Hot electron relaxation in one-dimensional models: Exact polaron dynamics versus relaxation in the presence of a Fermi sea

We present the exact solution for the time evolution of the electron and phonon momentum distribution for a one-dimensional polaron model with a linear electronic energy dispersion. The electron momentum distribution is shown to obey a Markovian quantum kinetic equation. Numerical results for the polaron model are compared to the corresponding exact results, when the negative momentum states are filled in the initial state. The presence of this Fermi sea modifies the dynamics except in the short time regime. The different long time dynamics might show up in comparison of hot electron relaxation of undoped and doped semiconductors.