Nonequilibrium Quantum Mechanics of Strongly Correlated Systems

该奖项支持理论研究和教育，以推进对远离平衡的强相关量子系统特性的基本理解。本研究的动机是对非平衡量子系统的实验。利用Keldysh图解方法，PI展示了如何将强大的概念，如平均场理论，识别关于平均场的重要波动和重整化群，推广到各种非平衡问题。PI将进一步以这些想法为基础，并将其应用于以下系统：a)。在非费米液体物理和量子相变等平衡态中表现出丰富行为的非平衡态量子杂质模型。在耗散量子临界点附近的空间扩展系统，并被电流驱动出平衡。强相关系统受到强烈的时间依赖性扰动，如哈密顿量参数的突然变化，或由强瞬态光脉冲引起的光激发。这些项目将涉及许多实验系统，如：非平衡纳米级器件，具有快速可调参数的光学晶格中的冷原子，强相关系统的非线性光谱和量子临界点附近的输运。将解决的基本问题包括：a)。接近平衡量子临界点的系统表现出普遍的行为。当这些系统被驱逐出平衡状态时，普遍性的概念是否仍然成立？非平衡系统的“有效温度”描述在多大程度上是有效的？一个非平衡驱动，如均匀电流，能产生新的与时间无关或与时间相关的动态相吗？是否有可能实现非平衡驱动的“有序-无序”量子相变？如果是这样的话，这种转变是否具有普遍性和临界指数的特征？该奖项还支持在新兴科学领域对研究生和本科生的指导和培训。非技术总结：该奖项支持理论研究和教育，旨在理解许多粒子系统，这些系统需要量子力学描述，并且由于大的扰动而与周围环境失去平衡。例如，在分子大小的材料（也称为纳米结构）中对电子施加电压。对于这些系统，用于理解和描述与周围环境平衡的系统的成功理论方法不起作用，PI旨在将这些平衡方法扩展到非平衡系统。这个普遍的问题也出现在原子和光学物理学、生物系统和量子信息理论中，PI的方法应该适用于广泛的非平衡系统。PI将以她之前的工作为基础，研究非平衡的纳米结构，并探索电流可以驱动即将转变为磁性或超导的材料进入可能不存在于平衡状态的新物质状态的可能性。她还将研究具有许多强相互作用粒子的非平衡量子系统，例如受强瞬态光脉冲影响的强相关材料。这项研究有助于对我们周围世界的广泛的基本理解。纳米结构和杂质系统的研究为未来电子器件和信息技术的设计奠定了理论基础。该奖项还支持在新兴科学领域对研究生和本科生的指导和培训。

TECHNICAL SUMMARYThis award supports theoretical research and education to advance fundamental understanding of the properties of strongly correlated quantum systems that have been driven far from equilibrium. This research is motivated by experiments on nonequilibrium quantum systems. Using Keldysh diagrammatic methods, the PI has shown how powerful concepts such as mean-field theory, identifying the important fluctuations about mean-field and the renormalization group can be generalized to a variety of nonequilibrium problems. The PI will further build on these ideas and apply them to the following systems:a). Nonequilibrium quantum impurity models which show rich behavior in equilibrium such as non-Fermi liquid physics and quantum phase transitions.b). Spatially extended systems near dissipative quantum critical points and driven out of equilibrium by current flow.c). Strongly correlated systems subjected to strong time dependent perturbations such as a sudden change of a parameter of the Hamiltonian, or by photo-excitation by strong transient light pulses. These projects will be relevant to a number of experimental systems such as: nonequilibrium nanoscale devices, cold atoms in optical lattices with rapidly tunable parameters, nonlinear optical spectroscopies of strongly correlated systems and transport near quantum critical points. Fundamental questions that will be addressed include:a). Systems near equilibrium quantum critical points show universal behavior. Do notions of universality still hold when these systems are driven out of equilibrium?b). To what extent is an "effective temperature" description of nonequilibrium systems valid?c). Can a nonequilibrium drive such as uniform current flow give rise to new kinds of time-independent or time-dependent dynamical phases?d). Is it possible to realize nonequilibrium driven ``ordering-disordering'' quantum phase transitions? If so can such transitions be characterized by universality and critical exponents?This award also supports guidance and training of graduate and undergraduate students in an emerging area of science.NON-TECHNICAL SUMMARY:This award supports theoretical research and education aimed towards understanding many particle systems that require a quantum mechanical description and are out of balance with their surroundings because of a large perturbation. Applying a voltage to electrons in a material with very small dimensions the size of molecules, otherwise known as a nanostructure, would be an example. For these systems, the successful theoretical methods developed to understand and describe systems that are in balance with their surroundings do not work and the PI aims to develop extensions of these equilibrium methods to nonequilibrium systems. This general problem also arises in atomic and optical physics, biological systems, and quantum information theory and the PI's approach should apply to a broad range of nonequilibrium systems. The PI will build on her previous work and study nanostructures out of equilibrium and explore the possibility that an electric current can drive materials that are near a transformation to magnetism or superconductivity into new states of matter that may not exist in equilibrium. She will also study nonequilibrium quantum systems that have many strongly interacting particles, such as strongly correlated materials subjected to intense transient pulses of light.This research contributes to the broad fundamental understanding of the world around us. The focus of the research on nanostructures and systems of impurities contributes to the theoretical foundations that will enable the design of possible future electronic devices and information technology.This award also supports guidance and training of graduate and undergraduate students in an emerging area of science.