RUI: NSF/DMR-BSF: Nonequilibrium Quantum Matter: Timescales and Self-Averaging

该奖项支持由国家科学基金会资助的PI和由以色列两国科学基金会（BSF）资助的PI之间的理论和计算研究合作。该合作将结合互补的技能和资源，对由许多相互作用的粒子组成的系统进行计算和理论研究，这些粒子远非平衡状态，并由量子力学描述。处于平衡状态的系统的性质不随时间而改变。相反，非平衡系统的性质，例如，纳米材料中的电子暴露在一阵光下，就会发生变化。本研究旨在促进对远离平衡态的系统如何放松以达到平衡态的理解。PI的目标是进一步理解由外场驱动的量子力学系统的动力学行为。理解非平衡态多体量子系统的性质是许多领域非常感兴趣的基本问题，包括原子、分子和凝聚态物理、量子信息科学和宇宙学。该团队的研究可能导致：*)预测和发现物质的新相，这些新相只出现在非平衡量子系统中。物质的新阶段与新兴技术和改进现有设备技术所需的新材料的发展密切相关。*)对量子计算的洞察。这些研究中使用的模型类似于那些在开发技术中使用的模型，这些技术可以操纵量子力学状态来执行计算，量子计算。对多体量子系统的理解的进步可以导致计算能力和加密技术的革命性发展。该项目将通过让女本科生参与研究，促进女性在STEM领域的参与。这将有助于激励年轻女性学习物理，方法是在开放参观日和参观女生高中等场所介绍拥有物理学位可以做些什么。PI还旨在通过将计算活动纳入本科科学课程，使斯特恩女子学院的课程现代化。通过这个项目开发的计算机代码和教程将在网上发布，以促进其他院校的教学和研究的整合。此次合作也将使斯特恩女子学院的本科生受益，她们将有机会在以色列的博士学位授予机构体验研究。技术概述：该奖项支持由国家科学基金会资助的PI和由以色列两国科学基金会（BSF）资助的PI之间的理论和计算研究合作。此次合作将结合互补的技能和资源，旨在推进对多体量子系统动力学的理解，这是理论和实验物理学前沿的一个突出挑战。它连接了原子、分子、凝聚态物质和高能物理等多种领域。新的理论和计算方法，以及对更长的连贯进化的实验途径，促使人们对这一学科产生了广泛的兴趣。特别关注的是由静态和驱动哈密顿量描述的相互作用系统的平衡、热化和局域化条件，这是PI和BSF-PI都做出了重要贡献的主题。然而，一个具有挑战性的问题仍然悬而未决，即这些系统达到平衡的时间。现有的结果，往往基于抽象的模型，是矛盾的。同样有争议的还有：标志着普遍行为开始的时间，相互作用系统中的索利斯时间是什么，指数行为的持续时间，以及这些时间尺度与驱动系统的加热时间尺度之间的关系。为了描述这些不同的时间尺度，该团队将考虑现实模型和实验观察结果，并将利用他们在量子混沌和随机矩阵理论方面的经验来识别一般行为并推导解析表达式。虽然PI主要关注与时间无关的汉密尔顿量，但BSF-PI将带来他在驱动系统方面的专业知识。除了动态和时间尺度，自平均也将是这个项目的中心主题。与遍历性相反，在相互作用的量子系统中脱离平衡的自平均受到的关注很少，尽管它对理论模型的发展以及实验和数值模拟的重要性，在这些领域获得许多实现可能是昂贵的。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 a theoretical and computational research collaboration between a PI funded by the National Science Foundation and a PI funded by the Israel Binational Science Foundation (BSF). The collaboration will combine complementary skills and resources to perform computational and theoretical studies of systems comprised of many interacting particles that are far from the state of equilibrium and which are described by quantum mechanics. The properties of systems in equilibrium do not change in time. In contrast the properties of nonequilibrium systems like, for example, the electrons in a nanomaterial that has been exposed to a burst of light, change. This research aims to advance understanding of how systems far from equilibrium relax to achieve the equilibrium state. The PI's aim is to further understand the dynamical behavior of quantum mechanical systems driven by external fields. Understanding the properties of many-body quantum systems out of equilibrium is a fundamental problem of great interest to many fields, including atomic, molecular, and condensed matter physics, quantum information science, and cosmology. The team's studies may lead to:*) the prediction and discovery of new phases of matter that only appear in quantum systems out of equilibrium. New phases of matter are tightly connected with the development of new materials needed in emerging technologies and to improve existing device technologies. *) insight into quantum computing. The models used in these studies are analogous to those used in the development of technologies that manipulate quantum mechanical states to perform computation, quantum computing. Advances in the understanding of many-body quantum systems can lead to revolutionary developments in both computational capabilities and encryption technologies.This project will foster the participation of women in STEM fields by engaging female undergraduate students in the research. It will help motivate young women to study physics by giving presentations about what can be done with a degree in physics in venues like open houses and visits to high schools for girls. The PI also aims to modernize the curriculum at Stern College for Women by integrating computational activities into the undergraduate science courses. Computer codes and tutorials developed through this project will be posted online to contribute to the integration of teaching and research at other institutions. The collaboration will also benefit the undergraduate students of Stern College for Women, who will have the opportunity to experience research at a PhD granting institution in Israel.TECHNICAL SUMMARYThis award supports a theoretical and computational research collaboration between a PI funded by the National Science Foundation and a PI funded by the Israel Binational Science Foundation (BSF). The collaboration will combine complementary skills and resources with an aim to advance understanding of the dynamics of many-body quantum systems, an outstanding challenge at the forefront of theoretical and experimental physics. It bridges fields as diverse as atomic, molecular, condensed matter, and high-energy physics. The widespread interest in the subject is prompted by new theoretical and computational methods, and by experimental access to ever longer coherent evolutions. Particular attention has been given to the conditions for equilibration, thermalization, and localization in interacting systems described by static and driven Hamiltonians, themes to which both the PI and the BSF-PI have made several important contributions. Yet, a challenging question that remains open refers to the time for these systems to equilibrate. Existing results, often based on abstract models, are contradictory. Also debated are: the time that marks the onset of universal behavior, what Thouless time is in interacting systems, the duration of exponential behaviors, and how these timescales relate with the heating timescale of driven systems. To characterize these various timescales, the team will consider realistic models and experimental observables, and will take advantage of their experience with quantum chaos and random matrix theory to identify general behaviors and derive analytical expressions. While the PI has mostly focused on time-independent Hamiltonians, the BSF-PI will bring in his expertise on driven systems. In addition to dynamics and timescales, self-averaging will also be a central topic of this project. Contrary to ergodicity, self-averaging in interacting quantum systems out of equilibrium has received very little attention, despite its importance to the development of theoretical models, as well as to experiments and numerical simulations, where access to many realizations may be costly.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.