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: 1606591
• 负责人: Alexander Abanov
• 金额: $ 27万
• 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: 2016
• 资助国家: 美国
• 起止时间: 2016-12-01 至 2020-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1606591&HistoricalAwards=false
• 关键词: Nonlinear; geometric; effects; quantum; condensed

Nontechnical SummaryThis award supports research and education in the development of theoretical methods to investigate strongly interacting quantum systems. Despite many recent advances, understanding these systems and developing appropriate theoretical tools remains one of the biggest challenges in condensed matter physics. Hydrodynamic methods are among few available approaches to the theory of strongly interacting systems. As the name implies, in certain situations it is feasible to view the complicated interacting quantum system as a fluid, and condense all the generally intractable details into virtual properties: density, velocity, viscosity, etc. As a result, phenomena well known from the study of fluids, such as vortices, shock waves, and turbulence, find analogs in systems of cold atoms or electrons. The project will lead the development of hydrodynamic approaches for a variety of condensed-matter and cold-atom systems. Part of the excitement associated with the proposed line of study stems from the opportunity to apply findings across different areas of research. The developed theoretical tools could be used in diverse fields of physics: quantum many-body theory, nonlinear dynamics, fluid dynamics, nuclear physics, cosmology, etc. The obtained results will be verified by numerical simulations and, ultimately, by comparison with experiments.The proposed research will provide a rich environment for the comprehensive training of graduate students in modern theoretical methods. The PI continues to give lectures on the uses of topology and geometry in condensed matter physics, and plans to prepare lecture notes for publication. The PI further plans to develop the notes into a book on topological aspects of condensed matter physics aimed at the broader community of scientists. The PI is enthusiastic about teaching math and physics to K-12 students in the enrichment program for children at Stony Brook, and to gifted high-school students in Russia.Technical SummaryThis award supports research and education in the development of theoretical methods to investigate strongly interacting quantum systems. Finding efficient ways to work with strongly interacting quantum systems is one of the most fundamental problems in condensed matter physics. It has been the focus of both experimental and theoretical research for the last three decades. To make progress in understanding systems with strong interactions, non-perturbative methods are needed. One of these few methods is the hydrodynamic approach, which provides a general framework for treating interacting quantum and classical systems. The project will develop new geometrical methods in condensed matter physics and look for applications to quantum transport phenomena.The proposed research is in the general direction of "geometrizing condensed matter physics", and progresses through the essential use of symmetries and effective descriptions. The PI expects to expand the understanding of the role of geometry in quantum many-body systems. The research uses geometric ideas and the hydrodynamic approach in studies of fractional quantum Hall systems and more general condensed matter systems. The proposed projects include thermal transport, and boundary-bulk relations for quantum Hall systems, anomalous hydrodynamics of quantum and classical systems, transport in chiral materials, and geometric aspects of out-of-equilibrium physics. Geometric ideas will be applied to analyze specific experiments on quantum transport.Part of the excitement associated with the proposed line of study stems from the opportunity to apply findings across different areas of research. The developed theoretical tools could be used in diverse fields of physics: quantum many-body theory, nonlinear dynamics, fluid dynamics, nuclear physics, cosmology, etc. The obtained results will be verified by numerical simulations and, ultimately, by comparison with experiments.The proposed research will provide a rich environment for the comprehensive training of graduate students in modern theoretical methods. The PI continues to give lectures on the uses of topology and geometry in condensed matter physics, and plans to prepare lecture notes for publication. The PI further plans to develop the notes into a book on topological aspects of condensed matter physics aimed at the broader community of scientists. The PI is enthusiastic about teaching math and physics to K-12 students in the enrichment program for children at Stony Brook, and to gifted high-school students in Russia.

非技术性总结该奖项支持研究和教育的理论方法的发展，以调查强相互作用的量子系统。尽管最近取得了许多进展，但理解这些系统并开发适当的理论工具仍然是凝聚态物理学中最大的挑战之一。流体动力学方法是强相互作用系统理论的少数可用方法之一。顾名思义，在某些情况下，将复杂的相互作用量子系统视为流体是可行的，并将所有通常难以处理的细节浓缩为虚拟属性：密度，速度，粘度等。该项目将领导各种凝聚物质和冷原子系统的流体动力学方法的发展。与拟议的研究路线相关的兴奋部分源于将研究结果应用于不同研究领域的机会。所开发的理论工具可应用于量子多体理论、非线性动力学、流体动力学、核物理、宇宙学等物理学领域。所获得的结果将通过数值模拟并最终与实验进行比较来验证。拟议的研究将为研究生现代理论方法的综合培养提供丰富的环境。PI继续在凝聚态物理学中讲授拓扑学和几何学的应用，并计划准备演讲稿以供出版。PI进一步计划将这些笔记发展成一本关于凝聚态物理学拓扑方面的书，面向更广泛的科学家群体。PI热衷于在斯托尼布鲁克的儿童丰富计划中向K-12学生教授数学和物理，以及向俄罗斯有天赋的高中生教授数学和物理。技术摘要该奖项支持在研究强相互作用量子系统的理论方法发展方面的研究和教育。寻找有效的方法来处理强相互作用的量子系统是凝聚态物理学中最基本的问题之一。在过去的三十年里，它一直是实验和理论研究的焦点。为了在理解强相互作用系统方面取得进展，需要非微扰方法。这几种方法之一是流体动力学方法，它提供了一个通用的框架来处理相互作用的量子和经典系统。该计划将发展凝聚态物理学的新几何方法，并寻求应用于量子输运现象。拟议的研究是在“凝聚态物理学的几何化”的大方向，并通过对称性的基本使用和有效的描述进行进展。PI希望扩大对量子多体系统中几何作用的理解。本研究将几何思想和流体力学方法应用于分数量子霍尔系统和更一般的凝聚态系统的研究。拟议的项目包括热输运，量子霍尔系统的边界-体积关系，量子和经典系统的反常流体动力学，手性材料的运输，以及平衡物理学的几何方面。几何思想将被应用于分析量子输运的具体实验。与拟议的研究路线相关的部分兴奋源于有机会将研究结果应用于不同的研究领域。所开发的理论工具可应用于量子多体理论、非线性动力学、流体动力学、核物理、宇宙学等物理学领域。所获得的结果将通过数值模拟并最终与实验进行比较来验证。拟议的研究将为研究生现代理论方法的综合培养提供丰富的环境。PI继续在凝聚态物理学中讲授拓扑学和几何学的应用，并计划准备演讲稿以供出版。PI进一步计划将这些笔记发展成一本关于凝聚态物理学拓扑方面的书，面向更广泛的科学家群体。PI热衷于在斯托尼布鲁克的儿童充实计划中向K-12学生教授数学和物理，并向俄罗斯的天才高中生教授数学和物理。