{"status":"public","quality_controlled":"1","title":"Derivation of the Landau–Pekar equations in a many-body mean-field limit","date_created":"2021-03-14T23:01:34Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","oa":1,"scopus_import":"1","publisher":"Springer Nature","publication_status":"published","date_published":"2021-02-26T00:00:00Z","abstract":[{"lang":"eng","text":"We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order."}],"department":[{"_id":"RoSe"}],"day":"26","type":"journal_article","file":[{"relation":"main_file","checksum":"23449e44dc5132501a5c86e70638800f","content_type":"application/pdf","file_name":"2021_ArchRationalMechAnal_Leopold.pdf","creator":"dernst","access_level":"open_access","date_updated":"2021-03-22T08:31:29Z","file_id":"9270","success":1,"file_size":558006,"date_created":"2021-03-22T08:31:29Z"}],"date_updated":"2023-08-07T14:12:27Z","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"month":"02","article_processing_charge":"No","isi":1,"file_date_updated":"2021-03-22T08:31:29Z","acknowledgement":"Financial support by the European Research Council (ERC) under the\r\nEuropean Union’s Horizon 2020 research and innovation programme (Grant Agreement\r\nNo 694227; N.L and R.S.), the SNSF Eccellenza Project PCEFP2 181153 (N.L) and the\r\nDeutsche Forschungsgemeinschaft (DFG) through the Research TrainingGroup 1838: Spectral\r\nTheory and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. N.L.\r\ngratefully acknowledges support from the NCCRSwissMAP and would like to thank Simone\r\nRademacher and Benjamin Schlein for interesting discussions about the time-evolution of\r\nthe polaron at strong coupling. D.M. thanks Marcel Griesemer and Andreas Wünsch for\r\nextensive discussions about the Fröhlich polaron.","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020"}],"ddc":["510"],"volume":240,"intvolume":"       240","year":"2021","article_type":"original","citation":{"mla":"Leopold, Nikolai K., et al. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 240, Springer Nature, 2021, pp. 383–417, doi:<a href=\"https://doi.org/10.1007/s00205-021-01616-9\">10.1007/s00205-021-01616-9</a>.","ieee":"N. K. Leopold, D. J. Mitrouskas, and R. Seiringer, “Derivation of the Landau–Pekar equations in a many-body mean-field limit,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 240. Springer Nature, pp. 383–417, 2021.","ama":"Leopold NK, Mitrouskas DJ, Seiringer R. Derivation of the Landau–Pekar equations in a many-body mean-field limit. <i>Archive for Rational Mechanics and Analysis</i>. 2021;240:383-417. doi:<a href=\"https://doi.org/10.1007/s00205-021-01616-9\">10.1007/s00205-021-01616-9</a>","apa":"Leopold, N. K., Mitrouskas, D. J., &#38; Seiringer, R. (2021). Derivation of the Landau–Pekar equations in a many-body mean-field limit. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-021-01616-9\">https://doi.org/10.1007/s00205-021-01616-9</a>","ista":"Leopold NK, Mitrouskas DJ, Seiringer R. 2021. Derivation of the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational Mechanics and Analysis. 240, 383–417.","chicago":"Leopold, Nikolai K, David Johannes Mitrouskas, and Robert Seiringer. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00205-021-01616-9\">https://doi.org/10.1007/s00205-021-01616-9</a>.","short":"N.K. Leopold, D.J. Mitrouskas, R. Seiringer, Archive for Rational Mechanics and Analysis 240 (2021) 383–417."},"ec_funded":1,"_id":"9246","language":[{"iso":"eng"}],"publication":"Archive for Rational Mechanics and Analysis","author":[{"id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","full_name":"Leopold, Nikolai K","last_name":"Leopold","first_name":"Nikolai K","orcid":"0000-0002-0495-6822"},{"id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","full_name":"Mitrouskas, David Johannes","first_name":"David Johannes","last_name":"Mitrouskas"},{"orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"has_accepted_license":"1","page":"383-417","doi":"10.1007/s00205-021-01616-9","publication_identifier":{"eissn":["14320673"],"issn":["00039527"]},"external_id":{"isi":["000622226200001"],"arxiv":["2001.03993"]}}