Nonequilibrium Quantum Mechanics of Strongly Correlated Systems

非技术总结：该奖项支持复杂系统动力学的研究和教育，其中量子力学以及许多粒子之间的强相互作用都很重要。这种具有挑战性的体制对新一代实验和量子设备有许多开放的相关问题。PI和她的研究小组将研究这些系统如何随时间进化，它们的集体时间行为是否可以显示一些与系统无关的普遍特性，以及在什么条件下它们初始状态的痕迹完全消失。这些项目将汇集来自不同物理领域的概念。该奖项具有很强的教育成分，涉及研究生和本科生的积极参与，以及博士后研究科学家。这些项目的结果将在讲习班和会议上提出，并将被纳入社区广泛阅读的期刊上的一篇评论文章。该项目将导致研究复杂系统动力学的新理论方法的发展，并将解决与量子信息和量子计算相关的基本问题。PI还将参与作为纽约大学物理系与当地学校持续合作伙伴关系一部分的外展活动。技术概述：该奖项支持强相关量子系统中非平衡现象的研究和教育。重点将是研究闭合和开放量子系统中的淬火动力学，并应用于冷原子气体、固态系统的超快速泵浦探针光谱和光物质耦合系统。该项目有几个组成部分：a)研究小组将以他们最近的工作为基础，在量子淬灭到孤立玻色子O(N)模型的临界点后发现普遍老化行为，并探索其他类型玻色子和费米子模型中的类似普遍性。大n和维度展开方法将用于研究时间演化，并确定中间时间的缩放行为和光锥动力学。b)研究小组还将研究量子猝灭后纠缠熵和纠缠谱的动力学。本研究将对临界淬火和强无序的一维相互作用系统进行研究。c)研究小组从相互作用场理论的大n极限中获得了一些精确的淬火动力学结果。这些精确的结果将被用作开发基于张量网络状态的时变分方法的基准。这些项目的目标不仅是获得量子猝灭后的普遍动力学的一般结果，而且是关于纠缠熵和纠缠谱的动力学的一般结果。因此，将获得关于量子猝灭后信息传播速度的结果，以及这如何取决于系统的激发程度、维度、与临界点的接近程度、相互作用的范围以及系统的遍历性。该项目还将导致研究非平衡量子系统的新方法的发展。该奖项具有很强的教育成分，涉及研究生，本科生和博士后研究科学家的积极参与。这些项目的成果将在研讨会和会议上发表，并将被纳入一篇关于量子猝灭的评论文章中。该奖项将导致研究非平衡现象的新理论方法的发展。此外，PI对纠缠动力学的研究将解决与量子信息和量子计算相关的基本问题。此外，PI还将参与作为纽约大学物理系与当地学校持续合作的一部分的外展活动。

NON-TECHNICAL SUMMARY:The award supports research and education on the dynamics of complex systems where both quantum mechanics as well as strong interactions between many particles are important. This challenging regime has many open questions of relevance for a new generation of experiments and quantum devices. The PI and her research team will study how such systems evolve in time, whether their collective temporal behavior can show some system-independent universal properties, and under what conditions traces of their initial state disappear completely. The projects will bring together concepts from diverse fields of physics.The award has a strong educational component that involves the active participation of graduate and undergraduate students, and a postdoctoral research scientist. The results of the projects will be presented at workshops and conferences, and will be incorporated in a review article in a journal widely read by the community. The project will lead to the development of new theoretical approaches to study the dynamics of complex systems, and will address fundamental questions of relevance to quantum information and quantum computing. The PI will also participate in outreach activities that are part of a continuing partnership between the NYU physics department and local schools.TECHNICAL SUMMARY:The award supports research and education on nonequilibrium phenomena in strongly correlated quantum systems. The focus will be to study quench dynamics in closed and open quantum systems with applications to cold-atomic gases, ultra-fast pump-probe spectroscopy of solid-state systems, and light-matter coupled systems.The project has several components:a) The research team will build on their recent work where universal aging behavior was found after a quantum quench to the critical point of an isolated bosonic O(N) model, and explore similar universality in other kinds of bosonic and fermionic models. Large-N and dimensional expansions methods will be used to study the time-evolution, and to identify scaling behavior at intermediate times, as well as light-cone dynamics.b) The research team will also study the dynamics of entanglement entropy and entanglement spectrum after a quantum quench. This study will be carried out for quenches to the critical point, as well as for interacting one-dimensional systems with strong disorder.c) The research team has access to some exact results for the quench dynamics coming from the large-N limit of interacting field theories. These exact results will be used as a benchmark for developing time-dependent variational methods based on tensor network states.The goal of the projects will be to obtain general results not only on universal dynamics after a quantum quench, but also on the dynamics of entanglement entropy and entanglement spectra. Thus, results will be obtained on how fast information travels after a quantum quench, and how this depends on how excited the system is, its dimensionality, proximity to a critical point, range of interactions, and how ergodic the system is. The project will also result in the development of new methods to study nonequilibrium quantum systems.The award has a strong educational component that involves the active participation of graduate, undergraduate students, and a postdoctoral research scientist. The results of the projects will be presented at workshops and conferences, and will be incorporated in a review article on quantum quenches. The award will lead to the development of new theoretical approaches to study nonequilibrium phenomena. Moreover the PI's study of entanglement dynamics will address fundamental questions of relevance to quantum information and quantum computing. In addition, the PI will participate in outreach activities that are part of a continuing partnership between the NYU physics department and local schools.