The Fast Recurrent Subspace on an N-Level Quantum Energy Transport Model

The fast recurrent subspace (the biggest support of all invariant states) of a weak coupling limit type quantum Markov semigroup modeling a quantum transport open system of $N$-energy levels is determined. This is achieved by characterizing the structure of all the invariant states and their spectra in terms of a natural generalization of the discrete Fourier transform operator. Finally, the attraction domains and long-time behaviour of the evolution are studied on hereditary subalgebras where faithful invariant states exist.