":"Seiringer, Robert","first_name":"Robert"}],"day":"05","ddc":["510"],"date_updated":"2025-09-23T09:41:03Z","publisher":"Springer","_id":"1704","external_id":{"isi":["000361007600006"],"arxiv":["1502.07205"]},"title":"Note on a family of monotone quantum relative entropies","article_processing_charge":"No","abstract":[{"text":"Given a convex function (Formula presented.) and two hermitian matrices A and B, Lewin and Sabin study in (Lett Math Phys 104:691–705, 2014) the relative entropy defined by (Formula presented.). Among other things, they prove that the so-defined quantity is monotone if and only if (Formula presented.) is operator monotone. The monotonicity is then used to properly define (Formula presented.) for bounded self-adjoint operators acting on an infinite-dimensional Hilbert space by a limiting procedure. More precisely, for an increasing sequence of finite-dimensional projections (Formula presented.) with (Formula presented.) strongly, the limit (Formula presented.) is shown to exist and to be independent of the sequence of projections (Formula presented.). The question whether this sequence converges to its &quot;obvious&quot; limit, namely (Formula presented.), has been left open. We answer this question in principle affirmatively and show that (Formula presented.). If the operators A and B are regular enough, that is (A − B), (Formula presented.) and (Formula presented.) are trace-class, the identity (Formula presented.) holds.","lang":"eng"}],"file_date_updated":"2020-07-14T12:45:13Z","doi":"10.1007/s11005-015-0787-5","citation":{"mla":"Deuchert, Andreas, et al. “Note on a Family of Monotone Quantum Relative Entropies.” <i>Letters in Mathematical Physics</i>, vol. 105, no. 10, Springer, 2015, pp. 1449–66, doi:<a href=\"https://doi.org/10.1007/s11005-015-0787-5\">10.1007/s11005-015-0787-5</a>.","apa":"Deuchert, A., Hainzl, C., &#38; Seiringer, R. (2015). Note on a family of monotone quantum relative entropies. <i>Letters in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s11005-015-0787-5\">https://doi.org/10.1007/s11005-015-0787-5</a>","ieee":"A. Deuchert, C. Hainzl, and R. Seiringer, “Note on a family of monotone quantum relative entropies,” <i>Letters in Mathematical Physics</i>, vol. 105, no. 10. Springer, pp. 1449–1466, 2015.","ista":"Deuchert A, Hainzl C, Seiringer R. 2015. Note on a family of monotone quantum relative entropies. Letters in Mathematical Physics. 105(10), 1449–1466.","short":"A. Deuchert, C. Hainzl, R. Seiringer, Letters in Mathematical Physics 105 (2015) 1449–1466.","chicago":"Deuchert, Andreas, Christian Hainzl, and Robert Seiringer. “Note on a Family of Monotone Quantum Relative Entropies.” <i>Letters in Mathematical Physics</i>. Springer, 2015. <a href=\"https://doi.org/10.1007/s11005-015-0787-5\">https://doi.org/10.1007/s11005-015-0787-5</a>.","ama":"Deuchert A, Hainzl C, Seiringer R. Note on a family of monotone quantum relative entropies. <i>Letters in Mathematical Physics</i>. 2015;105(10):1449-1466. doi:<a href=\"https://doi.org/10.1007/s11005-015-0787-5\">10.1007/s11005-015-0787-5</a>"},"corr_author":"1","department":[{"_id":"RoSe"}],"has_accepted_license":"1","oa_version":"Preprint","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","language":[{"iso":"eng"}],"month":"08","scopus_import":"1"},{"oa_version":"Published Version","scopus_import":"1","month":"01","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","project":[{"name":"NSERC Postdoctoral fellowship","_id":"26450934-B435-11E9-9278-68D0E5697425"}],"article_number":"013022","doi":"10.1088/1367-2630/17/1/013022","file_date_updated":"2020-07-14T12:45:20Z","citation":{"chicago":"Könenberg, Martin, Thomas Moser, Robert Seiringer, and Jakob Yngvason. “Superfluid Behavior of a Bose-Einstein Condensate in a Random Potential.” <i>New Journal of Physics</i>. IOP Publishing, 2015. <a href=\"https://doi.org/10.1088/1367-2630/17/1/013022\">https://doi.org/10.1088/1367-2630/17/1/013022</a>.","short":"M. Könenberg, T. Moser, R. Seiringer, J. Yngvason, New Journal of Physics 17 (2015).","ama":"Könenberg M, Moser T, Seiringer R, Yngvason J. Superfluid behavior of a Bose-Einstein condensate in a random potential. <i>New Journal of Physics</i>. 2015;17. doi:<a href=\"https://doi.org/10.1088/1367-2630/17/1/013022\">10.1088/1367-2630/17/1/013022</a>","ieee":"M. Könenberg, T. Moser, R. Seiringer, and J. Yngvason, “Superfluid behavior of a Bose-Einstein condensate in a random potential,” <i>New Journal of Physics</i>, vol. 17. IOP Publishing, 2015.","ista":"Könenberg M, Moser T, Seiringer R, Yngvason J. 2015. Superfluid behavior of a Bose-Einstein condensate in a random potential. New Journal of Physics. 