[{"status":"public","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"oa":1,"month":"08","ec_funded":1,"date_updated":"2023-12-13T11:31:14Z","issue":"4","arxiv":1,"abstract":[{"lang":"eng","text":"Recently the leading order of the correlation energy of a Fermi gas in a coupled mean-field and semiclassical scaling regime has been derived, under the assumption of an interaction potential with a small norm and with compact support in Fourier space. We generalize this result to large interaction potentials, requiring only |⋅|V^∈ℓ1(Z3). Our proof is based on approximate, collective bosonization in three dimensions. Significant improvements compared to recent work include stronger bounds on non-bosonizable terms and more efficient control on the bosonization of the kinetic energy."}],"year":"2023","article_number":"65","_id":"13225","file_date_updated":"2023-11-14T13:12:12Z","scopus_import":"1","ddc":["510"],"intvolume":"       247","citation":{"ieee":"N. P. Benedikter, M. Porta, B. Schlein, and R. Seiringer, “Correlation energy of a weakly interacting Fermi gas with large interaction potential,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 247, no. 4. Springer Nature, 2023.","ama":"Benedikter NP, Porta M, Schlein B, Seiringer R. Correlation energy of a weakly interacting Fermi gas with large interaction potential. <i>Archive for Rational Mechanics and Analysis</i>. 2023;247(4). doi:<a href=\"https://doi.org/10.1007/s00205-023-01893-6\">10.1007/s00205-023-01893-6</a>","short":"N.P. Benedikter, M. Porta, B. Schlein, R. Seiringer, Archive for Rational Mechanics and Analysis 247 (2023).","chicago":"Benedikter, Niels P, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00205-023-01893-6\">https://doi.org/10.1007/s00205-023-01893-6</a>.","apa":"Benedikter, N. P., Porta, M., Schlein, B., &#38; Seiringer, R. (2023). Correlation energy of a weakly interacting Fermi gas with large interaction potential. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-023-01893-6\">https://doi.org/10.1007/s00205-023-01893-6</a>","ista":"Benedikter NP, Porta M, Schlein B, Seiringer R. 2023. Correlation energy of a weakly interacting Fermi gas with large interaction potential. Archive for Rational Mechanics and Analysis. 247(4), 65.","mla":"Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 247, no. 4, 65, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00205-023-01893-6\">10.1007/s00205-023-01893-6</a>."},"publication_status":"published","doi":"10.1007/s00205-023-01893-6","oa_version":"Published Version","date_published":"2023-08-01T00:00:00Z","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Correlation energy of a weakly interacting Fermi gas with large interaction potential","license":"https://creativecommons.org/licenses/by/4.0/","acknowledgement":"RS was supported by the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227). MP acknowledges financial support from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (ERC StG MaMBoQ, Grant Agreement No. 802901). BS acknowledges financial support from the NCCR SwissMAP, from the Swiss National Science Foundation through the Grant “Dynamical and energetic properties of Bose-Einstein condensates” and from the European Research Council through the ERC AdG CLaQS (Grant Agreement No. 834782). NB and MP were supported by Gruppo Nazionale per la Fisica Matematica (GNFM) of Italy. NB was supported by the European Research Council’s Starting Grant FERMIMATH (Grant Agreement No. 101040991).\r\nOpen access funding provided by Università degli Studi di Milano within the CRUI-CARE Agreement.","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"01","project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems"}],"isi":1,"author":[{"full_name":"Benedikter, Niels P","orcid":"0000-0002-1071-6091","first_name":"Niels P","last_name":"Benedikter","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Porta","first_name":"Marcello","full_name":"Porta, Marcello"},{"first_name":"Benjamin","last_name":"Schlein","full_name":"Schlein, Benjamin"},{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert"}],"file":[{"access_level":"open_access","checksum":"2b45828d854a253b14bf7aa196ec55e9","file_id":"14535","creator":"dernst","date_created":"2023-11-14T13:12:12Z","date_updated":"2023-11-14T13:12:12Z","file_name":"2023_ArchiveRationalMechAnalysis_Benedikter.pdf","success":1,"file_size":851626,"content_type":"application/pdf","relation":"main_file"}],"article_type":"original","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2106.13185"],"isi":["001024369000001"]},"quality_controlled":"1","volume":247,"has_accepted_license":"1","date_created":"2023-07-16T22:01:08Z","publication":"Archive for Rational Mechanics and Analysis","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"RoSe"}]},{"citation":{"ama":"Benedikter NP. Bosonic collective excitations in Fermi gases. <i>Reviews in Mathematical Physics</i>. 