{"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2005.02098","open_access":"1"}],"abstract":[{"text":"We consider the Fröhlich Hamiltonian with large coupling constant α. For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corresponding energy, we provide a norm approximation of the evolution, valid up to times of order α2. The approximation is given in terms of a Pekar product state, evolved through the Landau-Pekar equations, corrected by a Bogoliubov dynamics taking quantum fluctuations into account. This allows us to show that the Landau-Pekar equations approximately describe the evolution of the electron- and one-phonon reduced density matrices under the Fröhlich dynamics up to times of order α2.","lang":"eng"}],"department":[{"_id":"RoSe"}],"issue":"4","date_published":"2021-10-01T00:00:00Z","publication_status":"published","date_updated":"2024-02-05T10:02:45Z","month":"10","article_processing_charge":"No","day":"01","type":"journal_article","status":"public","quality_controlled":"1","title":"Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron","scopus_import":"1","publisher":"Mathematical Sciences Publishers","date_created":"2024-01-28T23:01:43Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"oa_version":"Preprint","language":[{"iso":"eng"}],"_id":"14889","ec_funded":1,"article_type":"original","citation":{"ieee":"N. K. Leopold, D. J. Mitrouskas, S. A. E. Rademacher, B. Schlein, and R. Seiringer, “Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron,” <i>Pure and Applied Analysis</i>, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 653–676, 2021.","mla":"Leopold, Nikolai K., et al. “Landau–Pekar Equations and Quantum Fluctuations for the Dynamics of a Strongly Coupled Polaron.” <i>Pure and Applied Analysis</i>, vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 653–76, doi:<a href=\"https://doi.org/10.2140/paa.2021.3.653\">10.2140/paa.2021.3.653</a>.","short":"N.K. Leopold, D.J. Mitrouskas, S.A.E. Rademacher, B. Schlein, R. Seiringer, Pure and Applied Analysis 3 (2021) 653–676.","ista":"Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. 2021. Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. Pure and Applied Analysis. 3(4), 653–676.","apa":"Leopold, N. K., Mitrouskas, D. J., Rademacher, S. A. E., Schlein, B., &#38; Seiringer, R. (2021). Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/paa.2021.3.653\">https://doi.org/10.2140/paa.2021.3.653</a>","chicago":"Leopold, Nikolai K, David Johannes Mitrouskas, Simone Anna Elvira Rademacher, Benjamin Schlein, and Robert Seiringer. “Landau–Pekar Equations and Quantum Fluctuations for the Dynamics of a Strongly Coupled Polaron.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/paa.2021.3.653\">https://doi.org/10.2140/paa.2021.3.653</a>.","ama":"Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. <i>Pure and Applied Analysis</i>. 2021;3(4):653-676. doi:<a href=\"https://doi.org/10.2140/paa.2021.3.653\">10.2140/paa.2021.3.653</a>"},"publication_identifier":{"eissn":["2578-5885"],"issn":["2578-5893"]},"external_id":{"arxiv":["2005.02098"]},"doi":"10.2140/paa.2021.3.653","page":"653-676","author":[{"full_name":"Leopold, Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","first_name":"Nikolai K","last_name":"Leopold","orcid":"0000-0002-0495-6822"},{"full_name":"Mitrouskas, David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","first_name":"David Johannes","last_name":"Mitrouskas"},{"orcid":"0000-0001-5059-4466","full_name":"Rademacher, Simone Anna Elvira","id":"856966FE-A408-11E9-977E-802DE6697425","first_name":"Simone Anna Elvira","last_name":"Rademacher"},{"last_name":"Schlein","first_name":"Benjamin","full_name":"Schlein, Benjamin"},{"last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521"}],"publication":"Pure and Applied Analysis","project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020"},{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020"}],"acknowledgement":"Financial support by the European Union’s Horizon 2020 research and innovation programme\r\nunder the Marie Skłodowska-Curie grant agreement No. 754411 (S.R.) and the European\r\nResearch Council under grant agreement No. 694227 (N.L. and R.S.), as well as by the SNSF\r\nEccellenza project PCEFP2 181153 (N.L.), the NCCR SwissMAP (N.L. and B.S.) and by the\r\nDeutsche Forschungsgemeinschaft (DFG) through the Research Training Group 1838: Spectral\r\nTheory and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. B.S. gratefully\r\nacknowledges financial support from the Swiss National Science Foundation through the Grant\r\n“Dynamical and energetic properties of Bose-Einstein condensates” and from the European\r\nResearch Council through the ERC-AdG CLaQS (grant agreement No 834782). D.M. thanks\r\nMarcel Griesemer for helpful discussions.","year":"2021","volume":3,"intvolume":"         3"}