Nonequilibrium Quantum Mechanics of Strongly Correlated Systems

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。这一具有挑战性的制度有许多与新一代实验和量子设备相关的开放问题。PI和她的研究团队将研究这样的系统如何随时间演化，它们的集体时间行为是否可以表现出一些与系统无关的普适性质，以及在什么条件下它们的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。这些项目的成果将在讲习班和会议上介绍，并将纳入社区广泛阅读的期刊上的一篇评论文章。该项目将导致开发新的理论方法来研究复杂系统的动力学，并将解决与量子信息和量子计算相关的基本问题。PI还将参与纽约大学物理系与当地学校之间持续合作的外联活动。技术概要：该奖项支持强关联量子系统中非平衡现象的研究和教育。重点是研究封闭和开放量子系统中的猝灭动力学，并将其应用于冷原子气体、固态系统的超快泵浦-探测光谱和光物质耦合系统。该项目包括以下几个部分：a）研究团队将在最近的工作基础上，在孤立玻色子O（N）模型量子猝灭到临界点后发现普遍的老化行为，并探索其他类型玻色子和费米子模型中类似的普遍性。大N和维数展开方法将用于研究时间演化，并确定中间时间的标度行为，以及光锥动力学。B）研究团队还将研究量子猝灭后纠缠熵和纠缠谱的动力学。这项研究将进行淬火的临界点，以及相互作用的一维系统与强无序。c）研究小组已经获得了一些精确的结果，淬火动力学来自大N限制的相互作用场论。这些精确的结果将被用作发展基于张量网络态的含时变分方法的基准。该项目的目标将是不仅获得量子猝灭后的普遍动力学的一般结果，而且还获得纠缠熵和纠缠谱的动力学的一般结果。因此，将获得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兴奋程度，它的维度，接近临界点，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。这些项目的结果将在研讨会和会议上介绍，并将纳入一篇关于量子猝灭的评论文章。该奖项将导致新的理论方法来研究非平衡现象的发展。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还将参加外展活动，这些活动是纽约大学物理系与当地学校之间持续伙伴关系的一部分。

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.