开放量子系统的随机矩阵方法

H. Schomerus
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引用次数: 28

摘要

在过去的几十年里,大量的理论和数学工作都致力于开放量子系统的随机矩阵描述。在这些笔记中,基于2015年7月在Les Houches暑期学校“随机过程和随机矩阵”的讲座,我们回顾了底层模型的物理起源和数学结构,并收集了能够深入了解典型系统行为的关键预测。特别是,我们的目标是给出一个不同的特征是如何相互联系的想法。笔记主要集中在弹性散射,但也包括对相互作用系统的简短迂回,我们通过遍历性的首要问题来激励。第一章介绍随机矩阵理论中的一般概念,如厄米矩阵、酉矩阵、正定矩阵和非厄米矩阵的十个普适性类和集合。然后,我们回顾了构成统计描述基础的微观散射模型,并考虑了衰变、动力学和输运中随机散射的特征。最后一章简要介绍了安德森定位和交互系统中的定位。
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Random matrix approaches to open quantum systems
Over the past decades, a great body of theoretical and mathematical work has been devoted to random-matrix descriptions of open quantum systems. In these notes, based on lectures delivered at the Les Houches Summer School "Stochastic Processes and Random Matrices" in July 2015, we review the physical origins and mathematical structures of the underlying models, and collect key predictions which give insight into the typical system behaviour. In particular, we aim to give an idea how the different features are interlinked. The notes mainly focus on elastic scattering but also include a short detour to interacting systems, which we motivate by the overarching question of ergodicity. The first chapters introduce general notions from random matrix theory, such as the ten universality classes and ensembles of hermitian, unitary, positive-definite and non-hermitian matrices. We then review microscopic scattering models that form the basis for statistical descriptions, and consider signatures of random scattering in decay, dynamics and transport. The last chapter briefly touches on Anderson localization and localization in interacting systems.
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