基于规范场引力对偶，场论中的非局域可观测量同引力中不同维度的极值面面积优雅地联系起来，这为研究强耦合量子多体系统提供了一种新的工具。本项目旨在通过全息非局域可观测量探测黑洞相变、量子混沌以及宇宙奇点。我们拟研究旋转AdS黑洞的全息相变、探索量子纠缠与信息和热力学的关系、发展新的探测全息混沌的方法，讨论引力修正和量子修正对宇宙奇点全息特征的影响。我们还将发展解析方法研究全息相变和全息混沌。这一研究不仅拓展了非局域可观测量的应用范围，还有助于我们更深刻地理解强耦合体系中的相变、量子混沌和宇宙奇点这些现象的本质。

Based on the gauge field/gravity duality, the non-local observables in field theory are related elegantly with the areas of the extremal surfaces with different dimensions, which provides a new tool to study the strongly coupled quantum multibody systems. This project aims to probe the black hole phase transition, quantum chaos and cosmological singularity with holographic non-local observables. We will study the holographic phase transitions of rotating AdS black holes; explore the relations among the quantum entanglement, information and thermodynamics; develop a new way to probe the holographic chaos; discuss the effects of the gravity correction and quantum correction to the holographic signatures of cosmological singularities. We will also find the analytical methods to study the holographic phase transition and holographic chaos. This study not only extends the scope of applications of non-local observables, but also helps us to understand profoundly the nature of the phase transition, chaos as well as the cosmological singularities in strongly coupled systems.