Structure of completely positive quantum master equations with memory kernel

Abstract

Semi-Markov processes represent a well known and widely used class of random processes in classical probability theory. Here, we develop an extension of this type of non-Markovian dynamics to the quantum regime. This extension is demonstrated to yield quantum master equations with memory kernels which allow the formulation of explicit conditions for the complete positivity of the corresponding quantum dynamical maps, thus leading to important insights into the structural characterization of the non-Markovian quantum dynamics of open systems. Explicit examples are analyzed in detail.

13 pages, revtex, 2 figures

References in corpus (8)

• Non-Markovian generalization of the Lindblad theory of open quantum systems
• Completely Positive Post-Markovian Master Equation via a Measurement Approach
• Quantum Semi-Markov Processes
• Lindblad rate equations
• Non-Markovian dynamics of a single electron spin coupled to a nuclear spin bath
• Non-Markovian dynamics of a qubit coupled to an Ising spin bath
• Non-Markovian dynamics for bipartite systems
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