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Do phenomenological master equations with memory kernel always describe a non-Markovian quantum dynamics characterized by reverse flow of information? Is the integration over the past states of the system an unmistakable signature of non-Markovianity? We show by a counterexample that this is not always the case. We consider two commonly used phenomenological integro-differential master equations describing the dynamics of a spin 1/2 in a thermal bath. By using a recently introduced measure to quantify non-Markovianity [H.-P. Breuer, E.-M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)] we demonstrate that as far as the equations retain their physical sense, the key feature of non-Markovian behavior does not appear in the considered memory kernel master equations. Namely, there is no reverse flow of information from the environment to the open system. Therefore, the assumption that the integration over a memory kernel always leads to a non-Markovian dynamics turns out to be vulnerable to phenomenological approximations. Instead, the considered phenomenological equations are able to describe time-dependent and uni-directional information flow from the system to the reservoir associated to time-dependent Markovian processes.
Efficient simulations of the dynamics of open systems is of wide importance for quantum science and tech-nology. Here, we introduce a generalization of the transfer-tensor, or discrete-time memory kernel, formalism to multi-time measurement scenarios
Non-Markovian local in time master equations give a relatively simple way to describe the dynamics of open quantum systems with memory effects. Despite their simple form, there are still many misunderstandings related to the physical applicability an
We derive sufficient conditions for the memory kernel which guarantee legitimate (completely positive and trace-preserving) dynamical map. It turns out that these conditions provide a natural parameterizations of the dynamical map being a generalizat
We construct a large class of completely positive and trace preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics characterized by a continuous time evolution interrupted by jumps, randomly dis
Complete characterization of complete positivity preserving non-Markovian master equations is presented.