Polarons near the Čerenkov velocity

We derive a set of nonlinear equations which describe the transport of optical polarons in strong electric fields. In the limit of weak electron-phonon coupling, the equations are used to calculate the external force required to maintain a constant polaron velocity and the velocity dependence of the polaron’s effective mass for the velocities comparable to the Čerenkov velocity. The predictions of the transport equations are compared with mobility measurements in InSb and with the theory of Thornber and Feynman. The derivation of the transport equations is based upon a complex-time path-integral formulation of the transport of an electron interacting with a phonon field.