RUI: Oscillons and Casimir Forces in Classical and Quantum Field Theory

RUI：经典和量子场论中的振荡和卡西米尔力

• 批准号: 0855426
• 负责人: Noah Graham
• 金额: $ 12万
• 依托单位: Middlebury College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0855426&HistoricalAwards=false
• 关键词: RUI; Oscillons; Casimir; Forces; Classical

"This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5)."Field theories provide our best known description of the fundamental interactions of Nature. In many situations, one can make significant progress by considering the theory. Perturbatively, starting from a collection of waves propagating independently.This research project will address two situations in which this perturbative approach fails in a fundamental way. The first situation arises when one considers the possibility of waves forming coherent lumps that do not disperse. While static objects of this kind have been well studied, much less is known about solutions that undergo regular oscillations, called oscillons or breathers. Such objects are especially of interest in the early universe, when the large energies needed to form them are available. This project will investigate the existence of oscillons in particle physics models, the rate at which they would have formed in the early universe, and the potential role they could play in generating the out-of-equilibrium conditions necessary for baryogenesis, the process by which ordinary matter formed in the early universe.The second situation arises when one considers quantum mechanical effects that cannot be approximated by weak coupling. This project will focus on Casimir forces induced by quantum electromagnetic fluctuations in conductors or strong dielectrics, and their analogs in related theories. In such situations the Casimir force depends on coherent properties of the geometry and orientation of the objects, and differs qualitatively from the result one would obtain perturbatively. Recently developed techniques have made it possible to calculate Casimir forces for a broad set of new geometries and materials. These techniques will be used to study shape, orientation, and material dependence of Casimir forces and to formulate and attempt to prove universal theorems governing their behavior. Similar techniques will also be used to study Casimir energies of electroweak string solutions in the Standard Model of particle physics. The broader impacts are as follows: The techniques and results of this research are potentially applicable to a wide range of other branches of physics, applied physics, and nonlinear dynamics, as are the computational tools to be developed during the course of this work. The source code for these tools will be made publicly available for use by other researchers. This research program will also significantly impact the teaching of physics at Middlebury College, both through the undergraduates directly involved and through enhancements to the curriculum that will grow out of this work. Students participating in any of these aspects will have the opportunity to develop new skills in computational physics and nonlinear dynamics, and to use these skills to better understand fundamental concepts in physics.

“该奖项是根据2009年《美国复苏与再投资法》（公法111-5）资助的。”现场理论提供了我们对自然基本互动的最著名描述。在许多情况下，人们可以通过考虑该理论来取得重大进展。 扰动，从独立传播的波浪集开始。该研究项目将解决这种扰动方法以基本方式失败的两种情况。当人们认为波浪形成不分散的连贯肿块的可能性时，就会出现第一种情况。尽管对这种静态对象进行了充分的研究，但对经过常规振荡的解决方案（称为oscillons或呼吸器）的了解却少得多。 当可以使用大量能量时，这些物体在早期的宇宙中尤其引起人们的关注。该项目将调查粒子物理模型中oscillons的存在，它们在早期宇宙中形成的速率以及它们在产生重生生成所需的平衡状况中所起的潜在作用，而在早期宇宙中形成的普通物质在第二种情况下形成的过程。当一种情况下，当一种一种一种一种一种一种无法通过弱化的量子效应而产生的量子机械效应时会产生。该项目将重点放在导体或强介电上量子电磁波动引起的Casimir力以及相关理论中的类似物。在这种情况下，Casimir力取决于对象的几何形状和方向的相干性能，并且与结果的质量不同。最近开发的技术使计算Casimir力量为一系列新的几何和材料进行计算。这些技术将用于研究卡西米尔力量的形状，取向和物质依赖性，并制定和试图证明其行为的普遍定理。类似的技术也将用于研究粒子物理标准模型中电子弦弦溶液的Casimir能量。更广泛的影响如下：这项研究的技术和结果可能适用于广泛的其他物理，应用物理和非线性动力学，以及在这项工作过程中要开发的计算工具。这些工具的源代码将被其他研究人员公开使用。这项研究计划还将通过直接参与的本科生以及对将从这项工作中发展出来的课程的增强来重大影响米德尔伯里学院的物理教学。参与任何这些方面的学生将有机会发展计算物理和非线性动态方面的新技能，并使用这些技能更好地了解物理学的基本概念。