Nonlinear and geometric effects in quantum condensed matter systems

量子凝聚态物质系统中的非线性和几何效应

• 批准号: 2116767
• 负责人: Alexander Abanov
• 金额: $ 39万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-02-01 至 2025-01-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2116767&HistoricalAwards=false
• 关键词: Nonlinear; geometric; effects; quantum; condensed

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.

该奖项支持理论研究和教育，使用流体力学和几何方法来描述量子电子系统和活性物质的不寻常集体行为。活性物质由自驱动粒子的集合体组成，PI关注它们的组分或它们的集体行为的协调行为。该项目还专注于电子的协调或集体行为，这些行为可能是由它们在不同材料或设备中的强烈相互作用引起的。我们周围观察到的物质由大量微观粒子、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。当组成粒子之间不相互作用或相互作用很弱时，有很好的技术可以计算这种系统的性质。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。当组成粒子强烈相互作用时，从组成粒子的微观性质计算物质的集体性质就更具挑战性。对于某些种类的物质，已知的强有力的方法之一是流体动力学。在流体动力学中，物质的集体状态由流体密度、速度和温度随时间变化来表征。物理学家可以更容易地求解描述它们集体行为的方程，而不是考虑微观粒子。该方程包括粘度、可压缩性、热导率和其他流体性质作为参数。目前的挑战是如何从微观性质中推导出这些性质，并扩大流体力学的应用范围。PI计划将流体力学方法应用于具有特殊特性的量子力学和经典系统，例如在高磁场中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。对于这些材料，镜像不能完美地叠加在材料或物质状态上。例如，手性活性流体由自旋转子组成，其在微观尺度上连续注入能量和角动量。这些材料的集体流体动力学与常规流体动力学的描述有质的不同，研究的另一部分涉及极限形状现象的描述--随机系统中最可能出现的宏观状态。这种状态的特征通常是一个明确的边界分离冻结和液体空间区域。教授数学和物理的基础知识，并向高中生传达现代物理学前沿研究的价值是该项目的重要组成部分。PI将继续参与斯托尼布鲁克的儿童充实计划、斯托尼布鲁克13-16岁学生的科学夏令营以及俄罗斯天才高中生夏令营。技术总结该奖项支持理论研究和教育，使用流体力学和几何方法研究量子和经典集体现象，重点是电子流体和活性物质。近几十年来，人们对拓扑和几何方法在物理研究中的应用重新产生了兴趣。“凝聚态物理几何化”的总体趋势是对凝聚态系统的对称性的实质性运用和有效描述。这些描述往往具有几何意义，有利于新数学的存在和发展。物质拓扑相的广泛领域，主动系统集体行为的研究，混沌和失衡系统的研究只是受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学领域。它是统一使用流体力学和几何方法在量子和经典集体现象的研究。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的熔化问题，低维量子流体中大波动的几何问题，以及一维量子自旋链中可积性破缺和混沌行为的瞬子效应。几何思想在理解上述系统时特别有用。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学领域：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，核物理学，宇宙学等。所获得的结果可以通过相应系统的数值模拟进行验证，并最终与实验进行比较。该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

项目成果

Limit shape phase transitions: a merger of arctic circles

极限形状相变：北极圈的合并

• DOI: 10.1088/1751-8121/ac79ad
• 发表时间: 2022
• 期刊: Journal of Physics A: Mathematical and Theoretical
• 作者: Pallister, James S;Gangardt, Dimitri M;Abanov, Alexander G
• 通讯作者: Abanov, Alexander G

Chiral anomaly in Euler fluid and Beltrami flow

欧拉流体和贝尔特拉米流中的手性异常

• DOI: 10.1007/jhep06(2022)038
• 发表时间: 2022
• 期刊: Journal of High Energy Physics
• 影响因子: 5.4
• 作者: Wiegmann, P. B.;Abanov, A. G.
• 通讯作者: Abanov, A. G.

Slowly decaying zero mode in a weakly nonintegrable boundary impurity model

弱不可积边界杂质模型中缓慢衰减的零模式

• DOI: 10.1103/physrevb.108.165143
• 发表时间: 2023
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: Yeh, Hsiu-Chung;Cardoso, Gabriel;Korneev, Leonid;Sels, Dries;Abanov, Alexander G.;Mitra, Aditi
• 通讯作者: Mitra, Aditi

Hydrodynamics of low-dimensional quantum systems

低维量子系统的流体动力学

• DOI: 10.1088/1751-8121/acecc8
• 发表时间: 2023
• 期刊: Journal of Physics A: Mathematical and Theoretical
• 作者: Abanov, Alexander;Doyon, Benjamin;Dubail, Jérôme;Kamenev, Alex;Spohn, Herbert
• 通讯作者: Spohn, Herbert

Anomalies in fluid dynamics: flows in a chiral background via variational principle

流体动力学异常：通过变分原理在手性背景中流动

• DOI: 10.1088/1751-8121/ac9202
• 发表时间: 2022
• 期刊: Journal of Physics A: Mathematical and Theoretical
• 作者: Abanov, A G;Wiegmann, P B
• 通讯作者: Wiegmann, P B