The mechanisms of quantum transport have attracted the attention of researchers from different areas (physics, chemistry, mathematics), who have produced an important amount of scientific, experimental or theoretical, work focused on describing and modeling these complex mechanisms. \\ Due to their characteristics as complex systems, semigroups of weak coupling limit type, with degenerate Hamiltonian, are suitable for modeling these phenomena. In this talk we will discuss the mathematical structure of the infinitesimal generator of some of these semigroups and the set of their stationary states. We will also present what is Free-Decoherence Algebra of a dynamic quantum semigroup of Markov, some characterizations of it and its application in the quantum transport model of [1]. \\ \\ \noindent{\bf References} \\ [1] Aref'eva, Y., Volovich, I. and Kozyrev, S. 2015. Stochastic Limit Method and Interference in Quantum Many-particles Systems. Theoretical and Mathematical Physics 183(3) (2015) 782-799