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。近年来，这些观点对凝聚态系统的研究产生了深远的影响，无论是在理论层面还是在实验层面上。这个项目研究了量子引力系统中纠缠和混沌所起的作用。将凝聚态物理中的方法和纠缠和混沌的思想应用于引力系统：a)圈量子引力和空间的纠缠结构；b)动力学时空中量子场的纠缠产生。这项研究的结果预计将对环路量子引力的发展、弯曲时空中的量子场论，以及在非常早期的宇宙演化的一个阶段中两者之间的过渡产生直接影响。在循环量子引力的背景下，将开发新的方法来将时空的结构编码为量子几何的关联和纠缠。其目的是找出动力学的近似解，它编码了半经典时空的几何结构，并支持微扰场理论涨落。在微扰水平上，我们将研究宇宙学时空中量子场的纠缠产生，重点是重加热阶段、膨胀阶段和膨胀前的候选类BKL阶段的不稳定性。其目标是弥合环形量子引力和微扰量子场之间的差距。长期目标是将这两项工作的成果结合在一起，以研究量子引力模型，其中宇宙的膨胀前状态以其纠缠结构为特征，并确定这种纠缠结构可能在宇宙学可观测性中留下的印记，例如宇宙微波背景中的各向异性关联和宇宙大尺度结构中的密度关联。这一奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势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.