Non-Equilibrium Dynamics in Closed Interacting Quantum Systems

该奖项支持理论研究和教育，以理解量子系统远离平衡的动力学。统计力学是一种强大的形式体系，至少在原则上，它使我们能够确定处于平衡状态的材料的各种特性。远离平衡，例如当物质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，而且很少有一般原理存在。这个项目背后的基本问题是如何将描述微观和宏观系统的不同方法连接起来，将相应的量子和经典对应的方法合并到一个解释量子行为的统一框架中。该项目的另一个目标是寻找抑制系统中因外部刺激（如电磁辐射）而进入非平衡状态的热损失的协议。找到这样的协议对于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佳量子计算算法。该项目还将包括重新设计PI所在机构的研究生量子力学课程，根据现代发展对材料进行重大更新，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，指导和培训来自波士顿大学和其他机构的研究生和本科生。PI将继续为研究生和本科生提供教学评论和课堂笔记。该奖项支持理论研究和教育，以理解量子系统远离平衡的动力学。在平衡状态下，统计力学是一个强大的形式体系，它允许我们确定，至少在原则上，平衡相图，识别可能的相和相变，并表征材料的各种特性。在远离平衡的情况下，即使在基本层面上，情况也要复杂得多，而且很少有一般原则存在。该项目旨在以先前的工作为基础，并围绕三个平行主题发展新的理论思想：i)开发半经典相空间方法，以可控的方式以额外经典自由度或额外维度的形式编码量子相关性；ii)设计局部协议，用于快速制备多体态，使耗散损失最小化，以及理解复杂系统中绝热变换的一般结构及其对（预）热化、时间相关可积性、动态相变的影响；iii)理解周期驱动系统中稳定或近稳定状态的结构和鲁棒性。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，继续与各个实验小组积极合作，在实际系统中实施理论思想。该项目还将包括重新设计PI所在机构的研究生量子力学课程，根据现代发展对材料进行重大更新，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，指导和培训来自波士顿大学和其他机构的研究生和本科生。PI将继续为研究生和本科生提供教学评论和课堂笔记。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.