Nonequilibrium Quantum Mechanics of Strongly Correlated Systems

该奖项支持对处于高度激发态或非平衡态的复杂量子系统的理论研究。这些系统可以在无数的实验平台上实现，它们也是下一代设备的组成部分。然而，研究这类系统的理论方法仍处于起步阶段。量子系统也有一个定义特征，称为量子纠缠，这使得它们在质量上与经典系统不同。该项目将发展理论方法，不仅研究量子系统的经典度量，如电阻和粘度，还将开发研究量子纠缠的技术。纠缠的研究与美国国家科学基金会的量子飞跃计划非常一致，该计划的目标是推动量子力学的边界及其应用于下一代技术。这个项目也有很强的教育成分，因为它将导致下一代科学家的培训。PI和NSF资助的研究科学家将通过纽约大学gstem项目指导高中生，从而扩大参与范围。PI还致力于组织一系列会议，旨在将不同的科学家群体聚集在一起，这些科学家通常没有机会相互作用，但却有着共同的目标，即理解复杂系统中的非平衡现象。该奖项支持对强相关量子系统中非平衡现象的理论研究。该项目将发展场理论方法来研究远离平衡的输运、相关函数和纠缠测量。研究纠缠度量的形式化发展与NSF量子跃进计划是一致的。该项目也适用于目前在冷原子气体、固态系统的超快泵探光谱和光物质耦合系统中的实验。该项目有以下主要组成部分：(1)大n玻色子和费米子理论，以及自然考虑守恒定律的两粒子不可约形式，将被用于研究非平衡现象。量子淬火后的瞬态电导率和粘度将被研究。将研究相互作用的临界系统，目的是寻找新的脱离平衡的尺度物理，并探索临界慢模是否会引起输运中的异常。(2)采用增宽的Schwinger-Keldysh形式研究非时间有序相关器和Renyi纠缠熵。将发展受控的弱耦合展开来构造这些纠缠度量。该项目还具有很强的教育成分，因为它将培养一名研究生和一名博士后研究科学家。PI和NSF资助的研究科学家将通过纽约大学gstem项目指导高中生，从而扩大参与范围。PI还致力于组织一系列会议，旨在将不同群体的科学家聚集在一起，他们有着共同的目标，即理解复杂系统中的非平衡现象。该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。

NONTECHNICAL SUMMARYThis award supports theoretical research on complex quantum systems that are in a highly excited or nonequilibrium state. These systems can be realized in a myriad of experimental platforms, and they are also ingredients in the next generation of devices. Theoretical methods to study such systems are, however, still in their infancy. Quantum systems also have a defining feature, called quantum entanglement, that makes them qualitatively different from their classical counterparts. This project will develop theoretical methods to study not only classical metrics of quantum systems such as resistance and viscosity, but will also develop techniques to study quantum entanglement. The study of entanglement is well aligned with the NSF Quantum Leap initiative, whose goal is to push the boundaries of quantum mechanics and its applications to next generation technologies.This project also has a strong educational component as it will lead to the training of the next generation of scientists. The PI and NSF funded research scientists will broaden participation by mentoring high school students through the NYU-GSTEM program. The PI is also committed to organizing a series of conferences that aim to bring together diverse communities of scientists that usually do not have the opportunity to interact, but share the common goal of understanding nonequilibrium phenomena in complex systems. TEHCNICAL SUMMARYThis award supports theoretical research on nonequilibrium phenomena in strongly correlated quantum systems. The project will develop field-theoretic approaches to study transport, correlation functions, and entanglement measures far out of equilibrium. The development of a formalism for studying entanglement measures is well aligned with the NSF Quantum Leaps initiative. The project also applies to current experiments in cold-atomic gases, ultra-fast pump-probe spectroscopy of solid-state systems, and light-matter coupled systems. The project has the following major components: (1) Large-N bosonic and fermionic theories, along with the two-particle irreducible formalism that naturally takes into account conservation laws, will be employed to study nonequilibrium phenomena. Transient conductivity and viscosity following a quantum quench will be studied. Interacting critical systems will be studied, with the goal of searching for new scaling physics out of equilibrium and exploring whether critical slow modes can give rise to anomalies in transport. (2) An augmented Schwinger-Keldysh formalism will be employed to study out of time ordered correlators, and the Renyi entanglement entropy. Controlled weak-coupling expansions will be developed to construct these entanglement measures. The project also has a strong educational component as it will lead to the training of a graduate student and a postdoctoral research scientist. The PI and NSF funded research scientists will broaden participation by mentoring high school students through the NYU-GSTEM program. The PI is also committed to organizing a series of conferences that aim to bring together diverse communities of scientists who share the common goal of understanding nonequilibrium phenomena in complex systems.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.