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

这个奖项是根据2009年美国复苏和再投资法案(公法111-5)资助的。在许多情况下，人们可以通过考虑这一理论来取得重大进展。令人不安的是，从一组独立传播的波开始。这个研究项目将解决两种情况，在这两种情况下，这种微扰方法从根本上失败。当人们考虑波形成不分散的相干团块的可能性时，第一种情况就出现了。虽然这类静态物体已经得到了很好的研究，但对于经历规则振荡的溶液，即所谓的振子或呼吸子，人们所知的要少得多。这类天体在早期宇宙中尤其令人感兴趣，因为形成它们所需的巨大能量是可用的。这个项目将研究粒子物理模型中振荡的存在，它们在早期宇宙中形成的速度，以及它们在产生重力子发生所需的非平衡条件方面可能发挥的作用，重力子产生的过程是普通物质在早期宇宙中形成的过程。第二种情况是当人们考虑到不能用弱耦合近似的量子力学效应时。这个项目将集中在导体或强电介质中由量子电磁涨落引起的卡西米尔力，以及它们在相关理论中的类似情况。在这种情况下，Casimir力取决于物体的几何和取向的相干性质，并且与人们通过微扰获得的结果定性地不同。最近发展起来的技术使计算一系列新几何形状和新材料的卡西米尔力成为可能。这些技术将被用来研究卡西米尔力的形状、方向和材料依赖性，并制定和尝试证明支配它们行为的普遍定理。类似的技术也将被用来研究粒子物理标准模型中电弱弦溶液的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物理学、应用物理学和非线性动力学的广泛其他分支，以及在这项工作过程中开发的计算工具。这些工具的源代码将公开，供其他研究人员使用。这项研究计划还将通过直接参与的本科生和将从这项工作中成长起来的课程的增强，对米德尔伯里学院的物理教学产生重大影响。参与其中任何一个方面的学生都将有机会发展计算物理和非线性动力学方面的新技能，并利用这些技能更好地理解物理学的基本概念。

"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.