  We prove that every stationary state in the annihilator of all Kraus
operators of a weak coupling limit type Markov generator consists of two
pieces, one of them supported on the interaction-free subspace and the second
one on its orthogonal complement. In particular, we apply the previous result
to describe in detail the structure of a slightly modified quantum transport
model due to Arefeva, Kozyrev and Volovich (modified AKV's model) studied first
in Ref.\cite{gggq}, in terms of generalized annihilation and creation
operators.