2021;33(1). doi:<a href=\"https://doi.org/10.1142/s0129055x20600090\">10.1142/s0129055x20600090</a>","ieee":"N. P. Benedikter, “Bosonic collective excitations in Fermi gases,” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 1. World Scientific, 2021.","short":"N.P. Benedikter, Reviews in Mathematical Physics 33 (2021).","ista":"Benedikter NP. 2021. Bosonic collective excitations in Fermi gases. Reviews in Mathematical Physics. 33(1), 2060009.","apa":"Benedikter, N. P. (2021). Bosonic collective excitations in Fermi gases. <i>Reviews in Mathematical Physics</i>. World Scientific. <a href=\"https://doi.org/10.1142/s0129055x20600090\">https://doi.org/10.1142/s0129055x20600090</a>","mla":"Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 1, 2060009, World Scientific, 2021, doi:<a href=\"https://doi.org/10.1142/s0129055x20600090\">10.1142/s0129055x20600090</a>.","chicago":"Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” <i>Reviews in Mathematical Physics</i>. World Scientific, 2021. <a href=\"https://doi.org/10.1142/s0129055x20600090\">https://doi.org/10.1142/s0129055x20600090</a>."},"intvolume":"        33","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.08190"}],"oa_version":"Preprint","date_published":"2021-01-01T00:00:00Z","publication_status":"published","doi":"10.1142/s0129055x20600090","month":"01","ec_funded":1,"status":"public","publication_identifier":{"issn":["0129-055X"],"eissn":["1793-6659"]},"oa":1,"article_number":"2060009","_id":"7900","date_updated":"2023-09-05T16:07:40Z","arxiv":1,"issue":"1","abstract":[{"lang":"eng","text":"Hartree–Fock theory has been justified as a mean-field approximation for fermionic systems. However, it suffers from some defects in predicting physical properties, making necessary a theory of quantum correlations. Recently, bosonization of many-body correlations has been rigorously justified as an upper bound on the correlation energy at high density with weak interactions. We review the bosonic approximation, deriving an effective Hamiltonian. We then show that for systems with Coulomb interaction this effective theory predicts collective excitations (plasmons) in accordance with the random phase approximation of Bohm and Pines, and with experimental observation."}],"year":"2021","external_id":{"arxiv":["1910.08190"],"isi":["000613313200010"]},"quality_controlled":"1","volume":33,"article_processing_charge":"No","article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"RoSe"}],"date_created":"2020-05-28T16:47:55Z","publication":"Reviews in Mathematical Physics","publisher":"World Scientific","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","title":"Bosonic collective excitations in Fermi gases","project":[{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"author":[{"last_name":"Benedikter","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1071-6091","first_name":"Niels P","full_name":"Benedikter, Niels P"}],"isi":1,"day":"01"},{"month":"05","ec_funded":1,"status":"public","oa":1,"publication_identifier":{"issn":["0020-9910"],"eissn":["1432-1297"]},"_id":"7901","arxiv":1,"abstract":[{"lang":"eng","text":"We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree–Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy."}],"date_updated":"2023-08-21T06:30:30Z","year":"2021","intvolume":"       225","citation":{"chicago":"Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas.” <i>Inventiones Mathematicae</i>. Springer, 2021. <a href=\"https://doi.org/10.1007/s00222-021-01041-5\">https://doi.org/10.1007/s00222-021-01041-5</a>.","apa":"Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., &#38; Seiringer, R. (2021). Correlation energy of a weakly interacting Fermi gas. <i>Inventiones Mathematicae</i>. Springer. <a href=\"https://doi.org/10.1007/s00222-021-01041-5\">https://doi.org/10.1007/s00222-021-01041-5</a>","ista":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2021. Correlation energy of a weakly interacting Fermi gas. Inventiones Mathematicae. 225, 885–979.","mla":"Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi Gas.” <i>Inventiones Mathematicae</i>, vol. 225, Springer, 2021, pp. 885–979, doi:<a href=\"https://doi.org/10.1007/s00222-021-01041-5\">10.1007/s00222-021-01041-5</a>.","short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Inventiones Mathematicae 225 (2021) 885–979.","ieee":"N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Correlation energy of a weakly interacting Fermi gas,” <i>Inventiones Mathematicae</i>, vol. 225. Springer, pp. 885–979, 2021.","ama":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Correlation energy of a weakly interacting Fermi gas. <i>Inventiones Mathematicae</i>. 