17, 013022.","mla":"Könenberg, Martin, et al. “Superfluid Behavior of a Bose-Einstein Condensate in a Random Potential.” <i>New Journal of Physics</i>, vol. 17, 013022, IOP Publishing, 2015, doi:<a href=\"https://doi.org/10.1088/1367-2630/17/1/013022\">10.1088/1367-2630/17/1/013022</a>.","apa":"Könenberg, M., Moser, T., Seiringer, R., &#38; Yngvason, J. (2015). Superfluid behavior of a Bose-Einstein condensate in a random potential. <i>New Journal of Physics</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1367-2630/17/1/013022\">https://doi.org/10.1088/1367-2630/17/1/013022</a>"},"abstract":[{"text":"We investigate the relation between Bose-Einstein condensation (BEC) and superfluidity in the ground state of a one-dimensional model of interacting bosons in a strong random potential. We prove rigorously that in a certain parameter regime the superfluid fraction can be arbitrarily small while complete BEC prevails. In another regime there is both complete BEC and complete superfluidity, despite the strong disorder","lang":"eng"}],"article_processing_charge":"No","has_accepted_license":"1","department":[{"_id":"RoSe"}],"acknowledgement":"Support from the Natural Sciences and Engineering Research Council of Canada NSERC (MK and RS) and from the Austrian Science Fund FWF (JY, under project P 22929-N16) is gratefully acknowledged","external_id":{"isi":["000348759300007"]},"publisher":"IOP Publishing","_id":"1880","ddc":["530"],"date_updated":"2025-09-23T10:51:00Z","title":"Superfluid behavior of a Bose-Einstein condensate in a random potential","pubrep_id":"447","day":"15","author":[{"last_name":"Könenberg","full_name":"Könenberg, Martin","first_name":"Martin"},{"first_name":"Thomas","full_name":"Moser, Thomas","last_name":"Moser","id":"2B5FC9A4-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert"},{"first_name":"Jakob","full_name":"Yngvason, Jakob","last_name":"Yngvason"}],"isi":1,"quality_controlled":"1","file":[{"file_name":"IST-2016-447-v1+1_document_1_.pdf","date_created":"2018-12-12T10:12:44Z","access_level":"open_access","date_updated":"2020-07-14T12:45:20Z","relation":"main_file","checksum":"38fdf2b5ac30445e26a5d613abd84b16","file_id":"4963","content_type":"application/pdf","creator":"system","file_size":768108}],"volume":17,"publication":"New Journal of Physics","tmp":{"image":"/images/cc_by.png","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"},"publication_status":"published","fulldoi":"https://doi.org/10.1088/1367-2630/17/1/013022","publist_id":"5214","type":"journal_article","intvolume":"        17","status":"public","year":"2015","oa":1,"date_published":"2015-01-15T00:00:00Z","date_created":"2018-12-11T11:54:30Z"},{"date_published":"2015-01-01T00:00:00Z","oa":1,"date_created":"2018-12-11T11:46:40Z","type":"journal_article","year":"2015","status":"public","intvolume":"         2","publist_id":"7344","tmp":{"name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)"},"publication":"Journal de l'Ecole Polytechnique - Mathematiques","fulldoi":"https://doi.org/10.5802/jep.18","publication_status":"published","volume":2,"file":[{"file_id":"4974","content_type":"application/pdf","creator":"system","file_size":1084254,"file_name":"IST-2018-951-v1+1_2015_Thanh-Nam_Derivation_of.pdf","access_level":"open_access","date_created":"2018-12-12T10:12:53Z","checksum":"a40eb4016717ddc9927154798a4c164a","date_updated":"2020-07-14T12:46:35Z","relation":"main_file"}],"quality_controlled":"1","day":"01","pubrep_id":"951","author":[{"full_name":"Lewin, Mathieu","first_name":"Mathieu","last_name":"Lewin"},{"first_name":"Nam","full_name":"Phan Thanh, Nam","last_name":"Phan Thanh","id":"404092F4-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Rougerie","full_name":"Rougerie, Nicolas","first_name":"Nicolas"}],"page":"65 - 115","license":"https://creativecommons.org/licenses/by-nd/4.0/","ec_funded":1,"title":"Derivation of nonlinear gibbs measures from many-body quantum mechanics","ddc":["539"],"date_updated":"2021-01-12T08:00:52Z","publisher":"Ecole Polytechnique","_id":"473","department":[{"_id":"RoSe"}],"has_accepted_license":"1","abstract":[{"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.","lang":"eng"}],"doi":"10.5802/jep.18","file_date_updated":"2020-07-14T12:46:35Z","citation":{"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.","ieee":"M. Lewin, P. Nam, and N. Rougerie, “Derivation of nonlinear gibbs measures from many-body quantum mechanics,” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>, vol. 2. Ecole Polytechnique, pp. 65–115, 2015.","ama":"Lewin M, Nam P, Rougerie N. Derivation of nonlinear gibbs measures from many-body quantum mechanics. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. 2015;2:65-115. doi:<a href=\"https://doi.org/10.5802/jep.18\">10.5802/jep.18</a>","chicago":"Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “Derivation of Nonlinear Gibbs Measures from Many-Body Quantum Mechanics.” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. Ecole Polytechnique, 2015. <a href=\"https://doi.org/10.5802/jep.18\">https://doi.org/10.5802/jep.18</a>.","short":"M. Lewin, P. Nam, N. Rougerie, Journal de l’Ecole Polytechnique - Mathematiques 2 (2015) 65–115.","apa":"Lewin, M., Nam, P., &#38; Rougerie, N. (2015). Derivation of nonlinear gibbs measures from many-body quantum mechanics. