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arXiv · 2005.02098

Landau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron

Nikolai Leopold·David Mitrouskas·Simone Rademacher·Benjamin Schlein·Robert Seiringer
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Abstract

We consider the Fr\"ohlich Hamiltonian with large coupling constant $\alpha$. 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 $\alpha^2$. 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 Fr\"ohlich dynamics up to times of order $\alpha^2$.

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Nikolai Leopold, David Mitrouskas, Simone Rademacher, Benjamin Schlein, Robert Seiringer. 2020-05-05. Landau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. https://doi.org/10.2140/paa.2021.3.653

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