Nonequilibrium Quantum Mechanics of Strongly Correlated Systems

非技术总结该奖项支持对处于高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初级阶段。量子系统还有一个决定性的特征，称为量子纠缠，这使它们在性质上与经典系统不同。该项目将开发理论方法，不仅研究量子系统的经典度规，如电阻和粘性，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，该计划的目标是将量子力学及其应用推向下一代技术。该项目也具有很强的教育成分，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计划指导高中生来扩大参与。PI还致力于组织一系列会议，旨在将不同的科学家社区聚集在一起，这些科学家通常没有机会互动，但有着共同的目标，即了解复杂系统中的非平衡现象。技术总结该奖项支持对强关联量子系统中非平衡现象的理论研究。该项目将开发场论方法来研究传输、关联函数和远离平衡的纠缠测量。用于研究纠缠测量的形式主义的发展与美国国家科学基金会的量子跃迁倡议非常一致。该项目还适用于目前在冷原子气体、固态系统的超快泵浦-探测光谱和轻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主义，将被用于研究非平衡现象。我们将研究量子猝灭后的瞬时电导率和粘度。将研究相互作用的临界系统，目标是寻找新的脱离平衡的标度物理，并探索临界慢模式是否会导致输运中的异常。(2)利用增广的Schwinger-Keldysh形式来研究超时有序相关器和Renyi纠缠熵。我们将开发受控的弱耦合扩展来构建这些纠缠措施。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计划指导高中生来扩大参与。PI还致力于组织一系列会议，旨在将拥有了解复杂系统中非平衡现象的共同目标的不同科学家社区聚集在一起。该奖项反映了NSF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。

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.