Classical and quantum non-Markovianity

复杂系统中不相关自由度的消除往往导致非马尔可夫过程，其特征在于形成开放系统的相关变量的缩减集的动态中的记忆效应。近年来，关于非马尔可夫过程的定义、检测和控制的理论和实验研究在经典和量子非平衡系统中都引起了人们极大的兴趣，并在各个领域得到了广泛的应用。对于经典系统，马尔可夫动力学是唯一定义的标准马尔可夫条件的联合概率分布的层次结构的基础随机过程。虽然这个定义不能转移到量子体系中，但可以证明，量子马尔可夫性的一致表征可以基于开放系统（相关自由度）与其环境（不相关自由度）之间的信息流的性质。作为研究单元“降低非平衡系统的复杂性”的一部分，本项目关注远离平衡的多体系统中记忆效应和非马尔可夫行为的基本性质。基于一个典型的例子，一个复杂的动力系统，费米-帕斯塔-乌拉姆模型，我们将构建可观测的量，这是适合的表征和量化的系统和环境之间的信息流和随之而来的记忆效应。特别是，量子和经典记忆效应之间的关系，以及量子和经典相关的动力学的影响是至关重要的，在我们的调查。在这个项目中，我们将采用开放系统和非平衡统计物理理论的分析方法，以及使用Wigner表示和多组态时间相关Hartree方法的数值技术。

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.