--- _id: '9333' abstract: - lang: eng text: We revise a previous result about the Fröhlich dynamics in the strong coupling limit obtained in Griesemer (Rev Math Phys 29(10):1750030, 2017). In the latter it was shown that the Fröhlich time evolution applied to the initial state φ0⊗ξα, where φ0 is the electron ground state of the Pekar energy functional and ξα the associated coherent state of the phonons, can be approximated by a global phase for times small compared to α2. In the present note we prove that a similar approximation holds for t=O(α2) if one includes a nontrivial effective dynamics for the phonons that is generated by an operator proportional to α−2 and quadratic in creation and annihilation operators. Our result implies that the electron ground state remains close to its initial state for times of order α2, while the phonon fluctuations around the coherent state ξα can be described by a time-dependent Bogoliubov transformation. acknowledgement: 'I thank Marcel Griesemer for many interesting discussions about the Fröhlich polaron and also for valuable comments on this manuscript. Helpful discussions with Nikolai Leopold and Robert Seiringer are also gratefully acknowledged. This work was partially supported by the Deutsche Forschungsgemeinschaft (DFG) through the Research Training Group 1838: Spectral Theory and Dynamics of Quantum Systems. Open Access funding enabled and organized by Projekt DEAL.' article_number: '45' article_processing_charge: No article_type: original author: - first_name: David Johannes full_name: Mitrouskas, David Johannes id: cbddacee-2b11-11eb-a02e-a2e14d04e52d last_name: Mitrouskas citation: ama: Mitrouskas DJ. A note on the Fröhlich dynamics in the strong coupling limit. Letters in Mathematical Physics. 2021;111. doi:10.1007/s11005-021-01380-7 apa: Mitrouskas, D. J. (2021). A note on the Fröhlich dynamics in the strong coupling limit. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-021-01380-7 chicago: Mitrouskas, David Johannes. “A Note on the Fröhlich Dynamics in the Strong Coupling Limit.” Letters in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s11005-021-01380-7. ieee: D. J. Mitrouskas, “A note on the Fröhlich dynamics in the strong coupling limit,” Letters in Mathematical Physics, vol. 111. Springer Nature, 2021. ista: Mitrouskas DJ. 2021. A note on the Fröhlich dynamics in the strong coupling limit. Letters in Mathematical Physics. 111, 45. mla: Mitrouskas, David Johannes. “A Note on the Fröhlich Dynamics in the Strong Coupling Limit.” Letters in Mathematical Physics, vol. 111, 45, Springer Nature, 2021, doi:10.1007/s11005-021-01380-7. short: D.J. Mitrouskas, Letters in Mathematical Physics 111 (2021). date_created: 2021-04-18T22:01:41Z date_published: 2021-04-05T00:00:00Z date_updated: 2023-08-08T13:09:28Z day: '05' ddc: - '510' department: - _id: RoSe doi: 10.1007/s11005-021-01380-7 external_id: isi: - '000637359300002' file: - access_level: open_access checksum: be56c0845a43c0c5c772ee0b5053f7d7 content_type: application/pdf creator: dernst date_created: 2021-04-19T10:40:01Z date_updated: 2021-04-19T10:40:01Z file_id: '9341' file_name: 2021_LettersMathPhysics_Mitrouskas.pdf file_size: 438084 relation: main_file success: 1 file_date_updated: 2021-04-19T10:40:01Z has_accepted_license: '1' intvolume: ' 111' isi: 1 language: - iso: eng month: '04' oa: 1 oa_version: Published Version publication: Letters in Mathematical Physics publication_identifier: eissn: - '15730530' issn: - '03779017' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: A note on the Fröhlich dynamics in the strong coupling limit tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 111 year: '2021' ...