2021;225:885-979. doi:<a href=\"https://doi.org/10.1007/s00222-021-01041-5\">10.1007/s00222-021-01041-5</a>"},"file_date_updated":"2022-05-16T12:23:40Z","scopus_import":"1","ddc":["510"],"oa_version":"Published Version","date_published":"2021-05-03T00:00:00Z","doi":"10.1007/s00222-021-01041-5","publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Springer","title":"Correlation energy of a weakly interacting Fermi gas","isi":1,"author":[{"full_name":"Benedikter, Niels P","first_name":"Niels P","orcid":"0000-0002-1071-6091","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","last_name":"Benedikter"},{"full_name":"Nam, Phan Thành","last_name":"Nam","first_name":"Phan Thành"},{"full_name":"Porta, Marcello","first_name":"Marcello","last_name":"Porta"},{"last_name":"Schlein","first_name":"Benjamin","full_name":"Schlein, Benjamin"},{"full_name":"Seiringer, Robert","first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"file":[{"success":1,"file_size":1089319,"content_type":"application/pdf","relation":"main_file","access_level":"open_access","checksum":"f38c79dfd828cdc7f49a34b37b83d376","creator":"dernst","file_id":"11386","date_created":"2022-05-16T12:23:40Z","file_name":"2021_InventMath_Benedikter.pdf","date_updated":"2022-05-16T12:23:40Z"}],"acknowledgement":"We thank Christian Hainzl for helpful discussions and a referee for very careful reading of the paper and many helpful suggestions. NB and RS were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 694227). Part of the research of NB was conducted on the RZD18 Nice–Milan–Vienna–Moscow. NB thanks Elliott H. Lieb and Peter Otte for explanations about the Luttinger model. PTN has received funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy (EXC-2111-390814868). MP acknowledges financial support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (ERC StG MaMBoQ, grant agreement No. 802901). BS gratefully acknowledges financial support from the NCCR SwissMAP, from the Swiss National Science Foundation through the Grant “Dynamical and energetic properties of Bose-Einstein condensates” and from the European Research Council through the ERC-AdG CLaQS (grant agreement No. 834782). All authors acknowledge support for workshop participation from Mathematisches Forschungsinstitut Oberwolfach (Leibniz Association). NB, PTN, BS, and RS acknowledge support for workshop participation from Fondation des Treilles.","day":"03","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"quality_controlled":"1","volume":225,"external_id":{"isi":["000646573600001"],"arxiv":["2005.08933"]},"article_type":"original","article_processing_charge":"Yes (via OA deal)","type":"journal_article","department":[{"_id":"RoSe"}],"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Inventiones Mathematicae","page":"885-979","date_created":"2020-05-28T16:48:20Z"},{"_id":"10537","date_updated":"2023-08-17T06:19:14Z","abstract":[{"text":"We consider the quantum many-body evolution of a homogeneous Fermi gas in three dimensions in the coupled semiclassical and mean-field scaling regime. We study a class of initial data describing collective particle–hole pair excitations on the Fermi ball. Using a rigorous version of approximate bosonization, we prove that the many-body evolution can be approximated in Fock space norm by a quasi-free bosonic evolution of the collective particle–hole excitations.","lang":"eng"}],"arxiv":1,"year":"2021","month":"12","ec_funded":1,"status":"public","oa":1,"publication_identifier":{"issn":["1424-0637"]},"oa_version":"Preprint","date_published":"2021-12-02T00:00:00Z","publication_status":"published","doi":"10.1007/s00023-021-01136-y","citation":{"ama":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Bosonization of fermionic many-body dynamics. <i>Annales Henri Poincaré</i>. 2021. doi:<a href=\"https://doi.org/10.1007/s00023-021-01136-y\">10.1007/s00023-021-01136-y</a>","ieee":"N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Bosonization of fermionic many-body dynamics,” <i>Annales Henri Poincaré</i>. Springer Nature, 2021.","short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Annales Henri Poincaré (2021).","ista":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2021. Bosonization of fermionic many-body dynamics. Annales Henri Poincaré.","apa":"Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., &#38; Seiringer, R. (2021). Bosonization of fermionic many-body dynamics. <i>Annales Henri Poincaré</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-021-01136-y\">https://doi.org/10.1007/s00023-021-01136-y</a>","mla":"Benedikter, Niels P., et al. “Bosonization of Fermionic Many-Body Dynamics.” <i>Annales Henri Poincaré</i>, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s00023-021-01136-y\">10.1007/s00023-021-01136-y</a>.","chicago":"Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Bosonization of Fermionic Many-Body Dynamics.” <i>Annales Henri Poincaré</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00023-021-01136-y\">https://doi.org/10.1007/s00023-021-01136-y</a>."