The fast recurrent subspace on an $N$-level quantum energy transport model

Abstract: 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 state and their spectra in terms of a natural generalization of the Discrete Fourier Transform operator. Finally, the attraction domains and long-time behavior of the evolution are studied on hereditary subalgebras where faithful invariant states exist.