Stationary regime for the quantum dynamics of particles in a randomly varying potential

A study is made of the quantum dynamics of particles in a time-dependent random potential field with Gaussian distribution of the realization probabilities in an unbounded space. Constant absorption and a mono-energetic distributed source of particles are introduced in the Schroedinger equation. The time at which the source is switched on is taken into the infinite past. Under the assumption that the fluctuations of the random potential are stationary, it is proved that there exists a stationary limit for the density matrix averaged over the realizations of the potential. It is verified that this limit in the weak interaction approximation and also when the absorption length and the spatial scale of the source of the particles are of the order of the mean free length of the particles satisfies the ordinary stationary equation of radiative transfer in a scattering medium