Dynamics of a Strongly Coupled Polaron

We study the dynamics of large polarons described by the Fröhlich Hamiltonian in the limit of strong coupling. The initial conditions are (perturbations of) product states of an electron wave function and a phonon coherent state, as suggested by Pekar. We show that, to leading order on the natural time scale of the problem, the phonon field is stationary and the electron moves according to an effective linear Schrödinger equation