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).