{"abstract":[{"text":"We consider the Nelson model with ultraviolet cutoff, which describes the interaction between non-relativistic particles and a positive or zero mass quantized scalar field. We take the non-relativistic particles to obey Fermi statistics and discuss the time evolution in a mean-field limit of many fermions. In this case, the limit is known to be also a semiclassical limit. We prove convergence in terms of reduced density matrices of the many-body state to a tensor product of a Slater determinant with semiclassical structure and a coherent state, which evolve according to a fermionic version of the Schrödinger–Klein–Gordon equations.","lang":"eng"}],"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"scopus_import":"1","quality_controlled":"1","department":[{"_id":"RoSe"}],"author":[{"last_name":"Leopold","full_name":"Leopold, Nikolai K","orcid":"0000-0002-0495-6822","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","first_name":"Nikolai K"},{"orcid":"0000-0002-9166-5889","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","first_name":"Sören P","last_name":"Petrat","full_name":"Petrat, Sören P"}],"intvolume":"        20","citation":{"short":"N.K. Leopold, S.P. Petrat, Annales Henri Poincare 20 (2019) 3471–3508.","ama":"Leopold NK, Petrat SP. Mean-field dynamics for the Nelson model with fermions. <i>Annales Henri Poincare</i>. 2019;20(10):3471–3508. doi:<a href=\"https://doi.org/10.1007/s00023-019-00828-w\">10.1007/s00023-019-00828-w</a>","ista":"Leopold NK, Petrat SP. 2019. Mean-field dynamics for the Nelson model with fermions. Annales Henri Poincare. 20(10), 3471–3508.","ieee":"N. K. Leopold and S. P. Petrat, “Mean-field dynamics for the Nelson model with fermions,” <i>Annales Henri Poincare</i>, vol. 20, no. 10. Springer Nature, pp. 3471–3508, 2019.","mla":"Leopold, Nikolai K., and Sören P. Petrat. “Mean-Field Dynamics for the Nelson Model with Fermions.” <i>Annales Henri Poincare</i>, vol. 20, no. 10, Springer Nature, 2019, pp. 3471–3508, doi:<a href=\"https://doi.org/10.1007/s00023-019-00828-w\">10.1007/s00023-019-00828-w</a>.","apa":"Leopold, N. K., &#38; Petrat, S. P. (2019). Mean-field dynamics for the Nelson model with fermions. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-019-00828-w\">https://doi.org/10.1007/s00023-019-00828-w</a>","chicago":"Leopold, Nikolai K, and Sören P Petrat. “Mean-Field Dynamics for the Nelson Model with Fermions.” <i>Annales Henri Poincare</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00023-019-00828-w\">https://doi.org/10.1007/s00023-019-00828-w</a>."},"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)"},"isi":1,"ddc":["510"],"title":"Mean-field dynamics for the Nelson model with fermions","ec_funded":1,"status":"public","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_type":"original","date_created":"2019-08-11T21:59:21Z","oa_version":"Published Version","file_date_updated":"2020-07-14T12:47:40Z","date_published":"2019-10-01T00:00:00Z","month":"10","type":"journal_article","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"publication":"Annales Henri Poincare","_id":"6788","date_updated":"2023-08-29T07:09:06Z","file":[{"relation":"main_file","file_id":"6801","access_level":"open_access","file_name":"2019_AnnalesHenriPoincare_Leopold.pdf","creator":"dernst","date_updated":"2020-07-14T12:47:40Z","checksum":"b6dbf0d837d809293d449adf77138904","file_size":681139,"date_created":"2019-08-12T12:05:58Z","content_type":"application/pdf"}],"page":"3471–3508","issue":"10","doi":"10.1007/s00023-019-00828-w","external_id":{"arxiv":["1807.06781"],"isi":["000487036900008"]},"publication_status":"published","license":"https://creativecommons.org/licenses/by/4.0/","oa":1,"language":[{"iso":"eng"}],"year":"2019","volume":20,"publisher":"Springer Nature","day":"01"}