},"scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/2103.08224","open_access":"1"}],"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems"}],"author":[{"id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","last_name":"Benedikter","orcid":"0000-0002-1071-6091","first_name":"Niels P","full_name":"Benedikter, Niels P"},{"first_name":"Phan Thành","last_name":"Nam","full_name":"Nam, Phan Thành"},{"first_name":"Marcello","last_name":"Porta","full_name":"Porta, Marcello"},{"last_name":"Schlein","first_name":"Benjamin","full_name":"Schlein, Benjamin"},{"orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"isi":1,"acknowledgement":"NB was supported by Gruppo Nazionale per la Fisica Matematica (GNFM). RS was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 694227). PTN was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy (EXC-2111-390814868). MP was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (ERC StG MaMBoQ, Grant Agreement No. 802901). BS was supported by the NCCR SwissMAP, the Swiss National Science Foundation through the Grant “Dynamical and energetic properties of Bose-Einstein condensates,” and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program through the ERC-AdG CLaQS (Grant Agreement No. 834782).","day":"02","publisher":"Springer Nature","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Bosonization of fermionic many-body dynamics","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"RoSe"}],"date_created":"2021-12-12T23:01:28Z","publication":"Annales Henri Poincaré","external_id":{"isi":["000725405700001"],"arxiv":["2103.08224"]},"quality_controlled":"1","article_type":"original","article_processing_charge":"No"},{"year":"2020","date_updated":"2023-08-17T13:51:50Z","arxiv":1,"abstract":[{"lang":"eng","text":"While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.\r\n"}],"_id":"6649","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"oa":1,"status":"public","ec_funded":1,"month":"03","publication_status":"published","doi":"10.1007/s00220-019-03505-5","date_published":"2020-03-01T00:00:00Z","oa_version":"Published Version","ddc":["530"],"scopus_import":"1","file_date_updated":"2020-07-14T12:47:35Z","citation":{"ista":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2020. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. Communications in Mathematical Physics. 374, 2097–2150.","apa":"Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., &#38; Seiringer, R. (2020). Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03505-5\">https://doi.org/10.1007/s00220-019-03505-5</a>","mla":"Benedikter, Niels P., et al. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” <i>Communications in Mathematical Physics</i>, vol. 374, Springer Nature, 2020, pp. 2097–2150, doi:<a href=\"https://doi.org/10.1007/s00220-019-03505-5\">10.1007/s00220-019-03505-5</a>.","chicago":"Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03505-5\">https://doi.org/10.1007/s00220-019-03505-5</a>.","short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications in Mathematical Physics 374 (2020) 2097–2150.","ieee":"N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime,” <i>Communications in Mathematical Physics</i>, vol. 374. Springer Nature, pp. 2097–2150, 2020.","ama":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. <i>Communications in Mathematical Physics</i>. 2020;374:2097–2150. doi:<a href=\"https://doi.org/10.1007/s00220-019-03505-5\">10.1007/s00220-019-03505-5</a>"},"intvolume":"       374","day":"01","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"file_name":"2019_CommMathPhysics_Benedikter.pdf","date_updated":"2020-07-14T12:47:35Z","date_created":"2019-07-24T07:19:10Z","checksum":"f9dd6dd615a698f1d3636c4a092fed23","creator":"dernst","file_id":"6668","access_level":"open_access","content_type":"application/pdf","relation":"main_file","file_size":853289}],"project":[{"name":"FWF Open Access Fund","call_identifier":"FWF","_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1"},{"_id":"25C878CE-B435-11E9-9278-68D0E5697425","grant_number":"P27533_N27","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","call_identifier":"FWF"},{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems"}],"isi":1,"author":[{"last_name":"Benedikter","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","first_name":"Niels P","orcid":"0000-0002-1071-6091","full_name":"Benedikter, Niels P"},{"last_name":"Nam","first_name":"Phan Thành","full_name":"Nam, Phan Thành"},{"last_name":"Porta","first_name":"Marcello","full_name":"Porta, Marcello"},{"last_name":"Schlein","first_name":"Benjamin","full_name":"Schlein, Benjamin"},{"first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"title":"Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime","publisher":"Springer