Quench Dynamics of Low Dimensional Quantum Many Body Systems

低维量子多体系统的淬灭动力学

• 批准号: 1410583
• 负责人: Natan Andrei
• 金额: $ 30万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-10-01 至 2019-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1410583&HistoricalAwards=false
• 关键词: Quench; Dynamics; Low; Dimensional; Quantum

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.

非技术摘要 该奖项支持基础理论研究和教育，以促进对许多远离平衡状态的粒子（例如材料中的电子）的量子力学系统的概念理解。多年来，对非平衡过程的详细研究一直受到系统对外部脉冲响应的非常短的时间尺度的阻碍，以及将此类系统与环境隔离的困难。 随着可用于实验的各种新系统的出现，包括纳米电子和纳米机械装置、分子电子装置、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探测非平衡系统的基础实验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要。PI 将重点关注经历突然变化或猝灭的系统，并研究系统如何随时间响应。 要研究的系统由一类模型描述，这些模型在捕获的冷原子系统或纳米器件中进行了实验实现。 将开发理论工具来探索这些系统的时间演化。 PI 旨在利用这些工具进一步探索和识别远离平衡系统的热力学基础原理。 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独立于特定细节的许多系统，哪些方面特定于特定系统？当系统处于非平衡稳态时，它是否会最大化纠缠，这是一种将系统中可能彼此相距较远的不同部分联系起来的量子力学特性？这些项目描述了详细的实验系统，并用于发现控制它们的概念。 理论分析与实验系统具体研究相结合，为研究生的培养提供了良好的平台。 PI 将向从高中生到普通公众的广泛受众传达基础科学和研究成果。技术摘要该奖项支持强相关系统非平衡动力学的理论研究和教育。 重点放在可积哈密顿量描述的系统中的失超演化，这些系统可以通过实验实现。 PI 将开发研究非平衡系统动力学所需的理论工具。他将追求将 Yudson 表示推广到有限体积，这是允许用哈密顿量的 Bethe Ansatz 本征态表达任意初始状态及其演化所必需的。 PI 将研究各种系统，包括： Gaudin-Yang 模型描述了在连续线上移动的多组分粒子、费米子或玻色子，通过短程势相互作用。 PI 将研究费米海的相互作用淬灭以及吸引和排斥相互作用，目的是了解随后发生的不同阶段。特别令人感兴趣的是由自旋向上和自旋向下电子的不平衡驱动的淬灭到有限动量凝聚态。哈伯德哈密顿量描述的系统的格上也存在类似的问题。正弦戈登模型可以描述各种背景下的大量系统。 PI 将在从莫特绝缘体到超流体的淬灭的物理背景下研究这个模型，当周期性势的强度降低时，就会发生这种淬灭，这是一种在实验上进行了大量研究的量子相变。量子杂质系统，通常由近藤和安德森哈密顿主义者给出，出现在许多情况下。通过这些哈密顿量，PI 将研究以下的淬灭动力学： i．与引线耦合的杂质以确定近藤效应的时间演化，ii．附着在处于不同化学势的两条引线上的杂质，以确定由电压驱动的非平衡电流的时间演变。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 的量子多体物理和凝聚态理论研究生课程以及 PI 正在撰写的书中。