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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 timescales 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
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