# Quantum fluctuations for the dynamics of the strongly coupled polaron

We study the time evolution of the strongly coupled polaron described by the Fröhlich Hamiltonian with large coupling constant $\alpha$ . For initial data of Pekar product form with coherent phonon field and with sufficiently small energy, we provide a norm approximation of the time evolution valid for all 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. The proof is based on an adiabatic theorem for the Landau-Pekar equations and the persistence of the spectral gap.