Towards a theory of metastability in open quantum dynamics

TL;DR

This paper develops a theoretical framework for understanding metastability in open quantum systems by analyzing spectral properties of the generator of quantum dynamics, enabling low-dimensional approximations.

Contribution

It generalizes classical metastability concepts to quantum systems, introducing a spectral approach to identify and characterize metastable states and manifolds.

Findings

Spectral splitting indicates metastable states in quantum dynamics.

Low-dimensional models effectively approximate long-time behavior.

Metastable manifolds include disjoint states, noiseless subsystems, and decoherence-free subspaces.

Abstract

By generalising concepts from classical stochastic dynamics, we establish the basis for a theory of metastability in Markovian open quantum systems. Partial relaxation into long-lived metastable states - distinct from the asymptotic stationary state - is a manifestation of a separation of timescales due to a splitting in the spectrum of the generator of the dynamics. We show here how to exploit this spectral structure to obtain a low dimensional approximation to the dynamics in terms of motion in a manifold of metastable states constructed from the low-lying eigenmatrices of the generator. We argue that the metastable manifold is in general composed of disjoint states, noiseless subsystems and decoherence-free subspaces.