Weak-Coupling Theory of the Polaron Energy-Momentum Relation

Abstract

We present arguments to show that the energy-momentum relation for a polaron is quadratic for small $k$, but bends over and becomes horizontal when the energy approaches the optical-phonon energy above the ground state. We present a calculation for zero temperature based on a thermodynamic Green's-function theory which is especially designed to give a reliable polaron energy-momentum relation.