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.
Letters in Mathematical Physics
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.
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
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
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.
D. J. Mitrouskas, “A note on the Fröhlich dynamics in the strong coupling limit,” Letters in Mathematical Physics, vol. 111. Springer Nature, 2021.
Mitrouskas DJ. 2021. A note on the Fröhlich dynamics in the strong coupling limit. Letters in Mathematical Physics. 111, 45.
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.
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