We consider the random Schroedinger operator H=L+V, where L is the generator of a jump Markov process, and V is a random potential. We study the large-time behaviour of the solutions of the parabolic problem for H, both annealed (averaged with respect to the potential) and quenched (almost-sure with respect to the potential). The asymptotics we obtained typically do not coincide. This is joint work with Kamil Kaleta (Politechnika Wrocławska).