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

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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.