Strongly Interacting Quantum Dynamics

相互作用量子系统的动力学是现代物理学中许多基本问题的核心，包括理解强相关材料的输运性质以及纠缠和混沌在热化量子系统中的作用。此外，由于全息对应，强相互作用量子场论的动力学与黑洞物理学的关键方面密切相关，包括霍金的信息悖论。然而，由于缺乏在弱相互作用系统之外研究量子动力学的技术，解决这些问题的进展受到严重限制。本项目将通过建立全息量子场论和随机量子电路研究中出现的这些领域之间的联系，在多体量子系统和量子场论中有关纠缠、混沌和输运的基本和长期存在的问题上取得进展。特别是：(i)我们将发展多体量子混沌的有效场论描述，目前只存在于“最大混沌”系统的特殊情况下。这些理论将为描述大范围系统中的混沌提供一个通用框架。（ii）我们将利用最初在全息理论中确定的扩散和混沌之间的联系来发展多体量子系统和量子场论中输运的基本界限。这种界限将为理解强相关材料中的输运提供一个通用工具，并可以解释异常输运性质的存在，例如在奇怪金属中发现的线性电阻率。（iii）我们将通过推广随机量子电路中出现的“纠缠膜”技术，在量子场论中对纠缠动力学进行粗粒度描述，并将这些技术应用于引力系统，以解决黑洞蒸发过程中量子信息的命运。

The dynamics of interacting quantum systems is central to many fundamental questions in modern physics, including understanding the transport properties of strongly correlated materials and the role of entanglement and chaos in thermalizing quantum systems. Further, due to the holographic correspondence, the dynamics of strongly interacting quantum field theories is intimately connected to key aspects of black hole physics including Hawking's information paradox. Nevertheless, progress in addressing these questions has been severely limited by a lack of techniques to study quantum dynamics outside of weakly interacting systems. This project will make progress on fundamental and long-standing questions concerning entanglement, chaos and transport in many-body quantum systems and quantum field theory, by building on connections between these fields that have recently emerged in studies of holographic quantum field theories and random quantum circuits. In particular: (i) We will develop effective field theory descriptions of many-body quantum chaos, which currently only exist for the special case of `maximally chaotic' systems. These theories would provide a universal framework for describing chaos across a wide range of systems. (ii) We will use connections between diffusion and chaos originally identified in holographic theories to develop fundamental bounds on transport in many-body quantum systems and quantum field theory. Such bounds would provide a general tool for understanding transport in strongly correlated materials, and could explain the existence of anomalous transport properties such as the linear resistivity found in strange metals. (iii) We will develop a coarse-grained description of entanglement dynamics in quantum field theory by generalising `entanglement membrane' techniques that arise in random quantum circuits, and apply these to gravitational systems to address the fate of quantum information during the black hole evaporation.