Quantum Dynamics of Near-One-Dimensional Systems

近一维系统的量子动力学

• 批准号: 2309146
• 负责人: Marcos Rigol
• 金额: $ 36万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-01 至 2026-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2309146&HistoricalAwards=false
• 关键词: Quantum; Dynamics; Near; Dimensional; Systems

Understanding the behavior of many interacting particles whose dynamics is dictated by quantum rather than classical physics is a current frontier in science. In addition to its fundamental appeal, it is, for example, of relevance to understanding what happens when many qubits are coupled together to create and scale up quantum computers, as well as for the development of effective hydrodynamics descriptions equivalent to those used to describe classical fluids. The latter descriptions are used in a wide range of applications, e.g., in aeronautics, hydrology, and geophysics, and their quantum counterparts are expected to play a similarly important role in quantum technologies. Central roles in the outcomes of the quantum dynamics are played by the geometry of the quantum system and by the type of interactions between the particles. Of special interest in recent years has been the case in which the particles are cooled to ultra-low temperatures (nano Kelvins) and trapped in such a way that their motion is restricted to a line (one dimension). The goal of this project is two-fold, on the one hand the PI will develop and use theoretical tools to understand and quantitatively describe experiments in the ultra-low temperature regime, and on the other hand will theoretically study quantum states that can be created in those systems in the presence of different types of interactions and symmetries. This award will support the training of graduate students in quantum physics and computational physics. Some of the most important theory-experiment findings will be included in a graduate quantum mechanics book that the PI is co-writing. The PI will continue his recruiting efforts to attract graduate students from underrepresented groups to the physics graduate program at Penn State, and will continue his efforts to encourage members of those groups to pursue careers in Physics. In the context of theory-experiment collaborations, the PI plans to study the dynamics of near-one-dimensional ultracold gases following Bragg scattering pulses. The main goal of these studies will be to explore universal processes that occur at very short times, such as hydrodynamization (which also occurs in heavy-ion collisions in particle accelerators), and local equilibration processes that depend strongly on the nature and interactions in the system. At longer times, the PI plans to develop and use generalized hydrodynamics approaches to study the effect of dipolar interactions in the dynamics following sudden changes of a confining potential. For the latter studies, the PI and his group will consider thermodynamically stable states with repulsive contact interactions and metastable states with attractive contact interactions. Central to all the previous studies will be the characterization of the far-from-equilibrium states using rapidity and momentum distributions. Beyond near-integrable one dimensional systems, the PI and his group will use typical fidelity susceptibilities and spectral functions to study the onset of quantum chaos in 2D lattice systems. They will also study the properties of eigenstates of integrable and nonintegrable models with SU(2) symmetry, as well as far from equilibrium dynamics in those models. The latter studies will characterize the entanglement entropy and eigenstate thermalization (lack thereof) in the quantum-chaotic regime (at integrability). For the quantum dynamics, the goal is to understand prethermalization when the SU(2) symmetry is weakly broken, and the far-from-equilibrium dynamics of specially engineered initial states with support in exponentially small Hilbert space sectors.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.

理解许多相互作用的粒子的行为，这些粒子的动力学是由量子物理而不是经典物理决定的，这是当前科学的前沿。除了它的基本吸引力之外，它还与理解当许多量子比特耦合在一起以创建和扩大量子计算机时会发生什么有关，以及与用于描述经典流体的有效流体动力学描述的发展相当。后面的描述用于广泛的应用中，在航空学、水文学和地球物理学中，它们的量子对应物预计将在量子技术中发挥同样重要的作用。量子系统的几何结构和粒子之间的相互作用类型在量子动力学的结果中起着核心作用。近年来，特别令人感兴趣的是粒子被冷却到超低温（纳米开尔文）并被捕获，使其运动被限制在一条线（一维）上。该项目的目标是双重的，一方面，PI将开发和使用理论工具来理解和定量描述超低温条件下的实验，另一方面，将从理论上研究在存在不同类型的相互作用和对称性的情况下，可以在这些系统中创建的量子态。该奖项将支持量子物理学和计算物理学研究生的培训。一些最重要的理论实验发现将包含在PI正在共同撰写的研究生量子力学书籍中。PI将继续他的招聘工作，以吸引研究生从代表性不足的群体在宾夕法尼亚州立大学的物理研究生课程，并将继续他的努力，鼓励这些群体的成员追求物理学的职业生涯。在理论实验合作的背景下，PI计划研究布拉格散射脉冲后近一维超冷气体的动力学。这些研究的主要目标将是探索在非常短的时间内发生的普遍过程，例如流体动力学（也发生在粒子加速器中的重离子碰撞中），以及强烈依赖于系统中的性质和相互作用的局部平衡过程。在更长的时间里，PI计划开发和使用广义流体动力学方法来研究偶极相互作用在约束势突然变化后的动力学中的影响。对于后面的研究，PI和他的团队将考虑具有排斥接触相互作用的介稳态和具有吸引接触相互作用的亚稳态。所有以前的研究的中心将是使用快度和动量分布的远离平衡态的特性。除了近可积的一维系统，PI和他的团队将使用典型的保真度和光谱函数来研究二维晶格系统中量子混沌的发生。他们还将研究具有SU（2）对称性的可积和不可积模型的本征态的性质，以及这些模型中远离平衡态的动力学。后面的研究将描述纠缠熵和本征态热化（缺乏）在量子混沌制度（在可积性）。对于量子动力学，目标是理解SU（2）对称性弱破缺时的预热化，以及在指数级小希尔伯特空间扇区中支持的特殊工程初始状态的远离平衡的动力学。该奖项反映了NSF的法定使命，并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，被认为值得支持。