Typical and Non-typical Temporal Relaxation Processes in Macroscopic Quantum Systems

在微观层面上，孤立的多体系统的动力学通常表现出极其复杂(混沌)的行为。即使在任意长时间之后，与早期相比，时间演化通常不会有任何明显的简化，尤其是不会接近某个稳定状态。此外，动力学或初始条件的微小变化通常会导致微观系统状态在相当短的时间内发生较大的变化。相比之下，宏观层面上的可观测行为往往显得出人意料地简单和稳健，甚至似乎接近某种稳定的长时间限制，这在很大程度上独立于大多数微观细节。该项目的总体主要目标是在基本的量子力学基础上更好地理解其中一些问题，无论是定性还是定量。具体地说，在第二个资助期，第一个目标是进一步探讨前一个资助期的核心问题：未受扰动的系统的时间松弛通常如何随着(不太强烈)扰动而变化，例如，对两个原本孤立的子系统的耦合或其他不相互作用的粒子之间的相互作用进行建模？第二个目标是将这些概念扩展到受时间周期外部驱动的系统。进一步的主要问题涉及随机矩阵理论的概念基础和对特定模型系统的分析探索。

On the microscopic level, the dynamics of an isolated many-body system generically exhibits an extremely complicated (chaotic) behavior. Even after arbitrary long times, the temporal evolution usually does not admit any obvious simplifications compared to the early times, and, in particular, does not approach some steady state. Moreover, small changes of the dynamics or the initial conditions typically lead to large modifications of the microscopic system states after rather short times. In contrast, the observable behavior on the macroscopic level often appears to be surprisingly simple and robust, seemingly even approaching some steady long-time limit which is largely independent of most of the microscopic details.The overall main goal of the project is to better understand some of these issues on a fundamental, quantum mechanical basis, both qualitatively and quantitatively. Specifically, during the second funding period a first objective is to further pursue the central question of the previous funding period: How does the temporal relaxation of an unperturbed system typically change in response to a (not too strong) perturbation, modeling, for instance, the coupling of two otherwise isolated subsystems or the interaction between otherwise non-interacting particles? A second objective is to extend those concepts to systems which are subject to a time-periodic external driving. Further major issues concern the conceptual foundation of random matrix theory and the analytical exploration of specific model systems.