Nonequilibrium quantum mechanics of strongly correlated systems

强相关系统的非平衡量子力学

• 批准号: 2316598
• 负责人: Aditi Mitra
• 金额: $ 40.5万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-04-01 至 2027-03-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2316598&HistoricalAwards=false
• 关键词: Nonequilibrium; quantum; mechanics; strongly; correlated

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.

非技术摘要这一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加热到高温，这种情况不利于观察任何非平凡的量子现象。但是，如果系统具有某些对称性，则可能会限制加热。该奖项将探讨对称性和概括对称性的概念如何导致不受加热的平衡现象。该项目将从数学物理学，统计力学和凝结物理学中汇总出方法，其共同目标是研究广义对称性，以均衡。广义对称性的结果之一是，量子系统可以托管称为“非亚洲人”的对象。这些对象可用于存储长期稳定的内存。该项目将探讨如何在所谓的“嘈杂的中间量表量子”设备等实验平台中实现非亚伯人。该项目具有强大的教育成分，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已将数学物理学，统计力学，冷凝物质和高能量物理学的概念汇总在一起。 PI将适应理论凝结物理学的课程，以向学生介绍这些最近的发展。此外，PI和初级研究科学家将通过NYU-GELSTEM计划指导高中生，扩大参与。技术摘要这一奖项支持有关密切相关的量子系统中非平衡现象的理论研究。 重点将是双重的。一种是开发研究非阿布尔激发的方法，在高度非平衡环境中，对于量子计算至关重要，在当前嘈杂的中间尺度量子（NISQ）设备中可实现。第二个是开发方法来研究信息理论措施，以量化初始腐烂的增长方式和纠缠差。 在第一个主要推力中，PI将研究由融合类别构建的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操作员。当拓扑缺陷是可逆的时，这些是统一的对称性。当拓扑缺陷是不可逆转的时，这些作用是投影仪，是非亚伯式的，是不可变形的对称性的例子。后者也是广义对称性的示例，将探索它们对量子动力学的影响。要研究的浮球电路将包括单一电路，非统一电路和双统一电路，而无需集成性是关键要求。当将几个拓扑缺陷应用于电路并创建连接处时，将研究其对动态的影响。 将探索NISQ设备中拓扑缺陷的实现。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措施的时空传播，例如按时订购的相关器。目的是了解固有的噪声如何影响蝴蝶前的传播。此外，将如何探索与本地化范围的转变影响信息传播的近端。该项目具有强大的教育成分，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已将数学物理学，统计力学，冷凝物质和高能量物理学的概念汇总在一起。 PI将适应理论凝结物理学的课程，以向学生介绍这些最近的发展。此外，PI和初级研究科学家将通过NYU-GELSTEM计划指导高中生来扩大参与。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子和更广泛影响的评估评估标准来通过评估来支持的。