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arXiv:1406.4965 · The European Physical Journal B

Description of non-Markovian effect in open quantum system with the discretized environment method

Denis Lacroix A, Vazgen Sargsyan, G. G. Adamian, Nikolai Antonenko

Published Apr 1, 2015• 22 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2015-60052-3

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The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex structures are of central importance in many applications of quantum mechanics. The theoretical description, analysis and control of non-Markovian quantum processes play an important role in this context. While in a Markovian process an open system irretrievably loses information to its surroundings, non-Markovian processes feature a flow of information from the environment back to the open system, which implies the presence of memory effects and represents the key property of non-Markovian quantum behavior. Here, we review recent ideas developing a general mathematical definition for non-Markoviantiy in the quantum regime and a measure for the degree of memory effects in the dynamics of open systems which are based on the exchange of information between system and environment. We further study the dynamical effects induced by the presence of system-environment correlations in the total initial state and design suitable methods to detect such correlations through local measurements on the open system.
Abstract The non-Markovianity of an arbitrary open quantum system is analyzed in reference to the multi-time statistics given by its monitoring at discrete times. On the one hand, we exploit the hierarchy of inhomogeneous transfer tensors (TTs), which provides us with relevant information about the role of correlations between the system and the environment in the dynamics. The connection between the TT hierarchy and the CP-divisibility property is then investigated, by showing to what extent quantum Markovianity can be linked to a description of the open-system dynamics by means of the composition of one-step TTs only. On the other hand, we introduce the set of stochastic TT transformations associated with local measurements on the open system at different times and conditioned on the measurement outcomes. The use of the TT formalism accounts for different kinds of memory effects in the multi-time statistics and allows us to compare them on a similar footing with the memory effects present in non-monitored non-Markovian dynamics, as we illustrate on a spin-boson case study.