Abstract

We consider the Fröhlich 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 Fröhlich dynamics up to times of order ${\alpha }^2$.

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