Non-Equilibrium Dynamics in Closed Interacting Quantum Systems

该奖项支持理论研究，其总体目标是理解不平衡的相互作用量子力学系统，特别关注“量子混沌”。在日常生活中，混沌通常被定义为混乱，或者更准确地说，是缺乏任何秩序。在经典物理学中，混沌在数学上是通过粒子轨迹对轻微扰动的极强敏感性来定义的。这种敏感性存在于我们周围的许多现象背后，从不稳定的天气模式到平衡统计物理学的出现，最基本的例子是热力学第二定律。另一方面，在量子系统中，粒子没有很好的定义轨迹，因为它们的位置和速度由于不确定性原理不能同时定义。因此，用量子力学的语言来定义和理解微观世界中的混沌变得更加微妙，并且在过去的四十年中一直是一个积极辩论的主题。这个项目探索了通过量子态对小扰动的敏感性来定义量子混沌的新方法。通过这种语言，它旨在建立量子和经典混沌之间的直接联系，并探索当我们增加系统中的粒子数量时，它是如何出现的。该项目的另一个重点是寻找通过主动动态控制来抑制相互作用量子系统中的混沌的方法，这将导致开发有效的计算和能量转移方案。反过来，这些方案可以用于未来的技术中，以开发快速高效的量子计算机、量子模拟器、量子热机或冰箱。该奖项还支持教育和推广活动，包括培训研究生和本科生在凝聚态和统计物理前沿的主题，提供公开演讲和讲座，以及开发一本关于量子力学的新书，其中涵盖了标准教科书中通常找不到的领域的现代进展。该奖项支持旨在开发新的理论方法来理解非平衡相互作用系统，并将这些方法应用于现有和未来的实验装置的研究。该研究有三个主要重点：(1)项目的第一个主题侧重于PI最近开发的一种方法，该方法通过绝热规范势表示的绝热变形来表征量子混沌。PI将分析弱可积破微扰驱动下的可积和混沌状态之间转换的普遍性质，将该方法应用于无序、周期驱动等系统，并将其推广到经典非线性系统，如Fermi-Pasta-Ulam-Tsingou问题，以分析混沌的出现。(2)该项目第二个密切相关的主题是寻找近似局部绝热规范势，该势可用于识别不可积系统中的近似局部守恒律。目标是开发有效的局部反绝热和快进协议，以抑制相互作用系统中的耗散，这对于有效的信息和能量处理都很重要。该项目将致力于在驱动的Floquet系统、有限温度系统和具有局部无界频谱的非线性系统中设计这样的协议。特别强调的是开发实验相关协议，可以在不同的设置中实现，如超导量子比特，冷原子和捕获离子。(3)该项目的第三个主题将集中于研究量子和经典混沌之间的联系，通过使用PI最近开发的一种形式主义，该形式主义显示了经典哈密顿系统和量子特征态之间的对应关系，即使远离半经典极限。该奖项还支持教育和推广活动，包括培训研究生和本科生在凝聚态和统计物理前沿的主题，提供公开演讲和讲座，以及开发一本关于量子力学的新书，其中涵盖了标准教科书中通常找不到的领域的现代进展。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 SUMMARYThis award supports theoretical research with a general aim to understand interacting quantum mechanical systems that are out of equilibrium, with a particular focus on "quantum chaos". In everyday life chaos is usually defined as a mess, or more accurately, as a lack of any order. In classical physics, chaos is mathematically defined through very strong sensitivity of a particle's trajectory to slight perturbations. This sensitivity is behind many phenomena surrounding us, from unstable weather patterns to the emergence of equilibrium statistical physics, with the most fundamental example being the second law of thermodynamics. In quantum systems, on the other hand, particles do not have well defined trajectories, since their positions and velocities cannot be defined at the same time due to the uncertainty principle. Accordingly, defining and understanding chaos in the microscopic world in a quantum mechanical language becomes more subtle and has been a subject of active debate in the last four decades. This project explores new ways of defining quantum chaos through sensitivity of quantum states to small perturbations. Through this language it aims to establish direct connections between quantum and classical chaos and explore how it emerges as we increase the number of particles in the system. Another focus of the project is finding ways of suppressing chaos in interacting quantum systems by active dynamical control, which should lead to developing efficient computational and energy transfer schemes. These schemes, in turn, can be used in future technologies to develop fast and efficient quantum computers, quantum simulators, and quantum heat engines or refrigerators. This award also supports educational and outreach activities which involve training students at both graduate and undergraduate levels in topics at the forefront of condensed matter and statistical physics, delivering public talks and lectures, and developing a new book on quantum mechanics, which covers modern advances in the field that are not typically found in standard textbooks.TECHNICAL SUMMARYThis award supports research aimed at developing new theoretical approaches for understanding non-equilibrium interacting systems and on applying these approaches to existing and future experimental setups. The research has three main thrusts: (1) The first theme of the project focuses on a method recently developed by the PI, which characterizes quantum chaos through adiabatic deformations expressed through the adiabatic gauge potential. The PI will analyze universal properties of the transition between integrable and chaotic regimes driven by weak integrability breaking perturbations, apply this method to disordered, periodically driven and other systems, and extend it to classical nonlinear systems like the Fermi-Pasta-Ulam-Tsingou problem to analyze emergence of chaos. (2) The second closely related theme of the project focuses on finding approximate local adiabatic gauge potentials, which can be used to identify approximate local conservation laws in nonintegrable systems. The goal is to develop efficient local counter-diabatic and fast-forward protocols that suppress dissipation in interacting systems, which is important for both efficient information and energy processing. This project will aim to design such protocols in driven Floquet systems, finite-temperature systems, and non-linear systems with locally unbounded spectrum. A particular emphasis will be on developing experimentally relevant protocols, which can be realized in different setups like superconducting qubits, cold atoms and trapped ions. (3) The third theme of the project will focus on investigating the connections between quantum and classical chaos by using a formalism recently developed by the PI that shows a correspondence between classical Hamiltonian systems and quantum eigenstates even away from the semi-classical limit.This award also supports educational and outreach activities which involve training students at both graduate and undergraduate levels in topics at the forefront of condensed matter and statistical physics, delivering public talks and lectures, and developing a new book on quantum mechanics, which covers modern advances in the field that are not typically found in standard textbooks.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.