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. Ecole Polytechnique. <a href=\"https://doi.org/10.5802/jep.18\">https://doi.org/10.5802/jep.18</a>","mla":"Lewin, Mathieu, et al. “Derivation of Nonlinear Gibbs Measures from Many-Body Quantum Mechanics.” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>, vol. 2, Ecole Polytechnique, 2015, pp. 65–115, doi:<a href=\"https://doi.org/10.5802/jep.18\">10.5802/jep.18</a>."},"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"scopus_import":1,"month":"01","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version"},{"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1401.1727"}],"scopus_import":"1","month":"05","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","abstract":[{"lang":"eng","text":"We study a double Cahn-Hilliard type functional related to the Gross-Pitaevskii energy of two-components Bose-Einstein condensates. In the case of large but same order intercomponent and intracomponent coupling strengths, we prove Γ-convergence to a perimeter minimisation functional with an inhomogeneous surface tension. We study the asymptotic behavior of the surface tension as the ratio between the intercomponent and intracomponent coupling strengths becomes very small or very large and obtain good agreement with the physical literature. We obtain as a consequence, symmetry breaking of the minimisers for the harmonic potential."}],"citation":{"chicago":"Goldman, Michael, and Jimena Royo-Letelier. “Sharp Interface Limit for Two Components Bose-Einstein Condensates.” <i>ESAIM - Control, Optimisation and Calculus of Variations</i>. EDP Sciences, 2015. <a href=\"https://doi.org/10.1051/cocv/2014040\">https://doi.org/10.1051/cocv/2014040</a>.","short":"M. Goldman, J. Royo-Letelier, ESAIM - Control, Optimisation and Calculus of Variations 21 (2015) 603–624.","ama":"Goldman M, Royo-Letelier J. Sharp interface limit for two components Bose-Einstein condensates. <i>ESAIM - Control, Optimisation and Calculus of Variations</i>. 2015;21(3):603-624. doi:<a href=\"https://doi.org/10.1051/cocv/2014040\">10.1051/cocv/2014040</a>","ieee":"M. Goldman and J. Royo-Letelier, “Sharp interface limit for two components Bose-Einstein condensates,” <i>ESAIM - Control, Optimisation and Calculus of Variations</i>, vol. 21, no. 3. EDP Sciences, pp. 603–624, 2015.","ista":"Goldman M, Royo-Letelier J. 2015. Sharp interface limit for two components Bose-Einstein condensates. ESAIM - Control, Optimisation and Calculus of Variations. 21(3), 603–624.","mla":"Goldman, Michael, and Jimena Royo-Letelier. “Sharp Interface Limit for Two Components Bose-Einstein Condensates.” <i>ESAIM - Control, Optimisation and Calculus of Variations</i>, vol. 21, no. 3, EDP Sciences, 2015, pp. 603–24, doi:<a href=\"https://doi.org/10.1051/cocv/2014040\">10.1051/cocv/2014040</a>.","apa":"Goldman, M., &#38; Royo-Letelier, J. (2015). Sharp interface limit for two components Bose-Einstein condensates. <i>ESAIM - Control, Optimisation and Calculus of Variations</i>. EDP Sciences. <a href=\"https://doi.org/10.1051/cocv/2014040\">https://doi.org/10.1051/cocv/2014040</a>"},"doi":"10.1051/cocv/2014040","article_processing_charge":"No","department":[{"_id":"RoSe"}],"corr_author":"1","external_id":{"isi":["000356012000001"],"arxiv":["1401.1727"]},"date_updated":"2025-09-23T10:45:09Z","_id":"1807","publisher":"EDP Sciences","title":"Sharp interface limit for two components Bose-Einstein condensates","page":"603 - 624","day":"01","isi":1,"author":[{"first_name":"Michael","full_name":"Goldman, Michael","last_name":"Goldman"},{"first_name":"Jimena","full_name":"Royo-Letelier, Jimena","last_name":"Royo-Letelier","id":"4D3BED28-F248-11E8-B48F-1D18A9856A87"}],"quality_controlled":"1","volume":21,"publication":"ESAIM - Control, Optimisation and Calculus of Variations","fulldoi":"https://doi.org/10.1051/cocv/2014040","publication_status":"published","arxiv":1,"publist_id":"5303","type":"journal_article","issue":"3","status":"public","year":"2015","intvolume":"        21","date_published":"2015-05-01T00:00:00Z","oa":1,"date_created":"2018-12-11T11:54:07Z"},{"intvolume":"       104","year":"2014","status":"public","issue":"2","type":"journal_article","date_created":"2018-12-11T11:56:44Z","oa":1,"date_published":"2014-02-01T00:00:00Z","arxiv":1,"publication_status":"published","fulldoi":"https://doi.org/10.1007/s11005-013-0667-9","publication":"Letters in Mathematical Physics","publist_id":"4653","article_type":"original","quality_controlled":"1","volume":104,"page":"141 - 156","author":[{"first_name":"Yujin","full_name":"Guo, Yujin","last_name":"Guo"},{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert"}],"isi":1,"day":"01","_id":"2281","publisher":"Springer","date_updated":"2025-09-29T11:12:19Z","external_id":{"arxiv":["1301.5682"],"isi":["000330128000002"]},"title":"On the mass concentration for Bose-Einstein condensates with attractive interactions","article_processing_charge":"No","citation":{"ieee":"Y. Guo and R. Seiringer, “On the mass concentration for Bose-Einstein condensates with attractive interactions,” <i>Letters in Mathematical Physics</i>, vol. 104, no. 2. Springer, pp. 141–156, 2014.","ista":"Guo Y, Seiringer R. 2014. On the mass concentration for Bose-Einstein condensates with attractive interactions. Letters in Mathematical Physics. 