RUI: Scattering Theory Casimir Methods and Coherent Structures in the Early Universe

该奖项资助米德尔伯里学院的诺亚·格雷厄姆教授的研究活动。 这项工作是围绕两个不同的，但相关的，调查线组织。第一个研究方向集中在卡西米尔力，这是从量子力学波动的电荷和字段。 虽然卡西米尔力在我们的日常经验中可以忽略不计，但在小距离上-特别是在与下一代微机电设备相关的距离尺度上-它们可能变得重要。 最近的进展已经建立了一个系统的框架，计算这些力量在广泛的情况下，有关纳米技术。 在这种方法中，人们通过将卡西米尔力与光的反射和散射相关的基本量相关联来计算卡西米尔力。 这项工作将创造新的技术来计算必要的反射和散射数据，然后将结果应用到广泛的卡西米尔力计算。 用于分析光反射和散射的方法非常普遍，因此可能适用于物理和工程中的广泛问题。 第二个研究方向的重点是在宇宙膨胀和大爆炸之后的早期宇宙“再加热”时期，介子所起的作用-场论模型中出现的非线性运动方程的极长寿命、局部化、振荡解。 大规模的数值模拟将在理解混沌热背景中产生的光子的自组织行为方面发挥关键作用，这两条研究路线将在其他科学和工程领域以及学生的教育和培训方面产生更广泛的影响。 Casimir项目将开发具有广泛潜在应用的新计算技术，而Quatron项目将推动高性能并行计算的当前边界。 通过两个夏季研究项目和本研究的各个方面融入到米德尔伯里学院的本科课程，这两个项目也将为学生提供重要的新机会，学习基础物理和广泛适用的分析和计算技能。

This award funds the research activities of Professor Noah Graham at Middlebury College. The work is organized around two distinct, though related, lines of inquiry.The first research direction focuses on Casimir forces, which arise from quantum-mechanical fluctuations of charges and fields. While Casimir forces are negligible in our everyday experience, at small distances -- in particular, at distance scales relevant to the next generation of microelectromechanical devices -- they can become important. Recent progress has established a systematic framework for calculating these forces in a wide range of situations relevant to nanotechnology. In this approach, one calculates the Casimir force by relating it to fundamental quantities associated with the reflection and scattering of light. This work will create new techniques for computing the necessary reflection and scattering data, and then will apply the results to a wide range of Casimir force calculations. The methods to be used to analyze light reflection and scattering are very general, and thus potentially applicable to a wide range of problems in physics and engineering. The second research direction focuses on the role played by oscillons -- extremely long-lived, localized, oscillatory solutions to the nonlinear equations of motion that arise in field theory models -- during the "reheating" epoch of the early universe, following cosmic inflation and the Big Bang. Here large-scale numerical simulation will play a key role in understanding the self-organizing behavior through which oscillons emerge from a chaotic thermal background.Both of these lines of research will have significant broader impacts in other fields of science and engineering, and in education and training of students. The Casimir project will develop new computational techniques with a wide range of potential applications, while the oscillon project will push the current boundaries of high-performance parallel computing. Through both summer research projects and integration of aspects of this research into the undergraduate curriculum at Middlebury College, both projects will also offer significant new opportunities for students to learn both fundamental physics and broadly applicable analytic and computational skills.