Local master equations may fail to describe dissipative critical behavior

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.

9 pages, 7 figures. Minor changes in the introduction/conclusion and correction of several minor typos in equations

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• Quantum master equation for many-body systems: Derivation based on the Lieb-Robinson bound
• Time dependent Markovian master equation beyond the adiabatic limit
• Linear Ultrastrong Optomechanical Interaction
• Irreversible Entropy Production rate in a parametrically driven-dissipative System: The Role of Self-Correlation between Noncommuting Observables
• Quantum entanglement and Einstein-Podolsky-Rosen steering in ultrastrongly light-matter coupled system
• Exceptional point in self-consistent Markovian master equations
• Behavior of quantum coherence in the ultrastrong and deep strong coupling regimes of light-matter system
• Open harmonic chain without secular approximation