Nonlinear and geometric effects in quantum condensed matter systems

非技术总结该奖项支持使用流体力学和几何方法描述量子电子系统和活性物质的不寻常集体行为的理论研究和教育。活性物质由自驱动粒子的集合组成，而PI关注的是其组成部分或其集体行为的协调行为。该项目还侧重于电子在不同材料或设备中的强烈相互作用可能导致的协调或集体行为。我们观察到的周围物质由大量的微观粒子、原子、分子、离子和电子组成。了解大量粒子集合的性质对于技术进步至关重要。当组成粒子不相互作用或相互作用非常弱时，已有成熟的技术来计算这类系统的性质。在这种情况下，系统的性质可以通过对单粒子运动求和来获得。例如，良好金属中的气体或电子的性质。当组成粒子相互作用强烈时，从其组成粒子的微观性质计算物质的集体性质就更具挑战性了。对于某些类型的物质，已知的最有效的方法之一是流体动力学。在流体动力学中，物质的集体状态是由随时间变化的流体密度、速度和温度来表征的。物理学家可以更容易地求解描述其集体行为的方程，而不是考虑微观粒子。这些方程包括粘度、可压缩性、导热系数和其他流体性质作为参数。挑战是从微观性质中提取这些性质，并扩大流体动力学的有效范围和应用范围。PI计划将流体动力学方法应用于量子力学和具有特殊特征的经典系统，如产生量子霍尔效应的二维电子流体、手性材料和手性活性物质。对于这些材质，镜像不能完美地叠加在材质或物质状态上。例如，手性活性流体是由在微观尺度上持续注入能量和角动量的自旋转子组成的。这些材料的集体流体动力学本质上不同于传统流体力学的描述。研究的另一部分涉及对极限形状现象的描述--在随机系统中出现最可能的宏观状态。这种状态的特点通常是一条明确的边界，将冰冻和液体空间区域分开。向高中生教授数学和物理基础知识，并向高中生传达现代物理前沿研究的价值是该项目的重要组成部分。派将继续参加石溪儿童的丰富计划，石溪13-16岁学生的科学休眠夏令营，以及俄罗斯有天赋的高中生的夏令营。技术总结该奖项支持使用流体力学和几何方法研究量子和经典集体现象的理论研究和教育，重点是电子流体和活性物质。近几十年来，拓扑和几何方法在物理研究中的应用重新引起了人们的兴趣。“凝聚态物理几何化”的总体趋势是对凝聚态系统的对称性和有效描述的基本运用。这些描述往往具有几何意义，便于使用新数学的存在和发展。物质拓扑相的广泛领域，活跃系统集体行为的研究，混沌和非平衡系统的研究，都是受到这种方法强烈影响的几个领域。拟议的研究是在理论凝聚态物理领域。在量子和经典集体现象的研究中，使用流体力学和几何方法是统一的。该项目包括研究反常流体和奇输运系数，拓扑自由度和有效边界流体动力学之间的相互作用，二维库仑等离子体中熔化的方面，低维量子流体中大涨落的几何方面，以及瞬子对一维量子自旋链中可积破缺和混沌行为的影响。预计几何概念将对理解上述系统特别有用。本研究的特点为研究生的综合培养提供了良好的环境。在所描述的项目中开发的工具可以用于非常不同的物理领域：量子多体理论、可积模型、非线性动力学、经典可积性、流体动力学、核物理、宇宙学等。拟议的研究路线令人兴奋的部分原因是能够跨越障碍应用研究成果，有时将不同的研究领域分开。所获得的结果可以通过相应系统的数值模拟来验证，并最终通过与实验的比较来验证。这一奖项反映了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 theoretical research and education using hydrodynamics and geometric methods to describe unusual collective behavior of quantum electronic systems and active matter. Active matter consists of assemblies of self-driven particles and the PI focuses on the coordinated behavior of their constituents or their collective behavior. This project is also focused on the coordinated or collective behavior of electrons that can result from their strong interactions in diverse materials or devices. The matter we observe around us consists of vast numbers of microscopic particles, atoms, molecules, ions, and electrons. Understanding the properties of the collections of a huge number of particles is crucial for technological progress. There are well-developed techniques of computing the properties of such systems when the constituent particles do not interact or interact only very weakly with each other. In this case, the properties of the system can be obtained by summing over one-particle motions. Examples include the properties of gases or electrons in good metals.When constituent particles interact strongly, the computation of collective properties of matter from microscopic properties of its constituent particles is much more challenging. For some kinds of matter, one of the powerful methods known is fluid dynamics. In fluid dynamics, the collective state of matter is characterized by fluid density, velocity, and temperature as they vary with time. Instead of considering microscopic particles, physicists can more easily solve equations describing their collective behavior. The equations include viscosity, compressibility, thermal conductivity, and other fluid properties as parameters. The challenge is to derive those properties from microscopic properties and expand the range of validity and the scope of fluid dynamics applications.The PI plans to apply fluid dynamics methods to quantum mechanical and classical systems with unusual characteristics such as the fluid of electrons in two dimensions in high magnetic field that gives rise to the quantum Hall effects, chiral materials, and chiral active matter. For these materials, the mirror image cannot be perfectly superimposed on the material or state of matter. Chiral active fluids, for example, are composed of self-spinning rotors that continuously inject energy and angular momentum at the microscopic scale. The collective fluid dynamics of these materials are qualitatively different from the descriptions of conventional hydrodynamics.Another part of the research involves the description of the limit shape phenomenon - the appearance of a most probable macroscopic state in random systems. This state is usually characterized by a well-defined boundary separating frozen and liquid spatial regions.Teaching the basics of math and physics and communicating the values of cutting-edge research in modern physics to high school students is an essential part of the project. PI will continue to participate in the enrichment program for children in Stony Brook, in the science sleepaway camp for students 13-16 years old in Stony Brook, and the summer camp for gifted high school students in Russia.TECHNICAL SUMMARYThis award supports theoretical research and education using hydrodynamic and geometric methods to study quantum and classical collective phenomena with a focus on electronic fluids and active matter. Recent decades brought a renewed interest in applications of topological and geometric methods in physics research. The overall trend of “geometrization of condensed matter physics” is characterized by the essential use of symmetries and effective descriptions of condensed matter systems. Those descriptions often have geometric meanings facilitating the use of the existent and development of new mathematics. The broad field of topological phases of matter, studies of collective behavior of active systems, research in chaotic and out-of-equilibrium systems are just a few fields strongly affected by this approach. The proposed research is in the field of theoretical condensed matter physics. It is unified using hydrodynamic and geometric methods in studies of quantum and classical collective phenomena. This project includes studies of anomalous fluids and odd transport coefficients, the interplay between topological degrees of freedom and effective boundary fluid dynamics, aspects of melting in Coulomb plasma in two dimensions, geometrical aspects of large fluctuations in low dimensional quantum fluids, and instanton effects on integrability breaking and chaotic behavior in one-dimensional quantum spin chains. It is expected that geometric ideas will be especially useful in understanding the above systems. The character of the proposed research provides an excellent environment for the comprehensive training of graduate students. The tools developed in the described projects can be used in very different fields of physics: quantum many-body theory, integrable models, nonlinear dynamics, classical integrability, fluid dynamics, nuclear physics, cosmology, etc. Part of the excitement of the proposed line of studies is due to the ability to apply findings across barriers, sometimes separating different areas of research. The obtained results can be verified by numerical simulations of correspondent systems and, ultimately, by comparison with experiments.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.