104(2), 141–156.","short":"Y. Guo, R. Seiringer, Letters in Mathematical Physics 104 (2014) 141–156.","chicago":"Guo, Yujin, and Robert Seiringer. “On the Mass Concentration for Bose-Einstein Condensates with Attractive Interactions.” <i>Letters in Mathematical Physics</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s11005-013-0667-9\">https://doi.org/10.1007/s11005-013-0667-9</a>.","ama":"Guo Y, Seiringer R. On the mass concentration for Bose-Einstein condensates with attractive interactions. <i>Letters in Mathematical Physics</i>. 2014;104(2):141-156. doi:<a href=\"https://doi.org/10.1007/s11005-013-0667-9\">10.1007/s11005-013-0667-9</a>","mla":"Guo, Yujin, and Robert Seiringer. “On the Mass Concentration for Bose-Einstein Condensates with Attractive Interactions.” <i>Letters in Mathematical Physics</i>, vol. 104, no. 2, Springer, 2014, pp. 141–56, doi:<a href=\"https://doi.org/10.1007/s11005-013-0667-9\">10.1007/s11005-013-0667-9</a>.","apa":"Guo, Y., &#38; Seiringer, R. (2014). On the mass concentration for Bose-Einstein condensates with attractive interactions. <i>Letters in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s11005-013-0667-9\">https://doi.org/10.1007/s11005-013-0667-9</a>"},"doi":"10.1007/s11005-013-0667-9","abstract":[{"lang":"eng","text":"We consider two-dimensional Bose-Einstein condensates with attractive interaction, described by the Gross-Pitaevskii functional. Minimizers of this functional exist only if the interaction strength a satisfies {Mathematical expression}, where Q is the unique positive radial solution of {Mathematical expression} in {Mathematical expression}. We present a detailed analysis of the behavior of minimizers as a approaches a*, where all the mass concentrates at a global minimum of the trapping potential."}],"corr_author":"1","department":[{"_id":"RoSe"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1301.5682"}],"oa_version":"Preprint","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","month":"02","scopus_import":"1"},{"scopus_import":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","language":[{"iso":"eng"}],"month":"05","oa_version":"Submitted Version","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1311.2136"}],"project":[{"name":"NSERC Postdoctoral fellowship","_id":"26450934-B435-11E9-9278-68D0E5697425"}],"department":[{"_id":"RoSe"}],"abstract":[{"lang":"eng","text":"We prove the existence of scattering states for the defocusing cubic Gross-Pitaevskii (GP) hierarchy in ℝ3. Moreover, we show that an exponential energy growth condition commonly used in the well-posedness theory of the GP hierarchy is, in a specific sense, necessary. In fact, we prove that without the latter, there exist initial data for the focusing cubic GP hierarchy for which instantaneous blowup occurs."}],"citation":{"ieee":"T. Chen, C. Hainzl, N. Pavlović, and R. Seiringer, “On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti,” <i>Letters in Mathematical Physics</i>, vol. 104, no. 7. Springer, pp. 871–891, 2014.","ista":"Chen T, Hainzl C, Pavlović N, Seiringer R. 2014. On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti. Letters in Mathematical Physics. 104(7), 871–891.","chicago":"Chen, Thomas, Christian Hainzl, Nataša Pavlović, and Robert Seiringer. “On the Well-Posedness and Scattering for the Gross-Pitaevskii Hierarchy via Quantum de Finetti.” <i>Letters in Mathematical Physics</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s11005-014-0693-2\">https://doi.org/10.1007/s11005-014-0693-2</a>.","short":"T. Chen, C. Hainzl, N. Pavlović, R. Seiringer, Letters in Mathematical Physics 104 (2014) 871–891.","ama":"Chen T, Hainzl C, Pavlović N, Seiringer R. On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti. <i>Letters in Mathematical Physics</i>. 