Exact master equations for the non-Markovian decay of a qubit

Abstract

Exact master equations describing the decay of a two-state system into a structured reservoir are constructed. Employing the exact solution for the model we determine analytical expressions for the memory kernel of the Nakajima-Zwanzig master equation and for the generator of the corresponding time-convolutionless master equation. This approach allows a detailed investigation and comparison of the convergence behavior of the corresponding perturbation expansions. Moreover, we find that the structure of widely used phenomenological master equations with memory kernel may be incompatible with a non-perturbative treatment of the underlying microscopic model. We discuss several physical implications of our results on the microscopic analysis and the phenomenological modelling of non-Markovian quantum dynamics of open systems.

11 pages, no figures

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• Crossover Between Non-Markovian and Markovian Dynamics Induced by a Hierarchical Environment
• Dissipative dynamics of a solid-state qubit coupled to surface plasmons: from non-Markov to Markov regimes
• Heisenberg-Langevin vs. quantum master equation
• Exact Non-Markovian Master Equation and Dispersive Probing of Non-Markovian Process
• Suppression of ac Stark shift scattering rate due to non-Markovian behavior
• Perturbative Dynamics of Open Quantum Systems by Renormalization Group Method