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。这种系统的主要挑战之一是它们加热到高温，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，以及对对称性概念的概括，如何导致不受加热影响的失衡现象。该项目将汇集数学物理、统计力学和凝聚态物理的方法，共同的目标是研究非平衡状态下的广义对称性。广义对称性的一个结果是，量子系统可以承载被称为“非阿贝尔任意子”的物体。这些对象可以用来存储长时间稳定的记忆。该项目将探索如何在所谓的“噪声中尺度量子”设备等实验平台上实现非阿贝尔任意子。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汇集了数学物理、统计力学、凝聚态物质和高能物理的概念。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纽约大学gstem项目指导高中生，扩大参与范围。该奖项支持对强相关量子系统中非平衡现象的理论研究。重点将是双重的。一个是发展研究非阿贝尔激励的方法，这对量子计算至关重要，在高度非平衡设置下，在当前的噪声中尺度量子（NISQ）设备中实现。第二是发展方法来研究量化初始退相干如何增长和纠缠扩散的信息理论措施。在第一个主要推力中，PI将研究基于聚变类别构建的Floquet模型。在这些模型中，将探讨拓扑缺陷的作用，拓扑缺陷是可以在空间和时间方向上变形而不改变物理特性的算子。当拓扑缺陷可逆时，它们是酉对称的。当拓扑缺陷不可逆时，这些缺陷充当投影，是非阿贝尔的，并且是不可逆对称的例子。后者也是广义对称的例子，它们对量子动力学的影响将被探讨。要研究的Floquet电路将包括幺正电路、非幺正电路和双幺正电路，但不以可积性为关键要求。当几个拓扑缺陷应用到电路中，形成结，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形式来研究信息理论测量的时空传播，例如非时序相关器。目标是了解固有噪声如何影响蝴蝶锋的传播。此外，将探讨定位-非定位转换的接近性如何影响信息传播。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汇集了数学物理、统计力学、凝聚态物质和高能物理的概念。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纽约大学gstem项目指导高中生，扩大参与范围。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. 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.