Nature","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","page":"2097–2150","date_created":"2019-07-18T13:30:04Z","publication":"Communications in Mathematical Physics","has_accepted_license":"1","language":[{"iso":"eng"}],"department":[{"_id":"RoSe"}],"type":"journal_article","article_processing_charge":"No","article_type":"original","external_id":{"isi":["000527910700019"],"arxiv":["1809.01902"]},"quality_controlled":"1","volume":374},{"citation":{"chicago":"Benedikter, Niels P, Jérémy Sok, and Jan Solovej. “The Dirac–Frenkel Principle for Reduced Density Matrices and the Bogoliubov–de Gennes Equations.” <i>Annales Henri Poincare</i>. Birkhäuser, 2018. <a href=\"https://doi.org/10.1007/s00023-018-0644-z\">https://doi.org/10.1007/s00023-018-0644-z</a>.","apa":"Benedikter, N. P., Sok, J., &#38; Solovej, J. (2018). The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations. <i>Annales Henri Poincare</i>. Birkhäuser. <a href=\"https://doi.org/10.1007/s00023-018-0644-z\">https://doi.org/10.1007/s00023-018-0644-z</a>","ista":"Benedikter NP, Sok J, Solovej J. 2018. The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations. Annales Henri Poincare. 19(4), 1167–1214.","mla":"Benedikter, Niels P., et al. “The Dirac–Frenkel Principle for Reduced Density Matrices and the Bogoliubov–de Gennes Equations.” <i>Annales Henri Poincare</i>, vol. 19, no. 4, Birkhäuser, 2018, pp. 1167–214, doi:<a href=\"https://doi.org/10.1007/s00023-018-0644-z\">10.1007/s00023-018-0644-z</a>.","ieee":"N. P. Benedikter, J. Sok, and J. Solovej, “The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations,” <i>Annales Henri Poincare</i>, vol. 19, no. 4. Birkhäuser, pp. 1167–1214, 2018.","ama":"Benedikter NP, Sok J, Solovej J. The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations. <i>Annales Henri Poincare</i>. 2018;19(4):1167-1214. doi:<a href=\"https://doi.org/10.1007/s00023-018-0644-z\">10.1007/s00023-018-0644-z</a>","short":"N.P. Benedikter, J. Sok, J. Solovej, Annales Henri Poincare 19 (2018) 1167–1214."},"intvolume":"        19","ddc":["510","539"],"file_date_updated":"2020-07-14T12:46:31Z","scopus_import":"1","date_published":"2018-04-01T00:00:00Z","oa_version":"Published Version","publication_status":"published","doi":"10.1007/s00023-018-0644-z","month":"04","oa":1,"status":"public","_id":"455","year":"2018","date_updated":"2023-09-19T10:07:41Z","issue":"4","abstract":[{"lang":"eng","text":"The derivation of effective evolution equations is central to the study of non-stationary quantum many-body systems, and widely used in contexts such as superconductivity, nuclear physics, Bose–Einstein condensation and quantum chemistry. We reformulate the Dirac–Frenkel approximation principle in terms of reduced density matrices and apply it to fermionic and bosonic many-body systems. We obtain the Bogoliubov–de Gennes and Hartree–Fock–Bogoliubov equations, respectively. While we do not prove quantitative error estimates, our formulation does show that the approximation is optimal within the class of quasifree states. Furthermore, we prove well-posedness of the Bogoliubov–de Gennes equations in energy space and discuss conserved quantities"}],"external_id":{"isi":["000427578900006"]},"quality_controlled":"1","volume":19,"publist_id":"7367","article_processing_charge":"No","pubrep_id":"993","language":[{"iso":"eng"}],"department":[{"_id":"RoSe"}],"type":"journal_article","date_created":"2018-12-11T11:46:34Z","page":"1167 - 1214","publication":"Annales Henri Poincare","has_accepted_license":"1","alternative_title":["Annales Henri Poincare"],"title":"The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations","publisher":"Birkhäuser","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"file_size":923252,"relation":"main_file","content_type":"application/pdf","date_created":"2018-12-12T10:11:57Z","file_name":"IST-2018-993-v1+1_2018_Benedikter_Dirac.pdf","date_updated":"2020-07-14T12:46:31Z","access_level":"open_access","file_id":"4914","checksum":"883eeccba8384ad7fcaa28761d99a0fa","creator":"system"}],"author":[{"full_name":"Benedikter, Niels P","last_name":"Benedikter","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","first_name":"Niels P","orcid":"0000-0002-1071-6091"},{"last_name":"Sok","first_name":"Jérémy","full_name":"Sok, Jérémy"},{"full_name":"Solovej, Jan","last_name":"Solovej","first_name":"Jan"}],"isi":1,"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"01","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The authors acknowledge support by ERC Advanced Grant 321029 and by VILLUM FONDEN via the QMATH Centre of Excellence (Grant No. 10059). The authors would like to thank Sébastien Breteaux, Enno Lenzmann, Mathieu Lewin and Jochen Schmid for comments and discussions about well-posedness of the Bogoliubov–de Gennes equations."}]