Non-Equilibrium Dynamics in Closed Interacting Quantum Systems

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。技术概述该奖项支持理论研究和教育，重点是理解量子多粒子动力学的基本方面及其实验结果。一个关键的目标是发展一个一般的形式主义，代表各种经典极限附近的时间演化，例如粒子，波，混合，旋转等，并将其应用于各种非平衡系统。这项工作应大大建立在PI的早期工作，证明了这种方法的可行性。PI的目的是追求在各种情况下分析从经典到量子非平衡行为的交叉的可能性。PI打算将这种形式主义扩展到费米子系统和耦合到热浴的开放系统。量子动力学的这种表示将与其他现有的方法，如Keldysh技术和相空间方法进行对比。PI的形式主义与其他方法一起将被应用到具体的问题的根本利益，包括：热化在封闭系统，动力学的可积和不可积系统，形成拓扑缺陷，扰动的时间演化的外部测量，和缓慢和快速的动态，特别是在低维系统。将特别强调这些应用程序，可以在实验中进行测试。这项研究应该导致更好地理解指数大希尔伯特空间对多粒子动力学的作用，如果接近经典极限，这种指数复杂性如何变得越来越不相关，以及系统的可积性是否定性地影响量子到经典交叉的各个方面。PI还将解决其他基本问题，包括封闭系统中绝热过程的存在条件和违反。PI将探索在封闭系统中使用非线性动力学探针来检测准粒子统计的可能性，检测低维系统中的纠缠，了解渐近系综的性质，并将其与工作波动和熵产生的统计联系起来。不可积性，热化和系统的维数，这一切都可能在缓慢的动力学中发挥关键作用的作用将得到解决。所有主要的一般理论结果将通过具体的建议来补充，以在凝聚态，材料和冷原子系统中进行实验测试。PI将参与研究生水平及更高水平的教育活动，以开发，改进和加强量子力学，统计物理学，多体物理学和冷原子物理学的课程;贡献教学评论文章;参加国际学校的高级课程。非技术总结该奖项支持理论研究和教育，重点是理解量子力学相互作用多粒子系统的动力学。这种系统的例子包括材料和专用半导体结构中的电子以及冷却到非常低的温度并被光捕获的原子。本研究旨在为这类系统开发一种理论。部分研究集中在完全使用经典力学给出的轨迹语言来分析量子系统的动力学。这项工作突出了量子动力学，经典动力学和统计物理之间的非平凡联系。 PI还旨在促进对驱动量子力学相互作用多体系统的理解。对量子力学多体系统动力学的理解具有广泛的影响，并为可能导致未来技术的知识基础做出贡献。PI计划为广大非专业观众开发教育材料，并积极参与国内和国际会议，研讨会和学校。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).TECHNICAL SUMMARYThis award supports theoretical research and education focused on understanding fundamental aspects of quantum many-particle dynamics and their experimental consequences. A key goal is to develop a general formalism representing time evolution near various classical limits, for example particle, wave, mixed, rotational, etc., and apply it to various non-equilibrium systems. This work should significantly build on the PI's earlier work which proved the feasibility of this approach. The PI aims to pursue the possibility of analyzing the crossover from classical to quantum nonequilibrium behavior in various contexts. The PI intends to extend this formalism to fermionic systems and open systems coupled to a thermal bath. This representation of quantum dynamics will be contrasted with other existing approaches like the Keldysh technique and phase space methods. The PI's formalism together with other methods will be applied to specific problems of fundamental interest, including: thermalization in closed systems, dynamics of integrable and nonintegrable systems, formation of topological defects, perturbation of time evolution by external measurements, and slow and fast dynamics especially in low-dimensional systems. Special emphasis will be given to those applications, which can be tested in experiments. The research should lead to a better understanding of the role of the exponentially large Hilbert space on many-particle dynamics, how this exponential complexity becomes less and less relevant if one approaches the classical limit, and whether integrability of the system qualitatively affects various aspects of the quantum to classical crossover. The PI will also address other fundamental problems, including the conditions of existence and violation of adiabatic processes in closed systems. The PI will explore possibilities of using non-linear dynamical probes in closed systems to detect quasi-particle statistics, detect entanglement in low-dimensional systems, understand properties of asymptotic ensembles and connect them to statistics of work fluctuations and entropy generation. The role of nonintegrability, thermalization, and dimensionality of the system, which all likely play the crucial role in slow dynamics will be addressed. All major general theoretical results will be supplemented by specific proposals to experimentally test them in condensed matter, material, and cold atom systems.The PI will be engaged in educational activities at the graduate level and higher to develop, refine, and enhance courses in quantum mechanics, statistical physics, many-body physics, and physics of cold atoms; contribute pedagogical review articles; and participate in international schools on advanced topics. NON-TECHNICAL SUMMARYThis award supports theoretical research and education focused on understanding the dynamics of quantum mechanical interacting many-particle systems. Examples of such systems include electrons in materials and specialized semiconductor structures and atoms cooled to very low temperatures and trapped by light. This research seeks to develop a theory for these kinds of system. Part of the research focuses on analyzing the dynamics of quantum systems using entirely the language of the trajectories given by classical mechanics. This work highlights nontrivial connections between quantum dynamics, classical dynamics, and statistical physics. The PI also aims to advance understanding of driven quantum mechanical interacting many-body systems.The understanding of the dynamics of quantum mechanical many-body systems has broad consequences and contributes to intellectual foundations that may lead to future technologies.The PI plans to develop educational materials intended for a broad audience of non-specialists and to actively participate in domestic and international conferences, workshops, and schools.