Quantum scattering by a Brownian particle with complex potential

The one-dimensional Schrödinger potential is considered. Its potential depends randomly on the time: $q(x,t)=Q(x-y(t))$, where $y(t)$ is the trajectory of a Brownian particle. By means of results previously obtained the scattering operator, averaged over all possible trajectories of the Brownian particle, is calculated. Some physical consequences of the obtained results are discussed.