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。这类系统的主要挑战之一是它们加热到很高的温度，这种情况不利于观察任何不平凡的量子现象。然而，如果系统有一些对称性，这可能会限制供暖。该奖项将探索对称性以及对称性概念的泛化如何导致不受加热影响的平衡失衡现象。该项目将汇集数学物理、统计力学和凝聚态物理的方法，共同的目标是研究不平衡的广义对称性。广义对称性的一个结果是量子系统可以容纳被称为“非阿贝尔任意子”的物体。这些对象可用于存储长期稳定的内存。该项目将探索如何在实验平台上实现非阿贝尔任意子，例如所谓的“嘈杂的中间尺度量子”设备。该项目有很强的教育成分，因为它将涉及一名研究生、一名本科生和一名博士后研究科学家的积极参与。广义对称性的最新发展将数学物理、统计力学、凝聚态物质和高能物理的概念结合在一起。PI将调整她的理论凝聚态物理课程，向学生介绍这些最新的发展。此外，PI和初级研究科学家将通过纽约大学-GSTEM计划指导高中生，扩大参与范围。技术总结该奖项支持强关联量子系统中非平衡现象的理论研究。重点将是双重的。其一是发展研究非阿贝尔激发的方法，非阿贝尔激发对量子计算至关重要，在高度非平衡的环境下，可在当前嘈杂的中等尺度量子(NISQ)设备中实现。第二是开发方法来研究信息论方法，量化初始退相干的增长和纠缠的扩散。在第一个主要推力中，PI将研究由融合类别建立的Floquet模型。在这些模型中，将探索拓扑缺陷的作用，即可以在不改变物理的情况下在空间和时间方向上变形的算子。当拓扑亏损可逆时，它们是酉对称。当拓扑缺陷是不可逆的时，它们充当投影体，是非阿贝尔的，并且是不可逆对称的例子。后者也是广义对称性的例子，我们将探讨它们对量子动力学的影响。将要研究的Floquet电路将包括酉电路、非酉电路和对偶么正电路，而不是可积性是关键要求。当几个拓扑缺陷被施加到电路上，产生结时，它对动力学的影响将被研究。将探索在NISQ器件中实现拓扑缺陷的方法。在第二个推力中，PI将使用增广的Schwinger-Keldysh形式来研究信息理论测量的时空传播，例如超时有序相关器。目标是了解本征噪声如何影响蝴蝶锋面的传播。此外，还将探讨本地化-非本地化转变对信息传播的影响。该项目具有很强的教育成分，因为它将涉及研究生、本科生和博士后研究科学家的积极参与。广义对称性的最新发展将数学物理、统计力学、凝聚态物质和高能物理的概念结合在一起。PI将调整她的理论凝聚态物理课程，向学生介绍这些最新的发展。此外，PI和初级研究科学家将通过纽约大学-GSTEM项目指导高中生来扩大参与。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. One of the main challenges of such systems is that they heat to a high temperature, a situation which is detrimental to observing any non-trivial quantum phenomena. Nevertheless, if the system has some symmetries, this can limit heating. The award will explore how symmetries, and generalizing the notion of symmetries, can lead to phenomena out of equilibrium that are immune to heating. The project will bring together methods from mathematical physics, statistical mechanics, and condensed matter physics with the common goal being to study generalized symmetries, out of equilibrium. One consequence of generalized symmetries is that the quantum system can host objects known as "non-abelian anyons". These objects can be used to store memory that is stable for long times. The project will explore how non-abelian anyons can be realized in experimental platforms such as the so-called "Noisy Intermediate Scale Quantum" devices. The project has a strong educational component as it will involve the active participation of a graduate student, an undergraduate student, and a postdoctoral research scientist. Recent developments in generalized symmetries have brought together concepts from mathematical physics, statistical mechanics, condensed matter, and high energy physics. The PI will adapt her course on theoretical condensed matter physics to introduce students to these recent developments. In addition, the PI and the junior research scientists will broaden participation by mentoring high school students through the NYU-GSTEM program. TECHNICAL SUMMARYThis award supports theoretical research on nonequilibrium phenomena in strongly correlated quantum systems. The focus will be twofold. One is to develop methods to study non-abelian excitations, essential for quantum computing, in a highly non-equilibrium setting, realizable in current Noisy Intermediate Scale Quantum (NISQ) devices. The second is to develop methods to study information theoretic measures that quantify how an initial decoherence grows, and entanglement spreads. In the first major thrust, the PI will study Floquet models built out of a fusion category. In these models, the role of topological defects, operators that can be deformed in the space and time direction without changing the physics, will be explored. When the topological defects are invertible, these are unitary symmetries. When the topological defects are non-invertible, these act as projectors, are non-abelian, and are examples of non-invertible symmetries. The latter are also examples of generalized symmetries, and their effect on quantum dynamics will be explored. The Floquet circuits to be studied will include unitary circuits, non-unitary circuits, and dual-unitary circuits, without integrability being a key requirement. When several topological defects are applied to the circuit, creating junctions, its effect on the dynamics will be studied. The implementation of topological defects in NISQ devices will be explored. In the second thrust, the PI will employ an augmented Schwinger-Keldysh formalism to study the space-time propagation of information theoretic measures such as out of time ordered correlators. The goal will be to understand how intrinsic noise can affect propagation of the butterfly front. In addition, how proximity to localization-delocalization transitions affects information propagation will be explored.The project has a strong educational component as it will involve the active participation of a graduate student, an undergraduate student, and a postdoctoral research scientist. Recent developments in generalized symmetries have brought together concepts from mathematical physics, statistical mechanics, condensed matter, and high energy physics. The PI will adapt her course on theoretical condensed matter physics to introduce students to these recent developments. In addition, the PI and the junior research scientists will broaden participation by mentoring high school students through the NYU-GSTEM program.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.