Nonlinear and geometric effects in quantum condensed matter systems

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。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中最大的挑战之一。流体力学方法是研究强相互作用系统理论的几种有效方法之一。顾名思义，在某些情况下，可以将复杂的相互作用量子系统视为流体，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。因此，从流体研究中众所周知的现象，如漩涡、冲击波和湍流，在冷原子或电子系统中找到了类似的东西。该项目将引领各种凝聚态物质和冷原子系统的流体动力学方法的发展。拟议的研究路线令人兴奋的部分原因在于有机会将研究成果应用于不同的研究领域。所开发的理论工具可用于物理学的各个领域：量子多体理论、非线性动力学、流体动力学、核物理学、宇宙学等。所得结果将通过数值模拟并最终与实验比较来验证。本研究将为研究生的现代理论方法的全面培养提供一个丰富的环境。PI继续讲授拓扑和几何在凝聚态物理中的应用，并计划准备讲义出版。PI进一步计划将这些笔记发展成一本关于凝聚态物理拓扑方面的书，面向更广泛的科学家群体。PI热衷于为石溪分校（Stony Brook）的K-12学生和俄罗斯的天才高中生教授数学和物理。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。寻找处理强相互作用量子系统的有效方法是凝聚态物理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。为了在理解具有强相互作用的系统方面取得进展，需要非摄动方法。其中一种方法是流体力学方法，它为处理相互作用的量子系统和经典系统提供了一个总体框架。该项目将在凝聚态物理中发展新的几何方法，并寻找量子输运现象的应用。提出的研究是在“几何化凝聚态物理”的大方向上，并通过基本的使用对称性和有效的描述来推进。PI希望扩大对几何在量子多体系统中的作用的理解。该研究使用几何思想和流体动力学方法研究分数量子霍尔系统和更一般的凝聚态系统。提议的项目包括热输运，量子霍尔系统的边界-体关系，量子和经典系统的异常流体动力学，手性材料的输运，以及非平衡物理的几何方面。几何思想将应用于分析量子输运的具体实验。拟议的研究路线令人兴奋的部分原因在于有机会将研究成果应用于不同的研究领域。所开发的理论工具可用于物理学的各个领域：量子多体理论、非线性动力学、流体动力学、核物理学、宇宙学等。所得结果将通过数值模拟并最终与实验比较来验证。本研究将为研究生的现代理论方法的全面培养提供一个丰富的环境。PI继续讲授拓扑和几何在凝聚态物理中的应用，并计划准备讲义出版。PI进一步计划将这些笔记发展成一本关于凝聚态物理拓扑方面的书，面向更广泛的科学家群体。PI热衷于为石溪分校（Stony Brook）的K-12学生和俄罗斯的天才高中生教授数学和物理。

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.