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.

这项RUI奖为米德尔伯里学院（Middlebury College）教授诺亚·格雷厄姆（Noah Graham）教授的研究活动提供了资金。无论是进行物理实验还是在日常生活中使用眼睛和耳朵，我们都会通过波浪的反思来了解世界。 通常，这些波是由特定来源（例如灯泡或声纳ping）创建的。 但是，即使没有来源，量子力学和热效应也会自发地产生波动，从而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，这些波动产生了称为Casimir效应的力和相互作用。 具有异常特性的材料和结构 - 从不能放松的“扭曲”配置范围，到波浪无法逃脱的黑洞，到从平坦表面不对称反射光的非注射材料 - 又会引起相应的不寻常的casimir效应。 该项目将开发数学和计算工具来分析此类系统并预测所得的力和其他相关特性，例如传热速率。 随着微机械设备转移到越来越小的尺度时，这些计算可以为其设计提供可能的特征以及潜在的陷阱。 该项目还将产生更广泛的影响。 由于散射理论在物理和工程领域的许多领域都起着基本作用，因此该项目将为夏季学生通过计算和数学研究提供重要的机会来建立基本技能。此外，通过教育和宣传，该项目的影响将超出直接参与更广泛系，学院和当地社区的学生。 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散射不平等。 在每种情况下，由衡量对称性和破坏诸如平价和时间逆转之类的离散对称性产生的微妙之处可能会导致计算及其现象学预测的异常特征。 这些后果是根据真实和复杂波数的散射幅度来分析的，量子场理论问题可以通过量子力学，电磁学和统计力学分解为更熟悉的组件。 结果，这种方法为夏季研究生提供了重要的有意义的贡献机会，与此同时，他们将通过具体的计算和数值模拟来学习广泛适用的散射理论，波浪力学和计算物理学技术。这项奖项反映了NSF的法定任务，并通过评估智力的MERIT和BRADIT和BRADIT和BRADIT和BRADIT和BRADIT和BRADIT和BRADIT和BRADIT和BRADIT和BRADIT和BRADIT和BRADIT和广泛的影响。

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.