  We consider an open quantum system with dissipation, described by a Lindblad
Master equation (LME). For dissipation locally acting and sufficiently strong,
a separation of the relaxation time scales occurs, which, in terms of the
eigenvalues of the Liouvillian, implies a grouping of the latter in distinct
vertical stripes in the complex plane at positions determined by the
eigenvalues of the dissipator. We derive effective LME equations describing the
modes within each stripe separately, and solve them perturbatively, obtaining
for the full set of eigenvalues and eigenstates of the Liouvillian explicit
expressions correct at order $1/\Gamma$ included, where $\Gamma$ is the
strength of the dissipation. As a example, we apply our general results to
quantum $XYZ$ spin chains coupled, at one boundary, to a dissipative bath of
polarization.
