We review the methods and use of random quantum states with particular emphasis on recent theoretical developments and applications in various fields. The guiding principle of the review is the idea that random quantum states can be understood as classical probability distributions in the Hilbert space of the associated quantum system. We show how this central concept connects questions of physical interest that cover different fields such as quantum statistical physics, quantum chaos, mesoscopic systems of both non-interacting and interacting particles, including superconducting and spin–orbit phenomena, and stochastic Schrödinger equations describing open quantum systems.

中文翻译：

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随机量子态：最新发展和应用

我们回顾了随机量子态的方法和使用，特别强调了各个领域的最新理论发展和应用。该评论的指导原则是，随机量子态可以理解为相关量子系统的希尔伯特空间中的经典概率分布。我们展示了这个中心概念如何连接涵盖不同领域的物理问题，如量子统计物理学、量子混沌、非相互作用和相互作用粒子的介观系统，包括超导和自旋轨道现象，以及描述开放量子的随机薛定谔方程系统。