RUI: Casimir Forces From Scattering Theory

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。 微机电设备--可以嵌入集成电路芯片的微型机器--可以在碰撞时触发汽车安全气囊，检测视频游戏控制器的移动或智能手机的方向，感知汽车轮胎中的低气压，并提供稳定汽车悬架和飞行无人机所需的反馈。 随着这些设备的尺寸缩小到一微米或更小，一种称为卡西米尔力的特殊量子力学力将开始在其设计和功能中发挥重要作用。 与我们更熟悉的电荷之间的吸引力和排斥力不同，卡西米尔力来自海森堡测不准原理中固有的量子力学波动。 虽然卡西米尔力背后的物理机制已经被很好地理解了很多年，但直到最近，精确的计算才能用于最基本的例子。 新的技术，其中卡西米尔力表示的信息反射的光从每个单独的物体上的力的作用，极大地扩大了潜在的应用范围。 这项资助支持的研究将制定和实施这种散射数据的数值计算，使其有可能在与实验物理和纳米技术相关的广泛系统中计算卡西米尔力。这些通用计算工具也将适用于科学和工程中的其他问题。 因此，这一领域的研究通过促进具有许多潜在技术影响的科学进步来增进国家利益。 因为这种方法是围绕量子力学和电磁学的基本概念，它将有可能为本科生作出有意义的贡献，这项研究的同时，他们建立科学和计算技能，将服务于他们很好地在研究生或专业工作，在物理学中以及在科学和工程的广泛领域中。解决这个问题的技术方法将基于可变相位方法，这是本研究计划首次将其应用于电磁散射。 高性能并行计算将使其能够超越具有高度对称性的对象，以计算多通道散射中的完整T矩阵，用于具有位置和频率依赖性介电响应的材料。 这些工具，然后将被应用到计算卡西米尔力的情况下，目前的实验兴趣，如介质光栅深波纹，现有的技术的基础上的瑞利展开是不够的。

This award funds the research activities of Professor Noah Graham at Middlebury College. Microelectromechanical devices --- tiny machines that can be embedded within an integrated circuit chip --- can trigger car airbags in a collision, detect the movement of a video-game controller or the orientation of a smartphone, sense low air pressure in a car tire, and provide the feedback necessary to stabilize car suspensions and flying drones. As these devices shrink toward sizes of a micron or smaller, a special quantum-mechanical force called the Casimir force will begin to play an important role in their design and function. In contrast to the more familiar electric attraction and repulsion between opposite and like charges, the Casimir force arises from quantum-mechanical fluctuations inherent in Heisenberg's Uncertainty Principle. While the physical mechanism underlying the Casimir force has been well understood for many years, until recently precise calculations were only possible for the most elementary examples. New techniques, in which the Casimir force is expressed in terms of information about the reflection of light from each individual object on which the force is acting, have greatly expanded the range of potential applications. The research supported by this grant will formulate and implement numerical calculations of this scattering data, making it possible to calculate Casimir forces in a broad range of systems relevant to experimental physics and nanotechnology. These general-purpose computational tools will also be applicable to other problems in science and engineering. Research in this area thus advances the national interest by promoting the progress of science with many potential technological implications. And because this approach is centered around fundamental concepts in quantum mechanics and electromagnetism, it will be possible for undergraduate students to make meaningful contributions to this research at the same time as they build scientific and computational skills that will serve them well in graduate or professional work, both within physics and across a wide range of fields in science and engineering.The technical approach to this problem will be based on the variable phase method, which this research program is applying for the first time to electromagnetic scattering. High-performance parallel computation will make it possible to go beyond objects with a high degree of symmetry to calculate full T-matrices in multichannel scattering, for materials with position- and frequency-dependent dielectric response. These tools will then be applied to calculations of Casimir forces in cases of current experimental interest, such as dielectric gratings with deep corrugations, for which existing techniques based on the Rayleigh expansion are insufficient.