{"date_updated":"2023-10-17T11:26:45Z","month":"11","article_processing_charge":"No","day":"10","type":"journal_article","main_file_link":[{"url":"https://arxiv.org/abs/1904.12532","open_access":"1"}],"abstract":[{"lang":"eng","text":"We prove an adiabatic theorem for the Landau–Pekar equations. This allows us to derive new results on the accuracy of their use as effective equations for the time evolution generated by the Fröhlich Hamiltonian with large coupling constant α. In particular, we show that the time evolution of Pekar product states with coherent phonon field and the electron being trapped by the phonons is well approximated by the Landau–Pekar equations until times short compared to α2."}],"department":[{"_id":"RoSe"}],"issue":"7","publication_status":"published","date_published":"2021-11-10T00:00:00Z","scopus_import":"1","publisher":"Mathematical Sciences Publishers","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2022-02-06T23:01:33Z","oa_version":"Preprint","oa":1,"status":"public","title":" The Landau–Pekar equations: Adiabatic theorem and accuracy","quality_controlled":"1","publication_identifier":{"issn":["2157-5045"],"eissn":["1948-206X"]},"external_id":{"isi":["000733976600004"],"arxiv":["1904.12532"]},"author":[{"orcid":"0000-0002-0495-6822","last_name":"Leopold","first_name":"Nikolai K","full_name":"Leopold, Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87"},{"id":"856966FE-A408-11E9-977E-802DE6697425","full_name":"Rademacher, Simone Anna Elvira","last_name":"Rademacher","first_name":"Simone Anna Elvira","orcid":"0000-0001-5059-4466"},{"last_name":"Schlein","first_name":"Benjamin","full_name":"Schlein, Benjamin"},{"orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"publication":"Analysis and PDE","doi":"10.2140/APDE.2021.14.2079","page":"2079-2100","_id":"10738","language":[{"iso":"eng"}],"article_type":"original","citation":{"ieee":"N. K. Leopold, S. A. E. Rademacher, B. Schlein, and R. Seiringer, “ The Landau–Pekar equations: Adiabatic theorem and accuracy,” <i>Analysis and PDE</i>, vol. 14, no. 7. Mathematical Sciences Publishers, pp. 2079–2100, 2021.","mla":"Leopold, Nikolai K., et al. “ The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.” <i>Analysis and PDE</i>, vol. 14, no. 7, Mathematical Sciences Publishers, 2021, pp. 2079–100, doi:<a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">10.2140/APDE.2021.14.2079</a>.","short":"N.K. Leopold, S.A.E. Rademacher, B. Schlein, R. Seiringer, Analysis and PDE 14 (2021) 2079–2100.","ama":"Leopold NK, Rademacher SAE, Schlein B, Seiringer R.  The Landau–Pekar equations: Adiabatic theorem and accuracy. <i>Analysis and PDE</i>. 2021;14(7):2079-2100. doi:<a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">10.2140/APDE.2021.14.2079</a>","chicago":"Leopold, Nikolai K, Simone Anna Elvira Rademacher, Benjamin Schlein, and Robert Seiringer. “ The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.” <i>Analysis and PDE</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">https://doi.org/10.2140/APDE.2021.14.2079</a>.","apa":"Leopold, N. K., Rademacher, S. A. E., Schlein, B., &#38; Seiringer, R. (2021).  The Landau–Pekar equations: Adiabatic theorem and accuracy. <i>Analysis and PDE</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">https://doi.org/10.2140/APDE.2021.14.2079</a>","ista":"Leopold NK, Rademacher SAE, Schlein B, Seiringer R. 2021.  The Landau–Pekar equations: Adiabatic theorem and accuracy. Analysis and PDE. 14(7), 2079–2100."},"ec_funded":1,"year":"2021","volume":14,"intvolume":"        14","project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"isi":1,"acknowledgement":"N. L. and R. S. gratefully acknowledge financial support by the European Research Council\r\n(ERC) under the European Union’s Horizon 2020 research and innovation programme (grant\r\nagreement No 694227). B. S. acknowledges support from the Swiss National Science Foundation (grant 200020_172623) and from the NCCR SwissMAP. N. L. would like to thank\r\nAndreas Deuchert and David Mitrouskas for interesting discussions. B. S. and R. S. would\r\nlike to thank Rupert Frank for stimulating discussions about the time-evolution of a polaron.\r\n"}