Perturbative Criteria for the Ergodicity of Interacting Dissipative Quantum Lattice Systems

We analyze a class of quantum Feller semigroups describing the evolution of interacting quantum lattice systems, specified either as generic qudits or as fermions. The corresponding generators, which include both conservative and dissipative evolutions, are given by the superposition of local generators in the Lindblad form. The associated infinite volume dynamics can be obtained as the strong limit of the finite volume dynamics. 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.