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

宏观量子系统中的典型和非典型时间弛豫过程

• 批准号: 397303734
• 负责人: Professor Dr. Peter Reimann
• 金额: --
• 依托单位: Arbeitsgruppe Theorie der Kondensierten Materie
• 依托单位国家: 德国
• 项目类别: Research Units
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/397303734?language=en
• 关键词: Typical; Non; typical; Temporal; Relaxation

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.

在微观水平上，孤立的多体系统的动力学通常表现出极其复杂的（混乱）行为。即使在任意长时间之后，时间进化通常也不承认与早期相比的任何明显的简化，尤其是没有接近某种稳定状态。此外，动态或初始条件的小变化通常会在短时间内对微观系统状态进行大规模修改。相反，宏观级别上可观察到的行为通常似乎是令人惊讶的简单和健壮的，甚至似乎接近了一些稳定的长期限制，这在很大程度上与大多数显微镜细节无关。具体而言，在第二个融资期间，第一个目标是进一步追求上一个融资期的核心问题：不受干扰的系统的时间放松通常会响应于（不太强）扰动（例如，建模），例如两个其他孤立的子系统或其他非互动粒子之间的相互作用的建模？第二个目标是将这些概念扩展到受时间周期外部驾驶的系统。进一步的主要问题涉及随机矩阵理论的概念基础和特定模型系统的分析探索。