Quench Dynamics of Low Dimensional Quantum Many Body Systems

该奖项支持基础理论研究和教育，以推进对许多粒子（例如材料中的电子）的量子力学系统的概念理解，这些粒子远离平衡态。多年来，非平衡过程的详细研究一直受到阻碍，因为系统对外部脉冲的响应具有非常短的时间尺度，并且难以将此类系统与环境隔离。 随着各种新的实验系统的出现，包括纳米电子和纳米机械器件，分子电子器件，光学系统和激光束中捕获的冷原子气体，许多限制已经被克服，并且在控制和微调许多基础实验以探测非平衡系统方面取得了巨大进展。 该奖项解决了并行开发理论工具来描述它们的需求。PI将专注于经历突变或淬火的系统，并研究系统如何随时间响应。 待研究的系统由一类在被困冷原子系统或纳米器件中具有实验实现的模型描述。 将开发理论工具来探索这些系统的时间演化。PI旨在使用这些工具进一步探索和确定远离平衡的系统的热力学基础的基本原理。PI将解决几个问题，包括：是什么驱动系统达到平衡？动力学的哪些方面适用于许多独立于具体细节的系统，哪些方面是特定于特定系统的？当一个系统处于非平衡稳态时，它是否会使纠缠最大化？纠缠是一种量子力学性质，它将系统中可能彼此远离的不同部分联系起来。这些项目描述了详细的实验系统，并用于发现管理它们的概念。 将理论分析与实验系统的具体研究相结合，为研究生的培养提供了一个良好的平台。PI将把潜在的科学和研究成果传达给从高中生到普通公众的广泛受众。技术概述该奖项支持强关联系统的非平衡动力学的理论研究和教育。 重点放在淬火演化系统描述的可积哈密顿量，可以实现的实验。 PI将开发研究非平衡系统动力学所需的理论工具。他将追求推广的尤德森表示有限体积，这是必要的，以允许表达的任意初始状态的贝特Angloman本征态的哈密顿量，因此其演变。 PI将研究各种系统，包括：Gaudin-Yang模型描述多组分粒子，费米子或玻色子 在连续线上运动，通过短程势相互作用。PI将研究具有吸引力和排斥力相互作用的费米海的相互作用淬灭，目的是了解随之而来的不同阶段。特别令人感兴趣的是淬火成一个有限的动量凝聚态，驱动的不平衡的自旋和自旋下降的电子。类似的问题也出现在哈伯德哈密顿量描述的系统的晶格上，正弦-戈登模型可以在各种背景下描述大量的系统。PI将在周期势强度降低时发生的从Mott绝缘体到超流体的猝灭的物理背景下研究这个模型，这是一种实验研究得很多的量子相变。量子杂质系统，通常由Kondo和安德森哈密顿给出，出现在许多背景下。利用这些哈密顿量，PI将研究以下的猝灭动力学：耦合到铅的杂质，以确定近藤效应的时间演化，ii.一种附着在两个不同化学势的引线上的杂质，用于确定由电压驱动的非平衡电流的时间演化。该奖项还支持与研究生水平的研究相结合的教育活动。研究结果将被纳入PI的量子多体物理学和凝聚态理论的研究生课程，并纳入PI正在编写的一本书中。

NONTECHNICAL SUMMARY This award supports fundamental theoretical research and education to advance conceptual understanding of quantum mechanical systems of many particles, for example electrons in materials, that are far from the balanced state of equilibrium. The detailed study of nonequilibrium processes has been hampered over the years by the very short time scales that characterize the response of the system to external impulse, and the difficulty of isolating such systems from the environment. With the appearance of diverse new systems accessible to experiments, including nanoelectronic and nanomechanical devices, molecular electronic devices, optical systems, and cold atom gases trapped in beams of laser light, many limitations have been overcome and great progress has been made to control and fine tune many fundamental experiments to probe nonequilibrium systems. This award addresses a need to develop in parallel the theoretical tools to describe them.The PI will focus on systems that undergo an abrupt change, or quench, and investigate how the system responds with time. The systems to be investigated are described by a class of models that have experimental realizations in trapped cold atom systems or nanodevices. Theoretical tools will be developed to explore the time evolution of these systems. The PI aims to use these tools to go further to probe and identify the fundamental principles that underlie thermodynamics for systems that are far from equilibrium. The PI will address several questions, including: What drives a system to reach equilibrium? What aspects of the dynamics apply to many systems independent of specific details, and which ones are specific to a particular system? When a system is in a nonequilibrium steady state does it maximize entanglement, a quantum mechanical property that links different parts of the system that may be far from each other?The projects describe detailed experimental systems and are used to discover the concepts that govern them. Combining both the theoretical analysis with specific study of experimental systems provides an excellent platform for the training of graduate students. The PI will convey the underlying science and research results to a broad range of audiences from high school students to the general public.TECHNICAL SUMMARYThis award supports the theoretical research and education on the nonequilibrium dynamics of strongly correlated systems. The emphasis is placed on quench evolution in systems described by integrable Hamiltonians that can be realized by experiments. The PI will develop the theoretical tools needed to investigate the dynamics of nonequilibrium systems. He will pursue generalizations of the Yudson representation to finite volume that are necessary to allow the expression of an arbitrary initial state in terms of the Bethe Ansatz eigenstates of the Hamiltonian and hence its evolution. The PI will investigate a variety of systems, including:The Gaudin-Yang model describes multicomponent particles, fermions or bosons moving on the continuous line interacting via short range potential. The PI will study the interaction quench of a Fermi sea with attractive and repulsive interactions with the purpose of understanding the different phases that ensue. Of particular interest is the quench into a finite momentum condensed state, driven by an imbalance of spin-up and spin-down electrons. Similar questions arise on the lattice for systems described by the Hubbard Hamiltonian.The Sine-Gordon model can describe a large number of systems in a variety of contexts. The PI will study this model in the physical context of the quench from a Mott insulator to a superfluid that takes place when the strength of the periodic potential is reduced, a quantum phase transition much studied experimentally.Quantum impurity systems, typically given by the Kondo and Anderson Hamiltonians, appear in many contexts. With these Hamiltonians, the PI will investigate the quench dynamics of: i. an impurity coupled to a lead to determine time evolution of the Kondo effect, ii. An impurity attached to two leads held at different chemical potential to determine and the time evolution of the non equilibrium current driven by the voltage.This award also supports educational activities integrated with the research at the graduate level. The results of the research will be incorporated into the PI's graduate level courses on quantum many-body physics and condensed matter theory and into a book the PI is writing.