Dissipative quantum lattice systems

We analyze a class of quantum Feller semigroups describing the evolution of interacting quantum lattice systems. By regarding the interacting evolution as a perturbation of a non-interacting dissipative dynamics, we obtain a quantitative criterion that yields the uniqueness of the stationary state together with the exponential convergence of local observables. The analysis is based on suitable a priori bounds on the resolvent equation which yield quantitive estimates on the evolution of local observables.