{"doi":"10.1007/s00023-018-0644-z","department":[{"_id":"RoSe"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_published":"2018-04-01T00:00:00Z","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"}],"pubrep_id":"993","date_updated":"2023-09-19T10:07:41Z","issue":"4","author":[{"id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1071-6091","full_name":"Benedikter, Niels P","first_name":"Niels P","last_name":"Benedikter"},{"last_name":"Sok","full_name":"Sok, Jérémy","first_name":"Jérémy"},{"last_name":"Solovej","full_name":"Solovej, Jan","first_name":"Jan"}],"article_processing_charge":"No","oa":1,"intvolume":"        19","oa_version":"Published Version","scopus_import":"1","day":"01","isi":1,"alternative_title":["Annales Henri Poincare"],"type":"journal_article","_id":"455","publication":"Annales Henri Poincare","external_id":{"isi":["000427578900006"]},"volume":19,"status":"public","title":"The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations","file":[{"checksum":"883eeccba8384ad7fcaa28761d99a0fa","relation":"main_file","file_name":"IST-2018-993-v1+1_2018_Benedikter_Dirac.pdf","creator":"system","content_type":"application/pdf","file_id":"4914","file_size":923252,"date_updated":"2020-07-14T12:46:31Z","access_level":"open_access","date_created":"2018-12-12T10:11:57Z"}],"ddc":["510","539"],"date_created":"2018-12-11T11:46:34Z","page":"1167 - 1214","has_accepted_license":"1","publisher":"Birkhäuser","publist_id":"7367","language":[{"iso":"eng"}],"publication_status":"published","month":"04","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.","quality_controlled":"1","citation":{"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.","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>","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>.","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.","short":"N.P. Benedikter, J. Sok, J. Solovej, Annales Henri Poincare 19 (2018) 1167–1214.","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>","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>."},"file_date_updated":"2020-07-14T12:46:31Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2018"}