RUI: Quantum and Thermal Fluctuations in Monopoles, Spacetime, and Materials

这个Rui奖资助了米德尔伯里学院诺亚·格雷厄姆教授的研究活动。无论是进行物理实验，还是在日常生活中使用我们的眼睛和耳朵，我们都通过海浪的反射来了解世界。通常，这些波是由特定的源产生的，例如灯泡或声纳脉冲。然而，即使在没有源的情况下，量子力学和热效应也会自发地产生波动，根据相同的波散射规则传播和反射。在与纳米技术相关的短距离尺度上，这些波动产生了被称为卡西米尔效应的力和相互作用。具有不寻常性质的材料和结构-从不能解开的扭曲构型，到波不能逃逸的黑洞，再到从平面不对称反射光线的非互易材料-可以反过来产生相应的不寻常的卡西米尔效应。这个项目将开发数学和计算工具来分析这样的系统，并预测所产生的力和其他相关的性质，如热传输率。随着微机械设备向越来越小的规模发展，这些计算可以为其设计提供可能的特征和潜在的陷阱。该项目还将产生重大的更广泛的影响。由于散射理论在许多物理和工程领域发挥着基础性的作用，这个项目将为本科生暑期学生提供宝贵的机会，通过计算和数学研究来培养基本技能。此外，通过教育和外展，该项目的影响将从直接参与的学生扩展到更广泛的系、学院和当地社区。因此，该项目将通过推进基础和应用技术研究以及建设下一代科学家和工程师的核心科学和技术能力来促进关键的国家优先事项。更具体地说，这项工作将专注于计算涉及拓扑孤子、弯曲时空背景(如施瓦希尔德黑洞)和非互易材料(正向和反向散射幅度不相等)引起的量子和热涨落。在每一种情况下，规范对称性和离散对称性的破坏所产生的微妙之处，如宇称和时间反转，可能导致计算及其唯象预测中的不寻常特征。根据实波数和复波数的散射幅度，可以最有效地分析这些结果，通过这些幅度，可以将量子场论问题分解为基于量子力学、电磁学和统计力学的更熟悉的组成部分。因此，这种方法为本科生暑期研究提供了重要的机会，让他们做出有意义的贡献，同时他们将通过具体的计算和数值模拟学习广泛适用的散射理论、波力学和计算物理技术。该奖项反映了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。

This RUI award funds the research activities of Professor Noah Graham at Middlebury College.Whether we are carrying out a physics experiment or using our eyes and ears in everyday life, we learn about the world through the reflection of waves. Ordinarily, these waves are created by a specific source, such as a light bulb or a sonar ping. However, even in the absence of a source, quantum-mechanical and thermal effects will spontaneously generate fluctuations that propagate and reflect according to the same rules of wave scattering. At the short distance scales relevant to nanotechnology, these fluctuations give rise to forces and interactions known as Casimir effects. Materials and structures with unusual properties --- which can range from "twisted" configurations that cannot unwind, to black holes from which waves cannot escape, to nonreciprocal materials that reflect light asymmetrically from a flat surface --- can in turn give rise to correspondingly unusual Casimir effects. This project will develop mathematical and computational tools to analyze such systems and predict the resulting forces and other associated properties, such as the rate of heat transfer. As micromechanical devices move to smaller and smaller scales, these calculations can inform possible features, as well as potential pitfalls, of their design. This project will also have significant broader impacts. Because scattering theory plays a fundamental role in many areas of physics and engineering, this project will provide valuable opportunities for undergraduate summer students to build essential skills through computational and mathematical research. Moreover, through education and outreach, the impact of this project will extend beyond the students directly involved to the broader department, college, and local community as well. This project will thus promote key national priorities, both by advancing fundamental and applied technological research and by building the core scientific and technical capabilities of the next generation of scientists and engineers.More specifically, this work will focus on calculations involving quantum and thermal fluctuations due to topological solitons, curved spacetime backgrounds such as the Schwarzschild black hole, and nonreciprocal materials for which the amplitudes for forward and reverse scattering are unequal. In each of these cases, subtleties arising from gauge symmetry and breaking of discrete symmetries, such as parity and time reversal, can lead to unusual features in the calculation and its phenomenological predictions. These consequences are most effectively analyzed in terms of scattering amplitudes for both real and complex wave number, through which the quantum field theory problem can be broken down into more familiar components based in quantum mechanics, electromagnetism, and statistical mechanics. As a result, this approach offers significant opportunities for meaningful contributions by undergraduate summer research students, who at the same time will learn broadly applicable techniques of scattering theory, wave mechanics, and computational physics through concrete calculations and numerical simulations.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.