2014;104(7):871-891. doi:<a href=\"https://doi.org/10.1007/s11005-014-0693-2\">10.1007/s11005-014-0693-2</a>","mla":"Chen, Thomas, et al. “On the Well-Posedness and Scattering for the Gross-Pitaevskii Hierarchy via Quantum de Finetti.” <i>Letters in Mathematical Physics</i>, vol. 104, no. 7, Springer, 2014, pp. 871–91, doi:<a href=\"https://doi.org/10.1007/s11005-014-0693-2\">10.1007/s11005-014-0693-2</a>.","apa":"Chen, T., Hainzl, C., Pavlović, N., &#38; Seiringer, R. (2014). On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti. <i>Letters in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s11005-014-0693-2\">https://doi.org/10.1007/s11005-014-0693-2</a>"},"doi":"10.1007/s11005-014-0693-2","article_processing_charge":"No","title":"On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti","external_id":{"arxiv":["1311.2136"],"isi":["000336412300005"]},"date_updated":"2025-09-29T11:33:31Z","publisher":"Springer","_id":"2186","day":"07","isi":1,"author":[{"last_name":"Chen","full_name":"Chen, Thomas","first_name":"Thomas"},{"first_name":"Christian","full_name":"Hainzl, Christian","last_name":"Hainzl"},{"full_name":"Pavlović, Nataša","first_name":"Nataša","last_name":"Pavlović"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","first_name":"Robert"}],"page":"871 - 891","volume":104,"quality_controlled":"1","publist_id":"4793","publication":"Letters in Mathematical Physics","fulldoi":"https://doi.org/10.1007/s11005-014-0693-2","arxiv":1,"publication_status":"published","date_published":"2014-05-07T00:00:00Z","oa":1,"date_created":"2018-12-11T11:56:12Z","type":"journal_article","issue":"7","year":"2014","status":"public","intvolume":"       104"},{"publication":"Proceedings of the QMath12 Conference","arxiv":1,"publication_status":"published","fulldoi":"https://doi.org/10.1142/9789814618144_0007","conference":{"name":"QMath: Mathematical Results in Quantum Physics","end_date":"2013-09-13","start_date":"2013-09-10","location":"Berlin, Germany"},"publist_id":"5661","type":"conference","status":"public","year":"2014","oa":1,"date_published":"2014-01-01T00:00:00Z","date_created":"2018-12-11T11:52:28Z","page":"127 - 137","day":"01","author":[{"last_name":"Bräunlich","first_name":"Gerhard","full_name":"Bräunlich, Gerhard"},{"last_name":"Hainzl","first_name":"Christian","full_name":"Hainzl, Christian"},{"first_name":"Robert","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"quality_controlled":"1","citation":{"short":"G. Bräunlich, C. Hainzl, R. Seiringer, in:, Proceedings of the QMath12 Conference, World Scientific Publishing, 2014, pp. 127–137.","chicago":"Bräunlich, Gerhard, Christian Hainzl, and Robert Seiringer. “On the BCS Gap Equation for Superfluid Fermionic Gases.” In <i>Proceedings of the QMath12 Conference</i>, 127–37. World Scientific Publishing, 2014. <a href=\"https://doi.org/10.1142/9789814618144_0007\">https://doi.org/10.1142/9789814618144_0007</a>.","ama":"Bräunlich G, Hainzl C, Seiringer R. On the BCS gap equation for superfluid fermionic gases. In: <i>Proceedings of the QMath12 Conference</i>. World Scientific Publishing; 2014:127-137. doi:<a href=\"https://doi.org/10.1142/9789814618144_0007\">10.1142/9789814618144_0007</a>","ieee":"G. Bräunlich, C. Hainzl, and R. Seiringer, “On the BCS gap equation for superfluid fermionic gases,” in <i>Proceedings of the QMath12 Conference</i>, Berlin, Germany, 2014, pp. 127–137.","ista":"Bräunlich G, Hainzl C, Seiringer R. 2014. On the BCS gap equation for superfluid fermionic gases. Proceedings of the QMath12 Conference. QMath: Mathematical Results in Quantum Physics, 127–137.","mla":"Bräunlich, Gerhard, et al. “On the BCS Gap Equation for Superfluid Fermionic Gases.” <i>Proceedings of the QMath12 Conference</i>, World Scientific Publishing, 2014, pp. 127–37, doi:<a href=\"https://doi.org/10.1142/9789814618144_0007\">10.1142/9789814618144_0007</a>.","apa":"Bräunlich, G., Hainzl, C., &#38; Seiringer, R. (2014). On the BCS gap equation for superfluid fermionic gases. In <i>Proceedings of the QMath12 Conference</i> (pp. 127–137). Berlin, Germany: World Scientific Publishing. <a href=\"https://doi.org/10.1142/9789814618144_0007\">https://doi.org/10.1142/9789814618144_0007</a>"},"doi":"10.1142/9789814618144_0007","abstract":[{"lang":"eng","text":"We present a rigorous derivation of the BCS gap equation for superfluid fermionic gases with point interactions. Our starting point is the BCS energy functional, whose minimizer we investigate in the limit when the range of the interaction potential goes to zero.\r\n"}],"article_processing_charge":"No","department":[{"_id":"RoSe"}],"external_id":{"arxiv":["1403.2563"]},"publisher":"World Scientific Publishing","_id":"1516","date_updated":"2021-01-12T06:51:19Z","title":"On the BCS gap equation for superfluid fermionic gases","oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1403.2563","open_access":"1"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"month":"01"},{"day":"01","author":[{"last_name":"Bräunlich","first_name":"Gerhard","full_name":"Bräunlich, Gerhard"},{"last_name":"Hainzl","first_name":"Christian","full_name":"Hainzl, Christian"},{"first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}],"isi":1,"volume":26,"quality_controlled":"1","article_type":"original","publist_id":"5206","publication":"Reviews in Mathematical Physics","publication_status":"published","arxiv":1,"fulldoi":"https://doi.org/10.1142/S0129055X14500123","oa":1,"date_published":"2014-08-01T00:00:00Z","date_created":"2018-12-11T11:54:33Z","issue":"7","type":"journal_article","intvolume":"        26","status":"public","year":"2014","scopus_import":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","month":"08","language":[{"iso":"eng"}],"oa_version":"Submitted Version","main_file_link":[{"url":"http://arxiv.org/abs/1305.5135","open_access":"1"}],"article_number":"1450012","department":[{"_id":"RoSe"}],"doi":"10.1142/S0129055X14500123","citation":{"mla":"Bräunlich, Gerhard, et al. “Translation-Invariant Quasi-Free States for Fermionic Systems and the BCS Approximation.” <i>Reviews in Mathematical Physics</i>, vol. 26, no. 7, 1450012, World Scientific Publishing, 2014, doi:<a href=\"https://doi.org/10.1142/S0129055X14500123\">10.1142/S0129055X14500123</a>.","apa":"Bräunlich, G., Hainzl, C., &#38; Seiringer, R. (2014). Translation-invariant quasi-free states for fermionic systems and the BCS approximation. