Perturbation theory for open quantum systems at the steady state

We propose a theoretical method for studying open quantum systems at the steady state within the framework of the perturbation theory. This approach allow us to compute the density operator of the system perturbatively and, in principle, to obtain an expression for its density matrix elements explicitly. To illustrate our methodology, we provide a case study of a nonlinear two-level system coupled to a thermal reservoir and special attention is given to the relationship between nonlinearity and nonclassicality. In particular, this relation is quantified by considering the quantum measures as the nonclassical depth, nonclassical distance and the quantum fidelity. We find that the nonclassicality is originated at least by second order contribution of nonlinear terms in quantum dynamics. 2000 MSC: 46N50, 37N20, 46N5