Quantum kinetic model of a driven radiative two-level system

We introduce a system of two-level atoms in one dimension which allow collision-induced radiative transitions between the two states. In addition, we subject the system to a driving force. A linear, but non-local master equation in momentum is solved exactly, illustrating three results: the development of multi-streaming motion, the occurrence of acceleration reversals, and an observed approach to a steady state as the emission of radiation and the driving field balance each other. We relate our results to the theory of kinetic equations with internal degrees of freedom used in rarefied gas dynamics.