Dynamics of the strongly coupled polaron

We study the time evolution of the strongly coupled polaron which is a model for an electron moving in an ionic crystal. Its microscopic description is given by the Fr\"ohlich Hamiltonian. For initial data of Pekar product form with coherent phonon field and with sufficiently small energy, we provide an effective dynamics for the strongly coupled polaron. The effective dynamics 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. This is joint work with D. Feliciangeli, N. Leopold, D. Mitrouskas, B. Schlein and R. Seiringer.