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 quantum mutual information.
Highlights
Quantum master equations have been instrumental in the study of open quantum systems since their introduction by Pauli in 1928 [1]
In order to gain deeper insight on the nonequilibrium properties of the different quantum master equations, we examine the ratio of their steady-state mean occupation numbers and the corresponding quantum-Langevin-equation expressions a1†a1 ss/ a1†a1 Langevin for increasing temperature differences T
We have examined the ability of global and local quantum master equations to accurately describe dissipative critical phenomena using an illustrative system of two interacting damped harmonic oscillators with and without rotating-wave interaction
Summary
Quantum master equations have been instrumental in the study of open quantum systems since their introduction by Pauli in 1928 [1]. For boundary-driven processes where the system of interest is coupled to several reservoirs In this case, it has recently been shown that local master equations, that are commonly used to examine nonequilibrium phase transitions [17–28], may violate the second law of thermodynamics [29] and give rise to nonphysical results, such as incorrect steady-state distributions or nonzero currents for vanishing bath interactions [30–40], even in the limit of small bath couplings. It has recently been shown that local master equations, that are commonly used to examine nonequilibrium phase transitions [17–28], may violate the second law of thermodynamics [29] and give rise to nonphysical results, such as incorrect steady-state distributions or nonzero currents for vanishing bath interactions [30–40], even in the limit of small bath couplings These inconsistencies are related to the fact that local quantum master equations, whose total dissipator is the sum of the single-bath dissipators, incorrectly neglect bath-bath correlations, which are induced by intersystem interactions, in contrast to global quantum master equations [29–40]. We show that this feature is directly related to the inability of the local description to correctly capture intersystem correlations, which we quantify with the help of the quantum mutual information [9]
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