Nonlinear effects in quantum condensed matter systems

量子凝聚态物质系统中的非线性效应

• 批准号: 1206790
• 负责人: Alexander Abanov
• 金额: $ 30万
• 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: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1206790&HistoricalAwards=false
• 关键词: Nonlinear; effects; quantum; condensed; matter

TECHNICAL SUMMARYThis award supports theoretical research and education on strongly correlated electron systems. To make any progress in understanding systems with strong interactions nonperturbative methods are needed. The hydrodynamic approach provides a general framework for treating interacting quantum and classical systems.Hydrodynamic methods and methods developed in the field of classical integrable equations will be used to analyze nonlinear behavior of quantum interacting systems. The PI aims to develop a hydrodynamic description of cold atoms, fractional quantum Hall effect systems, and low-dimensional integrable models. The linearized version of the hydrodynamic description - bosonization is known to be very effective in one- dimensional physics. The PI will develop a nonlinear and dispersive hydrodynamic theory to study nonlinear effects, such as formation of dispersive shock waves and to describe higher-dimensional systems. The PI will also develop topological methods in condensed matter physics and apply exact results for quantum transport and integrable systems to topological insulators and superconductors, and to mesoscopic systems.The research lies at the interface with mathematics and provides a good environment for training graduate students. The PI is developing a course on topological terms for advanced graduate students and researchers and plans to make corresponding lecture notes publicly available in the near future. The PI teaches math and physics with enthusiasm to K-12 students in the enrichment program for children at Stony Brook and to gifted high school students in Russia.NON-TECHNICAL SUMMARY This award supports theoretical investigations of quantum mechanical systems of many electrons or atoms that interact strongly with each other. This remains a challenging and fruitful area of research. The PI aims to develop a hydrodynamic description of these systems. Within the framework of hydrodynamics, systems of electrons or atoms are viewed as fluids with effective properties, for example, density, velocity, and viscosity. As a result, well known phenomena in fluids have analogs in systems of very cold atoms and electrons. Examples include vortices, shock waves, and turbulence. The PI aims to develop a hydrodynamic approach to systems of cold atoms, to the fractional quantum Hall effect and to the "fluids" that arise in exactly solvable models. The fractional quantum Hall effect arises in electrons confined to two dimensions in artificial semiconductor structures or in a single layer of carbon atoms called graphene, and exposed to a high magnetic field. Under these conditions the interactions between electrons can become very strong. Research on quantum Hall systems has led to the notion of a new kind of order known as topological order which is reflected in topological insulators. Like ordinary insulators, for example rubber, topological insulators do not conduct electricity though the interior of the material. Unlike ordinary insulators, topological insulators are able to conduct electricity on their edges or boundaries through the formation of a new state of matter. Among the known topological insulators are compounds made of the elements bismuth and selenium, and bismuth and tellurium. The PI will also develop new theoretical methods and methods known in exactly solvable models and apply them to topological insulators and other states of electronic matter. The research lies at the interface with mathematics and provides a good environment for training graduate students. The PI is developing a course on topological terms for advanced graduate students and researchers and plans to make corresponding lecture notes publicly available in the near future. The PI teaches math and physics with enthusiasm to K-12 students in the enrichment program for children at Stony Brook and to gifted high school students in Russia.

技术总结该奖项支持强关联电子系统的理论研究和教育。要在理解强相互作用系统方面取得任何进展，就需要使用非微扰方法。流体动力学方法为处理相互作用的量子系统和经典系统提供了一个通用的框架。流体动力学方法和经典可积方程领域发展起来的方法将被用来分析量子相互作用系统的非线性行为。PI的目标是发展冷原子、分数量子霍尔效应系统和低维可积模型的流体动力学描述。众所周知，流体动力学描述的线性化版本-玻色化在一维物理中非常有效。PI将发展一种非线性和色散流体力学理论来研究非线性效应，如色散冲击波的形成，并描述更高维的系统。PI还将发展凝聚态物理中的拓扑方法，并将量子输运和可积系统的精确结果应用于拓扑绝缘体和超导体，以及介观系统。这项研究位于与数学的接口上，为培养研究生提供了良好的环境。PI正在为高级研究生和研究人员开发一门关于拓扑学术语的课程，并计划在不久的将来公开提供相应的课堂讲稿。PI热情地向Stony Brook儿童丰富计划中的K-12学生和俄罗斯有天赋的高中生教授数学和物理。非技术概述该奖项支持对许多相互作用强烈的电子或原子的量子力学系统的理论研究。这仍然是一个富有挑战性和成果的研究领域。PI旨在开发对这些系统的水动力学描述。在流体力学的框架内，电子或原子系统被视为具有有效性质的流体，例如密度、速度和粘度。因此，流体中众所周知的现象在非常冷的原子和电子系统中也有类似的情况。例如涡旋、冲击波和湍流。PI的目标是开发一种流体力学方法来研究冷原子系统、分数量子霍尔效应和在精确可解模型中出现的“流体”。分数量子霍尔效应出现在人造半导体结构中限制在二维的电子中，或者出现在被称为石墨烯的单层碳原子层中，并暴露在强磁场中。在这些条件下，电子之间的相互作用会变得非常强。对量子霍尔系统的研究引出了一种新的序的概念，即拓扑序，它反映在拓扑绝缘体中。与普通绝缘体(例如橡胶)一样，拓扑型绝缘体不通过材料内部导电。与普通绝缘子不同，拓扑绝缘子能够通过形成新的物质状态在其边缘或边界上导电。在已知的拓扑绝缘体中，有由元素铋和硒以及铋和碲组成的化合物。PI还将发展在精确可解模型中已知的新的理论方法和方法，并将它们应用于拓扑绝缘体和电子物质的其他状态。本研究立足于与数学的接口，为研究生的培养提供了良好的环境。PI正在为高级研究生和研究人员开发一门关于拓扑学术语的课程，并计划在不久的将来公开提供相应的课堂讲稿。PI热情地向石溪儿童丰富项目中的K-12学生和俄罗斯有天赋的高中生教授数学和物理。