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

RUI：单极子、时空和材料中的量子和热涨落

• 批准号: 2209582
• 负责人: Noah Graham
• 金额: $ 13.5万
• 依托单位: Middlebury College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-08-01 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2209582&HistoricalAwards=false
• 关键词: RUI; Quantum; Thermal; Fluctuations; Monopoles

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.

这个RUI奖资助了Middlebury College的Noah Graham教授的研究活动。无论我们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，我们都通过波的反射来了解世界。 通常，这些波是由特定的源产生的，比如灯泡或声纳。 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，这些波动根据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，这些波动会产生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”结构到波无法逃逸的黑洞，再到从平面不对称反射光的非互易材料-反过来又会引起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，并预测所产生的力和其他相关属性，如传热率。 随着微机械设备向越来越小的尺度发展，这些计算可以为它们的设计提供可能的特征以及潜在的陷阱。 该项目还将产生广泛的影响。 由于散射理论在物理和工程的许多领域中起着基础性的作用，该项目将为本科暑期学生提供宝贵的机会，通过计算和数学研究建立基本技能。此外，通过教育和推广，该项目的影响将超出直接参与的学生，扩大到更广泛的部门，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培养下一代科学家和工程师的核心科学和技术能力来促进国家的关键优先事项，更具体地说，这项工作将侧重于计算拓扑孤子、史瓦西黑洞等弯曲时空背景、以及前向和反向散射振幅不相等的非互易材料。 在每一种情况下，由规范对称性和离散对称性破缺引起的微妙之处，如宇称和时间反演，都可能导致计算及其唯象预言中的不寻常特征。 这些结果可以根据真实的和复数波数的散射振幅进行最有效的分析，通过该方法，量子场论问题可以被分解为基于量子力学、电磁学和统计力学的更熟悉的部分。 因此，这种方法为本科暑期研究生提供了有意义的贡献，他们同时将学习散射理论，波动力学，该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响进行评估来支持审查标准。

项目成果

Quantum energies of BPS vortices in D=2+1 and D=3+1

D=2 1 和 D=3 1 中 BPS 涡旋的量子能量

• DOI: 10.1103/physrevd.106.076013
• 发表时间: 2022
• 期刊: Physical Review D
• 影响因子: 5
• 作者: Graham, N.;Weigel, H.
• 通讯作者: Weigel, H.