Random matrix theory for quantum and classical metastability in local Liouvillians

We consider the effects of strong dissipation in quantum systems with a notion of locality, which induces a hierarchy of many-body relaxation timescales as shown by K. Wang, F. Piazza, and D. J. Luitz [Phys. Rev. Lett. 124, 100604 (2020)]. If the strength of the dissipation varies strongly in the system, additional separations of timescales can emerge, inducing a manifold of metastable states, to which observables relax first, before relaxing to the steady state. Our simple model, involving one or two ``good'' qubits with dissipation reduced by a factor $\ensuremath{\alpha}<1$ compared to the other ``bad'' qubits, confirms this picture and admits a perturbative treatment.