RUI: Quantum and Thermal Fluctuations in Monopoles, Spacetime, and Materials

Middlebury College, Middlebury VT

Investigators

Abstract

This RUI award funds the research activities of Professor Noah Graham at Middlebury College. Whether we are carrying out a physics experiment or using our eyes and ears in everyday life, we learn about the world through the reflection of waves. Ordinarily, these waves are created by a specific source, such as a light bulb or a sonar ping. However, even in the absence of a source, quantum-mechanical and thermal effects will spontaneously generate fluctuations that propagate and reflect according to the same rules of wave scattering. At the short distance scales relevant to nanotechnology, these fluctuations give rise to forces and interactions known as Casimir effects. Materials and structures with unusual properties --- which can range from "twisted" configurations that cannot unwind, to black holes from which waves cannot escape, to nonreciprocal materials that reflect light asymmetrically from a flat surface --- can in turn give rise to correspondingly unusual Casimir effects. This project will develop mathematical and computational tools to analyze such systems and predict the resulting forces and other associated properties, such as the rate of heat transfer. As micromechanical devices move to smaller and smaller scales, these calculations can inform possible features, as well as potential pitfalls, of their design. This project will also have significant broader impacts. Because scattering theory plays a fundamental role in many areas of physics and engineering, this project will provide valuable opportunities for undergraduate summer students to build essential skills through computational and mathematical research. Moreover, through education and outreach, the impact of this project will extend beyond the students directly involved to the broader department, college, and local community as well. This project will thus promote key national priorities, both by advancing fundamental and applied technological research and by building the core scientific and technical capabilities of the next generation of scientists and engineers. More specifically, this work will focus on calculations involving quantum and thermal fluctuations due to topological solitons, curved spacetime backgrounds such as the Schwarzschild black hole, and nonreciprocal materials for which the amplitudes for forward and reverse scattering are unequal. In each of these cases, subtleties arising from gauge symmetry and breaking of discrete symmetries, such as parity and time reversal, can lead to unusual features in the calculation and its phenomenological predictions. These consequences are most effectively analyzed in terms of scattering amplitudes for both real and complex wave number, through which the quantum field theory problem can be broken down into more familiar components based in quantum mechanics, electromagnetism, and statistical mechanics. As a result, this approach offers significant opportunities for meaningful contributions by undergraduate summer research students, who at the same time will learn broadly applicable techniques of scattering theory, wave mechanics, and computational physics through concrete calculations and numerical simulations. 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.