Non-Equilibrium Dynamics in Closed Interacting Quantum Systems

该奖项支持理论研究和教育，以了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主义，它使我们能够确定，至少在原则上，平衡状态下材料的各种性质。远离平衡，例如当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，并且很少有一般原理存在。该项目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物合并到一个统一的框架中，以解释量子行为。该项目的另一个目标是找到抑制系统热损失的协议，这些系统被外部刺激（如电磁辐射）带入非平衡状态。找到这样的协议对于许多科学和技术领域都很重要，从接近最大效率运行的快速热机的设计到最佳量子计算算法的开发。该项目还将涉及重新设计PI机构的研究生量子力学课程，通过现代发展显着更新材料并添加以计算为中心的模块。该项目还包括通过讨论和合作，对来自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讲义。该奖项支持理论研究和教育，以了解量子系统远离平衡的动力学。在平衡态，统计力学是一个强大的形式主义，它使我们能够确定，至少在原则上，平衡相图，以确定可能的阶段和相变，并表征各种性质的材料。离开均衡，即使在基本层面上，情况也要复杂得多，而且几乎没有一般原则。该项目旨在建立在以前的工作，并制定新的理论思想，重点是三个平行的主题：i）开发半经典相空间方法，以受控方式将量子相关性编码为额外经典自由度或额外维度的形式，二）设计快速制备许多-最大限度地减少耗散损失的身体状态，以及理解复杂系统中绝热变换的一般结构及其对（前）热化，时间相关可积性，动力学相变，和相关主题，以及iii）理解周期性驱动系统中稳态或近稳态的结构和鲁棒性。新的理论发现将应用于实验装置并进行测试，继续与各种实验小组积极合作，以在真实的系统中实现理论思想。该项目还将涉及重新设计PI机构的研究生量子力学课程，通过现代发展显着更新材料并添加以计算为中心的模块。该项目还包括通过讨论和合作，对来自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将继续为研究生和本科生提供教学评论和演讲笔记。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

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.