Nonlinear Effects in Quantum Condensed Matter Systems

量子凝聚态系统中的非线性效应

• 批准号: 0906866
• 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: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0906866&HistoricalAwards=false
• 关键词: Nonlinear; Effects; Quantum; Condensed; Matter

TECHNICAL SUMMARYThis award supports theoretical research and education with an aim to develop nonperturbative methods for systems with strong interactions. The PI will focus on the hydrodynamic approach which provides a general framework for treating interacting systems. The PI aims to develop such an approach to gain insight into quantum low-dimensional strongly interacting systems focusing on integrable models. The linearized version of the hydrodynamic description, bosonization, is very effective in one-dimension. The PI plans to extend this approach to nonlinear and dispersive hydrodynamic theory. In contrast to linear bosonization, the nonlinear theory will be suitable for studying nonlinear effects, such as formation of dispersive shock waves. Shock waves have been observed in systems of cold atoms, and these new tools would be timely.The PI will study several physical systems such as cold atoms, quantum dots, two-dimensional electron gas in quantum Hall regime, and spin chains using topological methods and exact results for quantum mesoscopic transport.The PI is writing a review on the use of topological methods in quantum condensed matter physics and delivers tutorial lectures to researchers in condensed matter physics. The PI is developing a new course on topological aspects in solid state physics which will be taught to physics graduate students in Stony Brook. The PI teaches mathematics in K-12 enrichment program and teaches physics and mathematics to gifted high school students in Russia.NONTECHNICAL SUMMARYThis award supports theoretical research and education with the aim of developing a new approach for strongly interacting quantum mechanical systems, like electrons in strongly correlated materials and low temperature gases of atoms trapped by laser beams. The PI's approach builds on a method that has been successfully applied to systems confined to one dimension. The PI will use these methods to study some of the most challenging problems in condensed matter physics, such as spin chains and the nature of new states of matter predicted to exist in gases of electrons confined to dimensions in semiconductor crystals in a perpendicular strong magnetic field. These topological states of matter may enable a new kind of computation based on the manipulation of quantum mechanical states. Unlike other proposals for quantum computing, topological states would be comparatively immune from environmental effects that would interfere with the operation of a quantum computer.The PI is writing a review on the use of topological methods in quantum condensed matter physics and delivers tutorial lectures to researchers in condensed matter physics. The PI is developing a new course on topological aspects in solid state physics which will be taught to physics graduate students in Stony Brook. The PI teaches mathematics in K-12 enrichment program and teaches physics and mathematics to gifted high school students in Russia.

技术总结该奖项支持理论研究和教育，旨在为具有强相互作用的系统开发非微扰方法。PI将侧重于流体动力学方法，它为处理相互作用的系统提供了一个一般框架。PI的目标是开发这样一种方法来深入了解专注于可积模型的量子低维强相互作用系统。流体动力学描述的线性化版本，玻色化，在一维中非常有效。PI计划将这种方法扩展到非线性和色散流体力学理论。与线性玻色化相比，非线性理论更适合于研究色散激波的形成等非线性效应。冲击波已经在冷原子系统中被观察到，这些新的工具将会在时间上被观察到。PI将使用拓扑方法和量子介观输运的精确结果来研究几个物理系统，如冷原子、量子点、量子霍尔区中的二维电子气和自旋链。PI正在撰写一篇关于拓扑方法在量子凝聚态物理中的应用的评论，并为凝聚态物理的研究人员提供辅导讲座。国际物理学会正在开发一门关于固态物理中的拓扑学方面的新课程，该课程将教授给石溪的物理研究生。PI教授K-12强化课程的数学，并向俄罗斯有天赋的高中生教授物理和数学。非技术总结该奖项支持理论研究和教育，旨在开发一种新的方法来研究强关联材料中的电子和被激光捕获的原子的低温气体等强相互作用的量子力学系统。PI的方法建立在一种方法的基础上，该方法已成功应用于一维系统。PI将使用这些方法来研究凝聚态物理学中一些最具挑战性的问题，例如自旋链和预测存在于垂直强磁场中的半导体晶体中受限于维度的电子气体中的新物质状态的性质。物质的这些拓扑态可能会使一种基于对量子力学状态的操纵的新型计算成为可能。与量子计算的其他提议不同，拓扑态相对不会受到干扰量子计算机运行的环境效应的影响。PI正在撰写一篇关于拓扑方法在量子凝聚态物理中的使用的评论，并为凝聚态物理学的研究人员提供辅导讲座。国际物理学会正在开发一门关于固态物理中的拓扑学方面的新课程，该课程将教授给石溪的物理研究生。PI在K-12强化计划中教授数学，并向俄罗斯有天赋的高中生教授物理和数学。