Foundations and measures of quantum non-Markovianity

By H. Breuer. 2012

198 citations recorded by the source corpus.

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 behaviour. Here, we review recent ideas developing a general mathematical definition for non-Markovianity 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/06ff5153e0454a1f85801357824ffe9a5877cecc

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Colloquium: Non-Markovian dynamics in open quantum systems (2015, methodology): “…quantitative measures for the degree of memory effects (see, e.g., (Breuer et al., 2009; Chruściński et al., 2011; Chruściński and Maniscalco, 2014; Luo et al., 2012; Rivas et al., 2010; Wolf et al., 2008), the tutorial paper (Breuer, 2012) and the recent review by Rivas et al. (2014)).”
Dynamics of non-Markovian open quantum systems (2015, methodology): “In doing so, we introduce the concept of non-Markovianity from a phenomenological point of view; a more quantitative analysis is provided in the next section and also reviewed by Breuer (2012); Breuer et al. (2015); and Rivas et al. (2014).”
Quantum trajectories and open many-body quantum systems (2014, background): “Already there has been a great deal of progress on treating nonmarkovian effects in open systems [1, 355], including through the extension of master equation techniques [356, 357] and stochastic wavefunction methods [358–360] on expanded Hilbert spaces.”