CAREER: Infinitely many new universality classes of hydrodynamics

University Of Colorado At Boulder, Boulder CO

Investigators

Abstract

NONTECHNICAL SUMMARY This 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.