Entanglement and Chaos in Quantum Gravitational Systems

纠缠和混沌在孤立量子系统的研究中起着核心作用。最近，这些想法在凝聚态系统的研究中产生了深远的影响，无论是在理论还是实验层面。这个项目研究纠缠和混沌在量子引力系统中所扮演的角色。从凝聚态物理学的方法和纠缠和混沌的想法被应用到引力系统：a）圈量子引力和空间的纠缠结构; B）量子场在动态时空中的纠缠产生。这项研究的结果预计将对环量子引力、弯曲时空中的量子场论以及极早期宇宙演化阶段两者之间的过渡产生直接影响。在圈量子引力的背景下，将开发新的方法来将时空结构编码为量子几何的关联和纠缠。目的是确定近似解的动力学编码的几何形状的半经典时空和支持微扰场论波动。在微扰水平上，将研究宇宙时空中量子场的纠缠产生，重点是再加热阶段、暴胀阶段和暴胀之前的候选BKL阶段的不稳定性。目标是弥合圈量子引力和微扰量子场之间的差距。长期目标是将这两条工作线的结果联合收割机结合起来，以研究量子引力模型，其中宇宙的前暴胀状态以其纠缠结构为特征，并确定这种纠缠结构可以在宇宙学观测值中留下的印记，例如宇宙微波背景中的各向异性相关性和大尺度宇宙中的密度相关性，该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Entanglement and chaos play a central role in the study of isolated quantum systems. Recently, these ideas have had a profound impact in the study of condensed matter systems, both at the theoretical and the experimental level. This project investigates the role played by entanglement and chaos in quantum gravitational systems. Methods from condensed matter physics and ideas on entanglement and chaos are applied to gravitational systems: a) Loop quantum gravity and the entanglement structure of space; b) Entanglement production by quantum fields in dynamical space-times. The results of this research are expected to have a direct impact on the development of loop quantum gravity, quantum field theory in curved spacetimes, and the transition between the two in a phase of the evolution of the very early universe. In the context of loop quantum gravity, new methods will be developed for encoding the architecture of spacetime into correlations and entanglement of the quantum geometry. The objective is to identify approximate solutions of the dynamics that encode the geometry of a semiclassical spacetime and support perturbative field theoretical fluctuations. At the perturbative level, the entanglement production by quantum fields in cosmological spacetimes will be studied, with focus on instabilities in the reheating phase, in the inflationary phase, and in a candidate BKL-like phase that precedes inflation. The objective is to bridge the gap between loop quantum gravity and perturbative quantum fields. The long-term goal is to combine results of the two lines of work in order to investigate models of quantum gravity where the pre-inflationary state of the universe is characterized by its entanglement structure and identify the imprints that such entanglement structure can leave in cosmological observables, such as anisotropy correlations in the cosmic microwave background and density correlations in the large-scale structure of the universe.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.