Kinetic equations for real scalar fields coupled to a continuum of atoms

We consider a model of a scalar field, with dispersion relation ω(k), coupled to a random medium of two level atoms. We investigate the dynamics of states with at most one quanta of excitation in the system. In a high frequency limit, the probability amplitudes are shown to satisfy kinetic equations. Under additional hypotheses on the dispersion relation, we obtain an analytically solvable expression in the diffusion limit.