  We employ the Lindblad master equation method to study the nonequilibrium
dynamics following a parametric quench in the Hamiltonian of an open,
two-dimensional superconducting system coupled to an external bath. Within our
approach we show how, in the open system, the dissipation works as an effective
stabilization mechanism in the time evolution of the system after the quench.
Eventually, we evidence how the mismatch between the phases corresponding to
the initial and to the final state of the system determines a dynamical phase
transition between the two distinct phases. Our method allows for fully
characterizing the dynamical phase transition in an open system in several
cases of physical relevance, by means of a combined study of the time-dependent
superconducting gap and of the fidelity between density matrices.
