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 in [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 $\alpha<1$ compared to the other "bad" qubits, confirms this picture and admits a perturbative treatment.