CAREER: Infinitely many new universality classes of hydrodynamics

非技术总结该奖项支持研究和教育，以发现可以在自然界中存在的新类型的流体。最广为人知的流体是我们周围的液态水或空气。支配这种液体和气体的方程式已经被理解了几百年。最近，在超冷原子的气体、流经金属的电子，甚至在高能粒子对撞机产生的夸克和胶子的等离子体中也发现了类似流体的行为。PI最近预测了这些先前发现的流体的奇异概括的无限家族。这个项目的目标是开发一种系统的方法来分类和理解新的流体动力学行为，并预测如何在使用超冷原子和量子材料的实验中发现这些新的流体。拟议的活动将导致一种更系统的方法来预测广泛物理系统的集体行为，从电子或金属自旋的量子流体，到液晶和其他软或活性物质的动力学，甚至到非平衡生物系统的集体行为，如细菌悬浮液或菌群。该奖项还支持教育和推广活动，包括为高级本科生和一年级研究生开设一门新的现代流体力学课程。这门新课程不会像传统课程那样专注于日常液体或气体的物理学，而是强调在经典流体和量子流体中产生流体动力学的所有许多物理环境：大气、电子液体、夸克-胶子等离子体、液晶和生物有机体的集体运动。这些努力将最终形成一套书本般的课堂讲稿，将免费向公众提供。PI还将领导一个暑期学校，暂定于2025年7月，在那里，一批广泛而多样化的美国顶尖研究生将学习凝聚态物理的尖端进展。本科生和研究生研究人员将参加该奖项资助的活动，该协会将通过部门外展计划，通过针对其当地社区的公开讲座进一步传播成果。技术摘要该奖项支持发现和分类无限多新的流体力学普适性类，以及无限多新的非平衡动力学不动点的研究和教育，这些新的非平衡动力学不动点推广了Kardar-Parisi-Zhang普适性类。这项研究有三个主要推动力。(1)发现了许多新的流体力学普适类，它们出现在具有多极和/或子系统对称性的约束量子系统中。通过加入进一步的守恒定律，如动量，或打破时空对称性，这些流体动力学理论可能在存在热涨落时变得不稳定，并流向新的非平衡普适类。(2)PI将发展新的有效的场论方法来系统地预测和分析这些新的普适类。这些场论将自然地描述非线性涨落流体力学，并有助于更好地理解统计物理的基础(包括涨落耗散定理和热力学的存在)在远离平衡的环境中。开发的数学方法也将有助于揭示奇异的非相对论碎片物质是否以及何时可以一致地耦合到重力。(3)最后，PI将用于预测这些新类型流体的实验实现。两种自然环境包括：限制在倾斜光学晶格中的超冷原子中的费米-哈伯德模型，以及受挫的量子磁铁。PI将为这些奇异的动力系统推导出适当的流体动力学描述，这有望导致发现奇异的磁流体动力学和其他具有更高形式对称性的模型。总而言之，这三个推力将有助于在具有非传统对称性的经典和量子多粒子系统中引入更系统和更具预测性的流体动力学方法。该奖项还支持教育和推广活动，包括为一年级研究生和高年级本科生开发一门关于流体力学的课程，作为一种有效的领域理论。本课程的教材，包括最终的一套课堂讲稿，将免费向公众开放。PI还将领导一个关于强关联量子材料动力学的暑期课程，帮助培训不同的下一代物理学家，掌握该领域的最先进技术。本科生和研究生研究人员将参加该奖项资助的活动，PI将通过部门外展计划，通过针对他所在社区的公开讲座进一步传播成果。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 research and education towards discovering new kinds of fluids that can exist in nature. The most well-known fluids are liquid water or the air around us. The equations that govern such liquids and gases have been understood for hundreds of years. More recently, fluid-like behavior has also been discovered in gases of ultracold atoms, electrons flowing through metals, and even in plasmas of quarks and gluons created at high energy particle colliders. The PI has recently predicted infinite families of exotic generalizations of these previously discovered fluids. The goal of this project is to develop a systematic way of classifying and understanding new kinds of hydrodynamic behavior and to predict how to discover these new fluids in experiments with ultracold atoms and quantum materials. The proposed activities will lead to a more systematic approach to predicting the collective behavior of a broad range of physical systems, ranging from quantum fluids of electrons or spins in metals, to the dynamics of liquid crystals and other soft or active matter, and even to the collective behaviors of non-equilibrium biological systems such as bacterial suspensions or flocks. This award also supports educational and outreach activities, including the development of a new course on modern hydrodynamics to be delivered to senior-level undergraduate and first-year graduate students. Rather than focusing on the physics of everyday liquids or gases, as is done in conventional treatments of the subject, this new course will emphasize all of the many physical settings in which hydrodynamics arises in both classical and quantum fluids: the atmosphere, electron liquids, quark-gluon plasma, liquid crystals, and the collective motion of living organisms. These efforts will culminate in a set of book-like lecture notes, which will be freely available to the public. The PI also will lead a summer school, tentatively scheduled for July 2025, at which a broad and diverse set of the nation's top graduate students will learn about cutting edge advances in condensed matter physics. Undergraduate and graduate student researchers will participate in the activities funded by this award, and the PI will further disseminate results through public lectures aimed at his local community through departmental outreach programs.TECHNICAL SUMMARY This award supports research and education towards the discovery and classification of infinitely many new universality classes of hydrodynamics, and infinitely many new non-equilibrium dynamical fixed points which generalize the Kardar-Parisi-Zhang universality class. The research has three main thrusts. (1) The discovery of many new universality classes of hydrodynamics, which arise in constrained quantum systems with multipole and/or subsystem symmetries. By incorporating further conservation laws such as momentum, or by breaking spacetime symmetries, these hydrodynamic theories can become unstable in the presence of thermal fluctuations, and flow to new non-equilibrium universality classes. (2) The PI will develop new effective field theory methods to systematically predict and analyze these new universality classes. These field theories will naturally describe nonlinear fluctuating hydrodynamics and help lead to better understandings of the foundations of statistical physics (including fluctuation-dissipation theorems and the existence of thermodynamics) in far-from-equilibrium settings. The mathematical methods developed will also help to uncover if and when exotic non-relativistic fracton matter can be coupled consistently to gravity. (3) Lastly, the PI will work to predict experimental realizations of these new kinds of fluids. Two natural settings include Fermi-Hubbard-like models in ultracold atoms confined in tilted optical lattices, and frustrated quantum magnets. The PI will deduce the appropriate hydrodynamic description for these exotic dynamical systems, which are expected to lead to the discovery of exotic generalizations of magnetohydrodynamics and other models with higher-form symmetries. Together, these three thrusts will help usher in a more systematic and predictive approach to hydrodynamics in classical and quantum many-particle systems with unconventional symmetries. This award also supports educational and outreach activities, including the development of a course on hydrodynamics as an effective field theory for first-year graduate students and senior undergraduate students. Course materials from this class, including an eventual set of lecture notes, will be freely available to the public. The PI will also lead a summer school on dynamics in strongly correlated quantum materials, helping to train the diverse next generation of physicists in the state-of-the-art in the field. Undergraduate and graduate student researchers will participate in the activities funded by this award, and the PI will further disseminate results through public lectures aimed at his local community through departmental outreach programs.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.