Interferometer Networks

My work has been to generalize complex network theory further, giving it the ability to describe complex networks with interference. I did this by working with complex networks whose edges have complex-number weights and solving the systems of equations those networks describe. This has proven to be a useful notation for describing interferometers, and I have used it to rederive the Michelson interferometer and the Sagnac Effect. To work with interferometer networks, I had to generalize the concepts of degree, clustering, and path length. Using these tools, I have analyzed complex generalizations of random networks, Watts-Strogatz networks, and the Kuramoto Model. Random networks have average complex network measures near zero and always converge to a stable solution when a system of equations was solved on their complex adjacency matrix. Watts-Strogatz networks and Complex Kuramoto models have network measures that depend on their input parameters, and certain choices create systems with no stable solution, which perpetually oscillate when solved numerically. More investigation is needed to determine how those complex network measures relate to instability, and what kind of network structure is necessary to create this instability.