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0129055X14500123\">https://doi.org/10.1142/S0129055X14500123</a>","ieee":"G. Bräunlich, C. Hainzl, and R. Seiringer, “Translation-invariant quasi-free states for fermionic systems and the BCS approximation,” <i>Reviews in Mathematical Physics</i>, vol. 26, no. 7. World Scientific Publishing, 2014.","ista":"Bräunlich G, Hainzl C, Seiringer R. 2014. Translation-invariant quasi-free states for fermionic systems and the BCS approximation. Reviews in Mathematical Physics. 26(7), 1450012.","chicago":"Bräunlich, Gerhard, Christian Hainzl, and Robert Seiringer. “Translation-Invariant Quasi-Free States for Fermionic Systems and the BCS Approximation.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2014. <a href=\"https://doi.org/10.1142/S0129055X14500123\">https://doi.org/10.1142/S0129055X14500123</a>.","short":"G. Bräunlich, C. Hainzl, R. Seiringer, Reviews in Mathematical Physics 26 (2014).","ama":"Bräunlich G, Hainzl C, Seiringer R. Translation-invariant quasi-free states for fermionic systems and the BCS approximation. <i>Reviews in Mathematical Physics</i>. 2014;26(7). doi:<a href=\"https://doi.org/10.1142/S0129055X14500123\">10.1142/S0129055X14500123</a>"},"abstract":[{"text":"We study translation-invariant quasi-free states for a system of fermions with two-particle interactions. The associated energy functional is similar to the BCS functional but also includes direct and exchange energies. We show that for suitable short-range interactions, these latter terms only lead to a renormalization of the chemical potential, with the usual properties of the BCS functional left unchanged. Our analysis thus represents a rigorous justification of part of the BCS approximation. We give bounds on the critical temperature below which the system displays superfluidity.","lang":"eng"}],"article_processing_charge":"No","title":"Translation-invariant quasi-free states for fermionic systems and the BCS approximation","acknowledgement":"We would like to thank Max Lein and Andreas Deuchert for valuable suggestions and remarks. Partial financial support by the NSERC (R.S.) is gratefully acknowledged.","external_id":{"arxiv":["1305.5135"],"isi":["000341933500002"]},"publisher":"World Scientific Publishing","_id":"1889","date_updated":"2025-09-29T13:07:59Z"},{"scopus_import":"1","month":"02","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa_version":"Submitted Version","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1301.5370"}],"article_number":"1350021","project":[{"_id":"26450934-B435-11E9-9278-68D0E5697425","name":"NSERC Postdoctoral fellowship"}],"department":[{"_id":"RoSe"}],"corr_author":"1","citation":{"short":"J. Bellazzini, R. Frank, É. Lieb, R. Seiringer, Reviews in Mathematical Physics 26 (2014).","chicago":"Bellazzini, Jacopo, Rupert Frank, Élliott Lieb, and Robert Seiringer. “Existence of Ground States for Negative Ions at the Binding Threshold.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2014. <a href=\"https://doi.org/10.1142/S0129055X13500219\">https://doi.org/10.1142/S0129055X13500219</a>.","ama":"Bellazzini J, Frank R, Lieb É, Seiringer R. Existence of ground states for negative ions at the binding threshold. <i>Reviews in Mathematical Physics</i>. 2014;26(1). doi:<a href=\"https://doi.org/10.1142/S0129055X13500219\">10.1142/S0129055X13500219</a>","ieee":"J. Bellazzini, R. Frank, É. Lieb, and R. Seiringer, “Existence of ground states for negative ions at the binding threshold,” <i>Reviews in Mathematical Physics</i>, vol. 26, no. 1. World Scientific Publishing, 2014.","ista":"Bellazzini J, Frank R, Lieb É, Seiringer R. 2014. Existence of ground states for negative ions at the binding threshold. Reviews in Mathematical Physics. 26(1), 1350021.","mla":"Bellazzini, Jacopo, et al. “Existence of Ground States for Negative Ions at the Binding Threshold.” <i>Reviews in Mathematical Physics</i>, vol. 26, no. 1, 1350021, World Scientific Publishing, 2014, doi:<a href=\"https://doi.org/10.1142/S0129055X13500219\">10.1142/S0129055X13500219</a>.","apa":"Bellazzini, J., Frank, R., Lieb, É., &#38; Seiringer, R. (2014). Existence of ground states for negative ions at the binding threshold. