Uniqueness regime for Markov dynamics on quantum lattice spin systems

TL;DR

This paper proves that weakly interacting quantum Markov processes on a lattice maintain a unique stationary state and exponential relaxation in the thermodynamic limit, even without reversibility assumptions.

Contribution

It establishes conditions under which quantum Markov dynamics have a unique stationary state and rapid relaxation, extending previous results to non-reversible processes.

Findings

Uniqueness of stationary state in the thermodynamic limit

Exponential relaxation for local observables

Applicability without reversibility assumptions

Abstract

We consider a lattice of weakly interacting quantum Markov processes. Without interaction, the dynamics at each site is relaxing exponentially to a unique stationary state. With interaction, we show that there remains a unique stationary state in the thermodynamic limit, i.e. absence of phase coexistence, and the relaxation towards it is exponentially fast for local observables. We do not assume that the quantum Markov process is reversible (detailed balance) w.r.t. a local Hamiltonian.