CQIS: Quantum Chaos and Quantum Gravity from Entanglement

这个项目解决的物理问题包括：“时间之箭”是如何从量子力学中出现的？如何在有许多粒子的量子系统中描述混沌？信息会在黑洞中丢失吗？我们怎样才能建立一个统一广义相对论和量子力学的量子引力理论呢？这些看似不同的基本问题都与量子纠缠的概念密切相关。在经典力学中，在多粒子系统（多体系统）中，由于混沌，很难预测一个复杂系统的未来。然而，与此同时，混沌引起的复杂性可以产生一种简单性，使我们可以忽略关于粒子个体运动的大多数细节，并通过流体力学和热力学等宏观理论有效地描述一个多体系统。这个项目将研究如何描述量子多体系统中的混沌，而不是经典多体系统，以及如何将其与热力学和流体动力学联系起来。从贝肯斯坦和霍金的著名著作开始，人们逐渐认识到热力学还与大自然的另一个深层奥秘——引力有着深刻的联系。爱因斯坦的广义相对论将引力描述为一种弯曲的动态时空几何理论。这个项目将研究时空几何如何作为多体系统中量子纠缠的描述而出现。该项目将为研究生在量子信息科学、高能物理和凝聚态物理等跨学科领域提供独特的研究经验。研究院将通过讲座、课堂、文章等方式，持续向大学生介绍该课题，并将研究成果传播到物理界以外。本课题利用量子纠缠研究量子混沌和量子引力。PI计划通过量子信息的非局域传播来表征量子混沌，并将李雅普诺夫指数等经典混沌中的准则推广到量子系统。利用多体量子混沌的纠缠准则，研究了混沌与孤立系统热化的关系。在物理上，多体系统中的混沌与量子信息的非局域传播有关，量子信息在孤立系统的热化过程中起着至关重要的作用。除了为理解量子热化提供更坚实的基础外，PI计划在对量子混沌的新理解的基础上进一步发展非平衡动力学的一般框架。此外，混沌也将使用在一定极限下可解但仍保持混沌的特殊模型来研究。与量子引力相关，PI计划使用随机张量网络（一种适合描述高度纠缠量子态的框架）研究全息二象性和量子引力。有了随机张量网络的新语言，就有可能量化纠缠特性是如何在紧急几何中编码的。全息二象性的不同方面将被研究，包括全局对称性、几何涨落以及爱因斯坦方程如何可能从纠缠中出现。PI还计划将获得的新认识应用于长期存在的黑洞信息悖论。

This project addresses physics questions such as: How does the "arrow of time" emerge from quantum mechanics? How can one characterize chaos in quantum systems with many particles? Does information get lost in a black hole? How can we develop a quantum gravity theory that unifies general relativity and quantum mechanics? These seemingly distinct fundamental questions are all deeply related to the concept of quantum entanglement. In classical mechanics in systems with many particles (many-body systems), because of chaos, it is difficult to predict anything about the future of a complicated system. At the same time, however, the complexity induced by chaos can generate a kind of simplicity that allows us to ignore most details about the individual motion of the particles and describe a many-body system efficiently by macroscopic theories such as hydrodynamics and thermodynamics. This project will investigate how to describe chaos in quantum many-body systems, as opposed to classical many-body systems, and how to relate it to thermodynamics and hydrodynamics. Since the famous work of Bekenstein and Hawking, it has been gradually realized that thermodynamics is also deeply related to another deep mystery of nature, namely gravity. Einstein's general relativity theory describes gravity as a theory of curved and dynamical space-time geometry. This project will investigate how the space-time geometry may emerge as a description of quantum entanglement in many-body systems. The project will provide graduate students with a unique research experience in the interdisciplinary area of quantum information science, high-energy physics and condensed matter physics. The PI will make sustained efforts to introduce the proposed research to undergraduate students and to disseminate the research results of this project beyond the physics community, by lectures, classes and articles.This project studies quantum chaos and quantum gravity using quantum entanglement. The PI plans to characterize quantum chaos by the nonlocal propagation of quantum information, and generalize the criteria in classical chaos such as Lyapunov exponents to quantum systems. Using entanglement criteria of many-body quantum chaos, the relation of chaos with thermalization of an isolated system will be investigated. Physically, chaos in many-body systems is associated with nonlocal propagation of quantum information, which plays an essential role in thermalization process of an isolated system. In addition to providing a more solid foundation to understand quantum thermalization, the PI plans to further develop a general framework of non-equilibrium dynamics based on the new understanding of quantum chaos. Furthermore, chaos will also be studied using special models that are solvable under certain limit but still preserve chaos. Related to quantum gravity, the PI plans to study holographic duality and quantum gravity using random tensor networks, a framework suitable for describing highly entangled quantum states. With the new language of random tensor networks, it is possible to quantify how entanglement properties are encoded in emergent geometry. Different aspects of the holographic duality will be investigated, including global symmetries, geometrical fluctuation and how Einstein's equations can possibly emerge from entanglement. The PI also plans to apply the new understanding obtained to the long-standing black hole information paradox.