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0129055X13500219\">https://doi.org/10.1142/S0129055X13500219</a>"},"doi":"10.1142/S0129055X13500219","abstract":[{"lang":"eng","text":"As the nuclear charge Z is continuously decreased an N-electron atom undergoes a binding-unbinding transition. We investigate whether the electrons remain bound and whether the radius of the system stays finite as the critical value Zc is approached. Existence of a ground state at Zc is shown under the condition Zc &lt; N-K, where K is the maximal number of electrons that can be removed at Zc without changing the energy."}],"article_processing_charge":"No","title":"Existence of ground states for negative ions at the binding threshold","external_id":{"arxiv":["1301.5370"],"isi":["000329928300004"]},"publisher":"World Scientific Publishing","_id":"1918","date_updated":"2025-09-29T12:19:33Z","day":"01","author":[{"full_name":"Bellazzini, Jacopo","first_name":"Jacopo","last_name":"Bellazzini"},{"first_name":"Rupert","full_name":"Frank, Rupert","last_name":"Frank"},{"full_name":"Lieb, Élliott","first_name":"Élliott","last_name":"Lieb"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert"}],"isi":1,"volume":26,"quality_controlled":"1","publist_id":"5176","publication":"Reviews in Mathematical Physics","publication_status":"published","arxiv":1,"fulldoi":"https://doi.org/10.1142/S0129055X13500219","oa":1,"date_published":"2014-02-01T00:00:00Z","date_created":"2018-12-11T11:54:42Z","issue":"1","type":"journal_article","intvolume":"        26","status":"public","year":"2014"},{"acknowledgement":"2014 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.\r\n\r\nThe research leading to these results has received funding from the European Research\r\nCouncil under the European Union’s Seventh Framework Programme ERC Starting Grant CoMBoS (Grant Agreement No. 239694; A.G. and R.S.), the U.S. National Science Foundation (Grant PHY 0965859; E.H.L.), the Simons Foundation (Grant # 230207; E.H.L) and the NSERC (R.S.). The work is part of a project started in collaboration with Joel Lebowitz, whom we thank for many useful discussions and for his constant encouragement.","external_id":{"isi":["000339732500011"],"arxiv":["1304.6344"]},"_id":"1935","publisher":"Springer","date_updated":"2025-09-29T12:08:54Z","ddc":["510"],"title":"Formation of stripes and slabs near the ferromagnetic transition","file_date_updated":"2022-05-24T08:30:40Z","doi":"10.1007/s00220-014-1923-2","citation":{"ista":"Giuliani A, Lieb É, Seiringer R. 2014. Formation of stripes and slabs near the ferromagnetic transition. Communications in Mathematical Physics. 331, 333–350.","ieee":"A. Giuliani, É. Lieb, and R. Seiringer, “Formation of stripes and slabs near the ferromagnetic transition,” <i>Communications in Mathematical Physics</i>, vol. 331. Springer, pp. 333–350, 2014.","ama":"Giuliani A, Lieb É, Seiringer R. Formation of stripes and slabs near the ferromagnetic transition. <i>Communications in Mathematical Physics</i>. 2014;331:333-350. doi:<a href=\"https://doi.org/10.1007/s00220-014-1923-2\">10.1007/s00220-014-1923-2</a>","chicago":"Giuliani, Alessandro, Élliott Lieb, and Robert Seiringer. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” <i>Communications in Mathematical Physics</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s00220-014-1923-2\">https://doi.org/10.1007/s00220-014-1923-2</a>.","short":"A. Giuliani, É. Lieb, R. Seiringer, Communications in Mathematical Physics 331 (2014) 333–350.","apa":"Giuliani, A., Lieb, É., &#38; Seiringer, R. (2014). Formation of stripes and slabs near the ferromagnetic transition. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-014-1923-2\">https://doi.org/10.1007/s00220-014-1923-2</a>","mla":"Giuliani, Alessandro, et al. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” <i>Communications in Mathematical Physics</i>, vol. 331, Springer, 2014, pp. 333–50, doi:<a href=\"https://doi.org/10.1007/s00220-014-1923-2\">10.1007/s00220-014-1923-2</a>."},"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"abstract":[{"text":"We consider Ising models in d = 2 and d = 3 dimensions with nearest neighbor ferromagnetic and long-range antiferromagnetic interactions, the latter decaying as (distance)-p, p &gt; 2d, at large distances. If the strength J of the ferromagnetic interaction is larger than a critical value J c, then the ground state is homogeneous. It has been conjectured that when J is smaller than but close to J c, the ground state is periodic and striped, with stripes of constant width h = h(J), and h → ∞ as J → Jc -. (In d = 3 stripes mean slabs, not columns.) Here we rigorously prove that, if we normalize the energy in such a way that the energy of the homogeneous state is zero, then the ratio e 0(J)/e S(J) tends to 1 as J → Jc -, with e S(J) being the energy per site of the optimal periodic striped/slabbed state and e 0(J) the actual ground state energy per site of the system. Our proof comes with explicit bounds on the