--- _id: '10738' 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. 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" article_processing_charge: No article_type: original author: - first_name: Nikolai K full_name: Leopold, Nikolai K id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87 last_name: Leopold orcid: 0000-0002-0495-6822 - first_name: Simone Anna Elvira full_name: Rademacher, Simone Anna Elvira id: 856966FE-A408-11E9-977E-802DE6697425 last_name: Rademacher orcid: 0000-0001-5059-4466 - first_name: Benjamin full_name: Schlein, Benjamin last_name: Schlein - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Leopold NK, Rademacher SAE, Schlein B, Seiringer R. The Landau–Pekar equations: Adiabatic theorem and accuracy. Analysis and PDE. 2021;14(7):2079-2100. doi:10.2140/APDE.2021.14.2079' apa: 'Leopold, N. K., Rademacher, S. A. E., Schlein, B., & Seiringer, R. (2021). The Landau–Pekar equations: Adiabatic theorem and accuracy. Analysis and PDE. Mathematical Sciences Publishers. https://doi.org/10.2140/APDE.2021.14.2079' chicago: 'Leopold, Nikolai K, Simone Anna Elvira Rademacher, Benjamin Schlein, and Robert Seiringer. “ The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.” Analysis and PDE. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/APDE.2021.14.2079.' ieee: 'N. K. Leopold, S. A. E. Rademacher, B. Schlein, and R. Seiringer, “ The Landau–Pekar equations: Adiabatic theorem and accuracy,” Analysis and PDE, vol. 14, no. 7. Mathematical Sciences Publishers, pp. 2079–2100, 2021.' 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.' mla: 'Leopold, Nikolai K., et al. “ The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.” Analysis and PDE, vol. 14, no. 7, Mathematical Sciences Publishers, 2021, pp. 2079–100, doi:10.2140/APDE.2021.14.2079.' short: N.K. Leopold, S.A.E. Rademacher, B. Schlein, R. Seiringer, Analysis and PDE 14 (2021) 2079–2100. date_created: 2022-02-06T23:01:33Z date_published: 2021-11-10T00:00:00Z date_updated: 2023-10-17T11:26:45Z day: '10' department: - _id: RoSe doi: 10.2140/APDE.2021.14.2079 ec_funded: 1 external_id: arxiv: - '1904.12532' isi: - '000733976600004' intvolume: ' 14' isi: 1 issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1904.12532 month: '11' oa: 1 oa_version: Preprint page: 2079-2100 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Analysis and PDE publication_identifier: eissn: - 1948-206X issn: - 2157-5045 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: ' The Landau–Pekar equations: Adiabatic theorem and accuracy' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 14 year: '2021' ...