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

该RUI奖资助明德学院Noah Graham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眼睛和耳朵，我们都是通过波的反射来了解世界的。通常，这些波是由一个特定的来源产生的，比如灯泡或声纳ping。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，这些波动按照波散射的相同规则传播和反射。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——从无法展开的“扭曲”结构，到波无法逃脱的黑洞，再到从平面不对称地反射光的非互易材料——反过来会产生相应的不寻常的卡西米尔效应。该项目将开发数学和计算工具来分析这些系统，并预测产生的力和其他相关特性，如传热速率。随着微机械设备向越来越小的尺度移动，这些计算可以告知其设计的可能特征以及潜在缺陷。该项目还将产生更广泛的重大影响。由于散射理论在物理和工程的许多领域起着重要的作用，这个项目将为本科生提供宝贵的机会，通过计算和数学研究来建立基本的技能。此外，通过教育和推广，这个项目的影响将超越直接参与的学生，扩展到更广泛的部门、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立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，这项工作将集中在涉及量子和热波动的计算上，这些波动是由拓扑孤子、弯曲时空背景（如史瓦西黑洞）以及正向和反向散射振幅不相等的非互易材料引起的。在每一种情况下，规范对称性和离散对称性的破坏（如宇称和时间反转）引起的微妙之处都可能导致计算及其现象学预测中的不寻常特征。这些结果在实波数和复波数的散射振幅方面得到了最有效的分析，通过这些结果，量子场论问题可以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，他们同时将通过具体计算和数值模拟学习散射理论、波动力学和计算物理等广泛适用的技术。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。

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.