Non-Equilibrium Dynamics in Closed Interacting Quantum Systems

非技术概述该奖项支持理论研究和教育，以了解脱离平衡的量子系统的动力学。统计力学是一种强大的形式主义，它允许我们至少在原则上确定处于平衡状态的材料的各种属性。远离平衡，例如，当一种材料受到外部电磁辐射时，即使在基本水平上，情况也要复杂得多，而且几乎不存在一般原理。这个项目背后的根本问题是如何在描述微观和宏观系统的不同方法之间架起桥梁，将相应的量子和经典系统合并到一个单一的统一框架中，来解释量子行为。该项目的另一个目标是找到协议，以抑制因外部刺激(如电磁辐射)而进入非平衡状态的系统中的热量损失。找到这样的协议对许多科学和技术领域都很重要，从设计接近最高效率的快速热机，到开发最优的量子计算算法。该项目还将涉及重新设计PI机构的量子力学研究生课程，根据现代发展大幅更新材料，并增加以计算为中心的模块。该项目还包括通过讨论和合作对波士顿大学和其他机构的研究生和本科生进行指导和培训。PI将继续提供针对研究生和本科生观众的教学评论和课堂讲稿。技术概述该奖项支持理论研究和教育，以了解脱离平衡的量子系统的动力学。在平衡点，统计力学是一种强大的形式主义，它允许我们至少在原则上确定平衡相图，识别可能的相和相变，并表征材料的各种性质。离开了均衡，即使是在基本层面上，情况也要复杂得多，几乎没有一般原则存在。该项目的目标是在以前工作的基础上，发展新的理论思想，专注于三个平行的主题：i)发展半经典相空间方法，以超经典自由度或额外维度的形式以受控的方式编码量子关联；ii)设计局部协议以最大限度地减少耗散损失，并了解复杂系统中绝热变换的一般结构及其对(预)热化、依赖时间的可积性、动态相变和相关主题的影响；以及iii)理解周期驱动系统中稳态或近稳态的结构和稳健性。新的理论发现将应用于实验装置，并在实验装置上进行测试，继续与各种实验小组积极合作，在真实系统中实施理论想法。该项目还将涉及重新设计PI机构的量子力学研究生课程，根据现代发展大幅更新材料，并增加以计算为中心的模块。该项目还包括通过讨论和合作对波士顿大学和其他机构的研究生和本科生进行指导和培训。PI将继续提供针对研究生和本科生观众的教学评论和课堂讲稿。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARY This award supports theoretical research and education towards understanding the dynamics of quantum systems away from equilibrium. Statistical mechanics is a powerful formalism that allows us to determine, at least in principle, various properties of materials at equilibrium. Away from equilibrium, for example when a material is subject to external electromagnetic radiation, the situation is much more complex even at a basic level, and very few general principles exist. The fundamental question underlying this project concerns how to bridge disparate approaches for describing microscopic and macroscopic systems, merging the corresponding quantum and classical counterparts into a single unifying framework that accounts for quantum behavior. Another goal of this project is finding protocols for suppressing heating losses in systems that are brought into nonequilibrium by external stimuli, such as electromagnetic radiation. Finding such protocols is important for many areas of science and technology, ranging from the design of fast heat engines that are operating near maximum efficiency, to the development of optimal quantum computation algorithms. The project will also involve redesigning the graduate quantum mechanics course at the PI's institution by significantly updating the materials with modern developments and by adding computation-centric modules. The project also involves mentoring and training of graduate and undergraduate students both from Boston University and from other institutions through discussions and collaborations. The PI will continue providing pedagogical reviews and lecture notes aimed at both graduate and undergraduate student audiences. TECHNICAL SUMMARY This award supports theoretical research and education towards understanding the dynamics of quantum systems away from equilibrium. At equilibrium, statistical mechanics is a powerful formalism that allows us to determine, at least in principle, equilibrium phase diagrams, to identify possible phases and phase transitions, and to characterize various properties of materials. Away from equilibrium, the situation is much more complex even at a basic level, and very few general principles exist. The project aims to build upon prior work and to develop new theoretical ideas focusing on three parallel topics: i) Developing semiclassical phase-space methods that encode quantum correlations in the form of extra classical degrees of freedom or extra dimensions in a controlled way, ii) Designing local protocols for the fast preparation of many-body states that minimize dissipative losses as well as understanding the general structure of adiabatic transformations in complex systems and their implications for (pre)thermalization, time-dependent integrability, dynamical phase transitions, and related topics, and iii) Understanding the structure and robustness of steady- or nearly-steady states in periodically driven systems. The new theoretical findings will be applied to and tested on experimental setups, continuing an active collaboration with various experimental groups to implement theoretical ideas in real systems. The project will also involve redesigning the graduate quantum mechanics course at the PI's institution by significantly updating the materials with modern developments and by adding computation-centric modules. The project also involves mentoring and training of graduate and undergraduate students both from Boston University and from other institutions through discussions and collaborations. The PI will continue providing pedagogical reviews and lecture notes aimed at both graduate and undergraduate student audiences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.