RUI: Scattering Approach to Quantum Fluctuations: Casimir Forces, Curved Spacetime, and Solitons

Middlebury College, Middlebury VT

Investigators

Abstract

This RUI award funds the research activities of Professor Noah Graham at Middlebury College in Middlebury, Vermont. We learn about our world via the reflection, transmission, and absorption of waves, from the light scattered by a blue sky to the rumble of seismic waves through the earth. As a result, the mathematical and computational tools for analyzing wave scattering play an essential role in our scientific and technological infrastructure. This research will develop and extend techniques of scattering theory and apply them both to answer questions about fundamental laws of physics and to analyze and design experiments studying microelectromechanical systems in nanotechnology. Because of the fundamental role scattering theory plays across science and engineering, this research is accessible to and provides valuable training for undergraduate students planning careers in a wide range of Science, Technology, Engineering, and Mathematics (STEM) fields. The project will thus promote key national priorities through both advances in fundamental and applied research and in building the core technical capabilities of the next generation of scientists and engineers. Through education and outreach, the impact of this project will extend beyond the students directly involved to the broader college and local community as well. More specifically, this research will develop extensions of the variable phase method in analytic scattering theory and then use these techniques to address subtle questions in quantum field theory. These applications include computations of quantum corrections to the energies and charges of magnetic monopoles in models of particle physics, analysis of the effects of quantum fluctuations in curved spacetime and their consequences for general relativity and quantum gravity, and precise determination of Casimir forces in systems relevant to nanotechnology. Because it reduces problems in quantum field theory to the simpler and more familiar properties of wave scattering, this approach offers significant opportunities for undergraduate students working on this research to build broadly applicable scientific and technical skills, as well as opportunities for pedagogical integration of this research with the physics curriculum. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.