Recursive approach for non-Markovian time-convolutionless master equations

Abstract

We consider a general open system dynamics and we provide a recursive method to derive the associated non-Markovian master equation in a perturbative series. The approach relies on a momenta expansion of the open system evolution. Unlike previous perturbative approaches of this kind, the method presented in this paper provides a recursive definition of each perturbative term. Furthermore, we give an intuitive diagrammatic description of each term of the series, which pro- vides an useful analytical tool to build them and to derive their structure in terms of commutators and anticommutators. We eventually apply our formalism to the evolution of the observables of the reduced system, by showing how the method can be applied to the adjoint master equation, and by developing a diagrammatic description of the associated series.

9 pages

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• Stochastic unravellings of non-Markovian completely positive and trace preserving maps
• Exact generator and its high order expansions in the time-convolutionless generalized master equation: Applications to the spin-boson model and exictation energy transfer
• Trajectory tracking for non-Markovian quantum systems
• Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity
• Non-Markovianity of photon dynamics in a birefringent crystal
• Unveiling coherent dynamics in non-Markovian open quantum systems: exact expression and recursive perturbation expansion
• On time-dependent projectors and on generalization of thermodynamical approach to open quantum systems
• Recursive perturbation approach to time-convolutionless master equations: Explicit construction of generalized Lindblad generators for arbitrary open systems
• Time-Convolutionless Master Equation Applied to Adiabatic Elimination
• Exact non-Markovian master equations: a generalized derivation for Gaussian systems
• Adapted projection operator technique for the treatment of initial correlations