Local master equations may fail to describe dissipative critical behavior

TL;DR

Local quantum master equations often fail to accurately describe dissipative critical behavior in open quantum systems due to their inability to capture intersystem correlations, as shown in a two-oscillator heat bath model.

Contribution

This paper critically evaluates the validity of local master equations in modeling dissipative critical phenomena, highlighting their limitations in capturing intersystem correlations.

Findings

Local master equations do not match exact quantum-Langevin results.

They fail to accurately predict steady-state occupation numbers.

Inability to characterize intersystem correlations is a key limitation.

Abstract

Local quantum master equations provide a simple description of interacting subsystems coupled to different reservoirs. They have been widely used to study nonequilibrium critical phenomena in open quantum systems. We here investigate the validity of such a local approach by analyzing a paradigmatic system made of two harmonic oscillators each in contact with a heat bath. We evaluate the steady-state mean occupation number for varying temperature differences and find that local master equations generally fail to reproduce the results of an exact quantum-Langevin-equation description. We relate this property to the inability of the local scheme to properly characterize intersystem correlations, which we quantify with the help of the quantum mutual information.