Nonlinear Effects in Quantum Condensed Matter Systems

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将专注于流体动力学的方法，它提供了一个通用的框架来处理相互作用的系统。PI旨在开发这样一种方法，以深入了解量子低维强相互作用系统，重点是可积模型。线性化的流体动力学描述，玻色化，是非常有效的一维。PI计划将这种方法扩展到非线性和色散流体动力学理论。与线性玻色化相反，非线性理论将适合于研究非线性效应，例如色散冲击波的形成。在冷原子系统中已经观察到了激波，这些新的工具将是及时的。PI将研究几个物理系统，如冷原子，量子点，量子霍尔区的二维电子气，和自旋链使用拓扑方法和量子介观输运的精确结果。PI正在撰写关于量子凝聚态物理中拓扑方法的使用的评论，并提供辅导讲座，凝聚态物理学的研究者。PI正在开发一门关于固态物理学拓扑方面的新课程，该课程将教授斯托尼布鲁克的物理研究生。PI在K-12丰富计划中教授数学，并为俄罗斯有天赋的高中生教授物理和数学。非技术性总结该奖项支持理论研究和教育，旨在开发强相互作用量子力学系统的新方法，如强相关材料中的电子和激光束捕获的原子低温气体。PI的方法建立在一个方法，已成功地应用于系统局限于一维。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半导体晶体中电子气体中的新物质状态的性质。这些物质的拓扑状态可能使一种基于量子力学状态操纵的新型计算成为可能。与其他量子计算方案不同的是，拓扑态相对不受环境影响，不会干扰量子计算机的运行。PI正在撰写一篇关于量子凝聚态物理中拓扑方法的评论，并为凝聚态物理研究人员提供辅导讲座。PI正在开发一门关于固态物理学拓扑方面的新课程，该课程将教授斯托尼布鲁克的物理研究生。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。

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.