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

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"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.