Random matrix theory for quantum and classical metastability in local Liouvillians

TL;DR

This paper investigates how strong, local dissipation in quantum systems creates multiple relaxation timescales and metastable states, with a simple model demonstrating the emergence of these states and their perturbative analysis.

Contribution

It introduces a model showing how spatially varying dissipation leads to metastability and multiple relaxation timescales in local Liouvillian systems.

Findings

Metastable states emerge due to dissipation heterogeneity.

Relaxation occurs in stages, first to metastable states then to steady state.

Perturbative treatment confirms the metastability mechanism.

Abstract

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.