CAREER: Infinitely many new universality classes of hydrodynamics

该奖项支持发现自然界中可能存在的新型流体的研究和教育。最著名的流体是液态水或我们周围的空气。控制这些液体和气体的方程已经被理解了几百年。最近，在超冷原子气体中，在流经金属的电子中，甚至在高能粒子对撞机产生的夸克和胶子等离子体中，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无限族奇异推广。该项目的目标是建立一种系统的方法来分类和理解新的流体动力学行为，并预测如何在超冷原子和量子材料的实验中发现这些新的流体。提出的活动将导致一个更系统的方法来预测广泛的物理系统的集体行为，从电子或金属中的自旋的量子流体，到液晶和其他软或活性物质的动力学，甚至是非平衡生物系统的集体行为，如细菌悬浮液或群。该奖项还支持教育和推广活动，包括开发一门面向高年级本科生和一年级研究生的现代流体力学新课程。这门新课程将侧重于流体力学在经典流体和量子流体中产生的许多物理环境：大气、电子液体、夸克-胶子等离子体、液晶和生物体的集体运动，而不是像传统课程那样专注于日常液体或气体的物理学。这些努力最终将形成一套类似书本的课堂讲稿，并将免费提供给公众。PI还将领导一个暑期学校，暂定于2025年7月，在那里，广泛而多样化的国家顶尖研究生将学习凝聚态物理学的前沿进展。本科生和研究生研究人员将参加由该奖项资助的活动，首席研究员将通过部门外展计划，通过面向当地社区的公开讲座，进一步传播研究成果。该奖项支持对发现和分类无限多新的流体力学普适性类和无限多新的非平衡动力不动点的研究和教育，这些不动点推广了kardar - paris - zhang普适性类。这项研究主要有三个重点。(1)在具有多极和/或子系统对称性的受限量子系统中发现了许多新的流体力学普适性类。通过结合更多的守恒定律，如动量，或通过打破时空对称性，这些流体力学理论在热波动的存在下会变得不稳定，并流向新的非平衡普适性类。(2) PI将开发新的有效的场论方法来系统地预测和分析这些新的普适性类。这些场论将自然地描述非线性波动流体动力学，并有助于更好地理解非平衡环境下统计物理的基础（包括波动耗散定理和热力学的存在）。所开发的数学方法也将有助于揭示外来的非相对论分数物质是否以及何时可以与重力一致地耦合。(3)最后，PI将致力于预测这些新型流体的实验实现。两种自然环境包括费米-哈伯德类模型，其中超冷原子被限制在倾斜的光学晶格中，以及受挫的量子磁体。PI将为这些奇异的动力系统推导出适当的流体力学描述，这有望导致磁流体力学的奇异推广和其他具有更高形式对称性的模型的发现。总之，这三个推力将有助于在具有非常规对称性的经典和量子多粒子系统中引入更系统和预测的流体动力学方法。该奖项还支持教育和推广活动，包括为一年级研究生和大四本科生开发一门关于流体力学的有效场论课程。本课程的课程资料，包括一套最终的课堂讲稿，将免费提供给公众。PI还将领导一个关于强相关量子材料动力学的暑期学校，帮助培养该领域最先进的下一代物理学家。本科生和研究生研究人员将参加由该奖项资助的活动，首席研究员将通过部门外展计划，通过面向当地社区的公开讲座，进一步传播研究成果。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 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.