RUI: Path Integrals and Charged Particle Dynamics

原子碰撞是探测原子和分子结构以及理解带电粒子与物质相互作用的动力学的一种行之有效的方法。由于它们的量子力学性质，参与碰撞的粒子必须被建模为物质波，而不是单个的点粒子。在过去的十年里，具有独特波形的粒子已经被创造出来。这些新的物质波形（称为涡旋波或扭曲粒子）的特性为纳米颗粒的控制和旋转提供了机会，提高了电子显微镜的分辨率，以及研究基本的原子性质，如磁矩和原子跃迁。目前，人们对扭曲粒子如何与单个原子或分子相互作用的理解非常有限。为了实现所提出的应用，有必要在最基本的水平上建立描述粒子与原子相互作用的理论模型。研究人员将开发和应用理论模型来描述扭曲粒子和原子之间碰撞的物理现象，以解释最近观察到的量子现象，并为未来的实验和应用提供指导。除了科学之外，该项目的另一个关键方面是将本科生纳入前沿研究和下一代物理学家的培训。通过模型的概念开发、实施和分析，学生将获得宝贵的实践研究经验。学生们还将在地区和国家会议上展示他们的成果，让他们对科学研究有更全面的认识，并鼓励他们在STEM领域从事职业。该项目的目标将通过开发两个不同的计算模型来实现。所有的模型都将被设计用于高性能计算机，并将并行化以提高效率。其中一个模型是基于时间相关路径积分量子轨迹（PIQTr）方法，该方法利用拉格朗日方法来研究量子力学。该模型将应用于电子捕获、相干、衍射、隧穿和量子反射等现象。将PIQTr模型应用于高维系统将需要实现数值技术，如自适应步长、蒙特卡罗积分和边界匹配技术。PIQTr模型的结果将提供碰撞过程的时间依赖分析，使研究人员能够观察相互作用的演变。第二个模型将用于研究电子涡旋束与原子的碰撞。这个模型将提供洞察轨道角动量转移，以及在碰撞过程中可能发生的方向和旋转效应。碰撞跃迁幅度的多极扩展将产生关于潜在选择规则或状态选择性可能性的信息。电子涡旋束研究的结果将以碰撞截面的形式呈现出来，可以用来指导实验工作者和其他对电子涡旋束应用感兴趣的人。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。

Atomic collisions are a well-established method for probing the structure of atoms and molecules, as well as understanding the dynamics of how charged particles interact with matter. Due to their quantum mechanical nature, the particles involved in the collision must be modeled as matter waves, not as individual point particles. In the last decade, particles with unique waveforms have been created. These new matter waveforms (known as vortex waves or twisted particles) have properties that offer the opportunity for control and rotation of nanoparticles and improved resolution in electron microscopy, as well as the study of fundamental atomic properties, such as the magnetic moment and atomic transitions. Currently, there is a very limited understanding of how twisted particles interact with individual atoms or molecules. In order to realize the proposed applications, it is necessary to develop theoretical models that describe the particles' interaction with atoms at the most basic level. The researchers will develop and apply theoretical models to describe the physics of collisions between twisted particles and atoms in order to explain recently observed quantum phenomena and provide guidance for future experiments and applications. In addition to the science, another key aspect of the project is the inclusion of undergraduate students in cutting-edge research and the training of the next generation of physicists. Participation in this project provides students with valuable hands-on research experience through conceptual development of the models, as well as implementation and analysis. The students will also present their results at regional and national conferences, giving them a more global view of scientific research and encouraging them to pursue careers in STEM fields.The goals of the project will be accomplished through the development of two distinct computational models. All of the models will be designed for use on high performance computers and will be parallelized to improve efficiency. One of the models is based on the time-dependent Path Integral Quantum Trajectory (PIQTr) method that utilizes a Lagrangian approach to quantum mechanics. This model will be applied to phenomena such as electron capture, coherence, diffraction, tunneling, and quantum reflection. Application of the PIQTr model to higher dimensional systems will require the implementation of numerical techniques, such as adaptive stepsize, Monte Carlo integration, and boundary matching techniques. The results of the PIQTr model will provide a time-dependent analysis of collision processes allowing researchers to view the evolution of the interaction. A second model will be developed for the study of electron vortex beam collisions with atoms. This model will provide insight into orbital angular momentum transfer, as well as orientation and rotation effects that may occur during the collision process. A multipole expansion of the collision transition amplitude will yield information regarding potential selection rules or the possibility of state selectivity. The results of the electron vortex beam studies will be in the form of collision cross sections that can be used to provide guidance to experimentalists and others interested in applications of electron vortex beams.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.