Derivation of the Redfield quantum master equation and corrections to it by the Bogoliubov method

Abstract

Following the ideas N. N. Bogoliubov used to derive the classical and quantum nonlinear kinetic equations, we give an alternative derivation of the Redfield quantum linear master equation, which is widely used in the theory of open quantum systems, as well as higher-order corrections to it. This derivation naturally considers initially correlated system-reservoir states arising from the previous system-reservoir dynamics. It turns out that the Redfield equation does not require any modifications in this case. The expressions of higher-order corrections are simpler than those obtained by other methods.

arXiv comment16 pages; new references and comments in comparison with the journal version

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• Time-convolutionless master equations for composite open quantum systems
• Long-time Markovianity of multi-level systems in the rotating wave approximation
• Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity
• Local generation of entanglement with Redfield dynamics
• On time-dependent projectors and on generalization of thermodynamical approach to open quantum systems
• Repeated temperature measurements in quantum thermodynamics
• Explicit noise and dissipation operators for quantum stochastic thermodynamics
• Exact non-Markovian master equations: a generalized derivation for Gaussian systems
• Adapted projection operator technique for the treatment of initial correlations