Non-Equilibrium Dynamics in Closed Interacting Quantum Systems

封闭相互作用量子系统中的非平衡动力学

• 批准号: 1506340
• 负责人: Anatoli Polkovnikov
• 金额: $ 34.88万
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-01 至 2018-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1506340&HistoricalAwards=false
• 关键词: Non; Equilibrium; Dynamics; Closed; Interacting

NONTECHNICAL SUMMARYThis award supports theoretical research and education aimed to advance understanding of robust properties of quantum mechanical systems far from the steady state of equilibrium. The study of nonequilibrium systems lies at the forefront of experimental and theoretical research, and will likely play an important role in future technology. However, current understanding of nonequilibrium systems is limited. In particular, there are no systematic theoretical approaches like the ones that exist for systems that are in equilibrium. This project will address fundamental questions regarding the relationship between the evolution of nonequilibrium systems and the geometry of their states, and contribute to understanding the nature of steady states, phases, and phase transitions in systems that receive periodic external stimuli. In addition, the PI aims to develop new computational methods for simulating the dynamics of quantum systems. The predictions of this project will be compared with current state-of-the-art experiments, and could stimulate new experiments. NSF funds will fully support one graduate student, and in addition will contribute to the training of students and postdocs both from Boston University and other institutions through discussions and collaborations. It is anticipated that the results of this work will be published in scientific journals, and will be reported at various conferences, seminars, schools, and colloquia aimed at a broader audience. The PI will write pedagogical reviews and lecture notes aimed at both graduate and undergraduate student audiences.TECHNICAL SUMMARYThis award supports theoretical research and education focused on addressing fundamental questions about the nature of non- equilibrium interacting systems, and the practical applications of conceptual advances to specific experimental setups. The PI aims to address the relation between quantum dynamics and geometry, investigate emergent equations of motion of slow macroscopic degrees of freedom coupled to interacting correlated systems, understand the nature of non-equilibrium steady states in driven systems, and find systematic ways of interpolating between quantum and classical dynamics. Specific problems, which will be addressed, include microscopic derivation of dynamics of slow degrees of freedom, like positions and shapes of macroscopic objects, coupled to fast interacting quantum systems; finding general relations among kinematic coefficients like mass tensor, response functions and the quantum geometric tensor; and finding leading corrections to conventional Hamiltonian dynamics. The PI will also carry out the theoretical analysis of steady states and transient dynamics in periodically driven systems both isolated and coupled to the environment. This work will aim at understanding energy localization and ergodicity, emergent conservation laws, phases and phase transitions and others. The third topic will focus on developing new numerical methods for simulating quantum dynamics. The key idea is to extend semiclassical methods to higher dimensional phase space by introducing extra degrees of freedom representing correlation functions. The PI aims to apply these ideas to specific experimentally relevant setups. The proposal will also involve close collaboration with experimental groups that focus on explaining existing results and the implementation of theoretical ideas in new experiments. NSF funds will fully support one graduate student, and in addition will contribute to the training of students and postdocs both from Boston University and other institutions through discussions and collaborations. It is anticipated that the results of this work will be published in scientific journals, and will be reported at various conferences, seminars, schools, and colloquia aimed at a broader audience. The PI will write pedagogical reviews and lecture notes aimed at both graduate and undergraduate student audiences.

该奖项支持理论研究和教育，旨在促进对远离稳定平衡状态的量子力学系统的鲁棒性的理解。非平衡系统的研究处于实验和理论研究的前沿，并可能在未来的技术中发挥重要作用。然而，目前对非平衡系统的理解是有限的。特别是，没有系统的理论方法，像那些存在于平衡系统的理论方法。该项目将解决有关非平衡系统演化与其状态几何之间关系的基本问题，并有助于理解接受周期性外部刺激的系统中的稳态、相和相变的本质。此外，PI的目标是开发新的计算方法来模拟量子系统的动力学。这个项目的预测将与目前最先进的实验进行比较，并可能刺激新的实验。NSF基金将全额支持一名研究生，此外还将通过讨论和合作为波士顿大学和其他机构的学生和博士后的培训做出贡献。预计这项工作的结果将发表在科学期刊上，并将在各种会议、研讨会、学校和针对更广泛受众的座谈会上报告。PI将撰写针对研究生和本科生受众的教学评论和课堂笔记。该奖项支持理论研究和教育，重点是解决有关非平衡相互作用系统本质的基本问题，以及将概念进步应用于特定实验装置的实际应用。PI旨在解决量子动力学和几何之间的关系，研究耦合到相互作用的相关系统的慢宏观自由度的紧急运动方程，理解驱动系统中非平衡稳态的本质，并找到量子动力学和经典动力学之间的系统插值方法。具体的问题，这将被解决，包括慢自由度动力学的微观推导，如宏观物体的位置和形状，耦合到快速相互作用的量子系统；寻找质量张量、响应函数和量子几何张量等运动系数之间的一般关系；并找到对传统哈密顿动力学的重要修正。PI还将在孤立和耦合于环境的周期性驱动系统中进行稳态和瞬态动力学的理论分析。这项工作将旨在理解能量的局部化和遍历性，紧急守恒定律，相和相变等。第三个主题将集中于发展新的数值方法来模拟量子动力学。关键思想是通过引入表示相关函数的额外自由度，将半经典方法扩展到高维相空间。PI旨在将这些想法应用于特定的实验相关设置。该提案还将涉及与实验小组的密切合作，重点是解释现有结果和在新实验中实施理论思想。NSF基金将全额支持一名研究生，此外还将通过讨论和合作为波士顿大学和其他机构的学生和博士后的培训做出贡献。预计这项工作的结果将发表在科学期刊上，并将在各种会议、研讨会、学校和针对更广泛受众的座谈会上报告。PI将撰写针对研究生和本科生受众的教学评论和课堂笔记。