Non-Equilibrium Dynamics in Closed Interacting Quantum Systems

该奖项支持理论研究和教育，旨在促进对远离平衡稳态的量子力学系统的鲁棒特性的理解。 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，就像那些存在于平衡系统中的方法。该项目将解决有关非平衡系统的演变和它们的状态的几何形状之间的关系的基本问题，并有助于理解的性质的稳定状态，阶段，并在系统中接受周期性的外部刺激相变。此外，PI旨在开发新的计算方法来模拟量子系统的动力学。该项目的预测将与当前最先进的实验进行比较，并可能激发新的实验。 NSF的资金将完全支持一名研究生，此外还将通过讨论和合作，为来自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在科学期刊上发表，并将在各种会议、研讨会、学校和面向更广泛受众的座谈会上报告。PI将针对研究生和本科生的观众撰写教学评论和讲座笔记。技术总结该奖项支持理论研究和教育，重点解决有关非平衡相互作用系统的性质的基本问题，以及概念进步在特定实验装置中的实际应用。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缓慢宏观自由度的运动方程，理解驱动系统中非平衡稳态的性质，并找到在量子和经典动力学之间插值的系统方法。具体的问题，这将得到解决，包括微观推导动力学的慢自由度，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;找到一般的运动学系数之间的关系，如质量张量，响应函数和量子几何张量;并找到领先的校正传统的哈密顿动力学。PI还将对与环境隔离和耦合的周期性驱动系统的稳态和瞬态动力学进行理论分析。这项工作的目的是理解能量的局部化和遍历性，涌现守恒定律，相位和相变等。第三个主题将侧重于开发新的数值方法来模拟量子动力学。其核心思想是通过引入额外的自由度来表示关联函数，从而将半经典方法推广到高维相空间。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，这些实验小组专注于解释现有结果并在新实验中实施理论思想。NSF的资金将完全支持一名研究生，此外还将通过讨论和合作，为来自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在科学期刊上发表，并将在各种会议、研讨会、学校和面向更广泛受众的座谈会上报告。PI将针对研究生和本科生的读者撰写教学评论和讲义。

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.