Classical and quantum non-Markovianity

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The elimination of irrelevant degrees of freedom in complex systems often leads to a non-Markovian process featuring memory effects in the dynamics of a reduced set of relevant variables which form an open system. In recent years theoretical and experimental studies on the definition, detection and control of non-Markovian processes have attracted a huge amount of interest both in classical and quantum nonequilibrium systems, and havefound a multitude of applications in diverse fields. For classical systems Markovian dynamics is uniquely defined by the standard Markov condition for the hierarchy of joint probability distributions of the underlying stochastic process. While this definition cannot be transferred to the quantum regime, it can be shown that a consistent characterization of quantum Markovianity can be based on the properties of the flow of information between the open system (relevant degrees of freedom) and its environment (irrelevant degrees of freedom). As part of the Research Unit ''Reducing complexity of nonequilibrium system'' the present project is concerned with fundamental properties of memory effects and non-Markovian behavior in many-body systems far from equilibrium. Based on a paradigmatic example of a complex dynamical system, the Fermi-Pasta-Ulam model, we will construct observable quantities which are suitable for the characterization and quantification of the information flow between system and environment and the ensuing memory effects. In particular, the relation between quantum and classical memory effects as well as the impact of quantum and classical correlations on the dynamics are of central importance in our investigations. In this project we will employ analytical methods from the theory of open system and nonequilibrium statistical physics, as well as numerical techniques using the Wigner representation and the multiconfiguration time-dependent Hartree method.