Quantum Dynamics of Near-One-Dimensional Systems

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，例如，它对于理解当许多量子比特耦合在一起创建和扩大量子计算机时会发生什么，以及开发与用于描述经典流体的有效流体动力学描述相同的有效流体动力学描述，都具有重要意义。后一种描述被广泛应用于航空、水文学和地球物理学中，它们的量子对应物有望在量子技术中发挥类似的重要作用。量子系统的几何形状和粒子之间相互作用的类型在量子动力学的结果中扮演着中心角色。近年来特别令人感兴趣的情况是，粒子被冷却到超低温(纳米开尔文)，并被困住，使其运动被限制在一条线上(一维)。这个项目的目标有两个，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。该奖项将支持对量子物理和计算物理研究生的培训。一些最重要的理论-实验发现将包括在国际和平研究所正在合著的一本量子力学研究生书籍中。PI将继续努力招募来自代表性不足群体的研究生进入宾夕法尼亚州立大学的物理学研究生项目，并将继续努力鼓励这些群体的成员追求物理学职业生涯。在理论和实验合作的背景下，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很短的时间内发生的普遍过程，例如流体动力化(也发生在粒子加速器中的重离子碰撞中)，以及在很大程度上依赖于系统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力学方法来研究禁闭势突然变化后动力学中偶极相互作用的影响。对于后者的研究，Pi和他的团队将考虑具有排斥接触相互作用的热力学稳定态和具有吸引接触相互作用的亚稳态。所有先前研究的中心将是使用快度和动量分布来表征远离平衡态。除了几乎可积的一维系统外，Pi和他的团队将使用典型的保真极化率和谱函数来研究2D晶格系统中量子混沌的开始。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动力学的特性。后面的研究将描述量子混沌区域(在可积性下)的纠缠熵和本征态热化(不存在)。对于量子动力学，目标是了解SU(2)对称性被微弱破坏时的预热化，以及指数级小的希尔伯特空间部门中有支持的特殊工程初始态的远离平衡的动力学。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。

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.