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 alpha < 1 compared to the other bad qubits, confirms this picture and admits a perturbative treatment.

Automated summary

This study investigates the effects of strong dissipation in quantum systems with a notion of locality, revealing the emergence of a manifold of metastable states due to variations in the dissipation strength. The findings are confirmed through a perturbative treatment using a simple model involving good and bad qubits with reduced dissipation.