Nonequilibrium quantum mechanics of strongly correlated systems

非技术总结该奖项支持对处于高度激发或非平衡状态的复杂量子系统的理论研究。这种系统的主要挑战之一是它们会加热到高温，这种情况不利于观察任何非平凡的量子现象。然而，如果系统具有一些对称性，这可以限制加热。该奖项将探讨对称性以及对称性概念的推广如何导致不受加热影响的平衡现象。该项目将汇集数学物理，统计力学和凝聚态物理的方法，共同目标是研究广义对称性，平衡。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”的对象。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“噪声中间尺度量子”设备。该项目具有很强的教育成分，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汇集了数学物理、统计力学、凝聚态和高能物理的概念。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NYU-GSTEM计划指导高中学生来扩大参与。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。一个是开发方法来研究非阿贝尔激发，量子计算所必需的，在一个高度非平衡的设置，实现在当前的噪声中间尺度量子（NISQ）设备。第二个是开发方法来研究信息理论的措施，量化初始退相干如何增长，纠缠传播。 在第一个主要的推动力，PI将研究Floquet模型建立了一个融合的类别。在这些模型中，拓扑缺陷的作用，可以在空间和时间方向变形而不改变物理的运营商，将被探讨。当拓扑亏损是可逆的，这些是酉对称。当拓扑缺陷是不可逆的，这些作为投影仪，是非阿贝尔的，是不可逆对称的例子。后者也是广义对称性的例子，它们对量子动力学的影响将被探讨。将要研究的Floquet电路将包括酉电路、非酉电路和对偶酉电路，而可积性不是关键要求。当几个拓扑缺陷被应用到电路，创建结，其对动力学的影响将被研究。 将探讨NISQ器件中拓扑缺陷的实现。在第二个推力中，PI将采用增强的Schwinger-Keldysh形式主义来研究信息理论测量的时空传播，例如时间有序的传播。我们的目标是了解固有噪声如何影响蝴蝶阵面的传播。此外，如何接近本地化-离域转换影响信息传播将explored.The项目有很强的教育成分，因为它将涉及一个研究生，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汇集了数学物理、统计力学、凝聚态和高能物理的概念。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NYU-GSTEM项目指导高中生来扩大参与范围。该奖项反映了NSF的法定使命，并通过使用基金会的智力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. 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.