difference e 0(J)-e S(J) at small but positive J c-J, and also shows that in this parameter range the ground state is striped/slabbed in a certain sense: namely, if one looks at a randomly chosen window, of suitable size ℓ (very large compared to the optimal stripe size h(J)), one finds a striped/slabbed state with high probability.","lang":"eng"}],"article_processing_charge":"No","has_accepted_license":"1","department":[{"_id":"RoSe"}],"oa_version":"Published Version","scopus_import":"1","language":[{"iso":"eng"}],"month":"10","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"journal_article","intvolume":"       331","status":"public","year":"2014","oa":1,"date_published":"2014-10-01T00:00:00Z","date_created":"2018-12-11T11:54:48Z","publication":"Communications in Mathematical Physics","arxiv":1,"publication_status":"published","fulldoi":"https://doi.org/10.1007/s00220-014-1923-2","publist_id":"5159","quality_controlled":"1","file":[{"date_updated":"2022-05-24T08:30:40Z","relation":"main_file","checksum":"c8423271cd1e1ba9e44c47af75efe7b6","date_created":"2022-05-24T08:30:40Z","access_level":"open_access","file_name":"2014_CommMathPhysics_Giuliani.pdf","file_size":334064,"creator":"dernst","content_type":"application/pdf","file_id":"11409","success":1}],"article_type":"original","volume":331,"page":"333 - 350","day":"01","author":[{"full_name":"Giuliani, Alessandro","first_name":"Alessandro","last_name":"Giuliani"},{"first_name":"Élliott","full_name":"Lieb, Élliott","last_name":"Lieb"},{"full_name":"Seiringer, Robert","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521"}],"isi":1},{"volume":108,"quality_controlled":"1","isi":1,"author":[{"full_name":"Correggi, Michele","first_name":"Michele","last_name":"Correggi"},{"full_name":"Giuliani, Alessandro","first_name":"Alessandro","last_name":"Giuliani"},{"full_name":"Seiringer, Robert","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer"}],"day":"13","date_created":"2018-12-11T11:55:18Z","date_published":"2014-10-13T00:00:00Z","oa":1,"year":"2014","status":"public","intvolume":"       108","type":"journal_article","issue":"2","publist_id":"5044","fulldoi":"https://doi.org/10.1209/0295-5075/108/20003","publication_status":"published","arxiv":1,"publication":"EPL","article_number":"20003","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","month":"10","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1404.4717"}],"oa_version":"Submitted Version","title":"Validity of spin-wave theory for the quantum Heisenberg model","date_updated":"2025-09-29T11:55:55Z","_id":"2029","publisher":"IOP Publishing","external_id":{"arxiv":["1404.4717"],"isi":["000344913300003"]},"acknowledgement":"239694; ERC; European Research Council","department":[{"_id":"RoSe"}],"article_processing_charge":"No","abstract":[{"text":"Spin-wave theory is a key ingredient in our comprehension of quantum spin systems, and is used successfully for understanding a wide range of magnetic phenomena, including magnon condensation and stability of patterns in dipolar systems. Nevertheless, several decades of research failed to establish the validity of spin-wave theory rigorously, even for the simplest models of quantum spins. A rigorous justification of the method for the three-dimensional quantum Heisenberg ferromagnet at low temperatures is presented here. We derive sharp bounds on its free energy by combining a bosonic formulation of the model introduced by Holstein and Primakoff with probabilistic estimates and operator inequalities.","lang":"eng"}],"doi":"10.1209/0295-5075/108/20003","citation":{"mla":"Correggi, Michele, et al. “Validity of Spin-Wave Theory for the Quantum Heisenberg Model.” <i>EPL</i>, vol. 108, no. 2, 20003, IOP Publishing, 2014, doi:<a href=\"https://doi.org/10.1209/0295-5075/108/20003\">10.1209/0295-5075/108/20003</a>.","apa":"Correggi, M., Giuliani, A., &#38; Seiringer, R. (2014). Validity of spin-wave theory for the quantum Heisenberg model. <i>EPL</i>. IOP Publishing. <a href=\"https://doi.org/10.1209/0295-5075/108/20003\">https://doi.org/10.1209/0295-5075/108/20003</a>","ieee":"M. Correggi, A. Giuliani, and R. Seiringer, “Validity of spin-wave theory for the quantum Heisenberg model,” <i>EPL</i>, vol. 108, no. 2. IOP Publishing, 2014.","ista":"Correggi M, Giuliani A, Seiringer R. 2014. Validity of spin-wave theory for the quantum Heisenberg model. EPL. 108(2), 20003.","chicago":"Correggi, Michele, Alessandro Giuliani, and Robert Seiringer. “Validity of Spin-Wave Theory for the Quantum Heisenberg Model.” <i>EPL</i>. IOP Publishing, 2014. <a href=\"https://doi.org/10.1209/0295-5075/108/20003\">https://doi.org/10.1209/0295-5075/108/20003</a>.","short":"M. Correggi, A. Giuliani, R. Seiringer, EPL 108 (2014).","ama":"Correggi M, Giuliani A, Seiringer R. Validity of spin-wave theory for the quantum Heisenberg model. <i>EPL</i>. 2014;108(2). doi:<a href=\"https://doi.org/10.1209/0295-5075/108/20003\">10.1209/0295-5075/108/20003</a>"}}]