Transition Maps between Hilbert Subspaces and Quantum Energy Transport

We use a natural generalization of the discrete Fourier transform to define transition maps between Hilbert subspaces and the global transport operator Z. By using these transition maps as Kraus (or noise) operators, an extension of the quantum energy transport model of describing the dynamics of an open quantum system of N-levels is presented. We deduce the structure of the invariant states which can be recovered by transporting states supported on the first level.