Grant: Subatomic Physics Envelope - Individual

The research involved falls into three related fields of interest. The first is systems in which quantum effects are important. Quantum theory has proven difficult to interpret, with properties such as "being in two places at once" being quite unintuitive. There has been experimental work recently though on systems, usually at low temperatures, for which quantum effects are pronounced. We will study examples of such systems, such as Bose-Einstein condensation, using finite temperature field theory in order to understand better the origin of their quantum properties. Attention will be paid to systems near a critical point, in which a sharp cross-over from one type of behavior to another occurs. The second area involves quantum computers and quantum information. During the development of quantum theory it was realized that a computer built on the principles of quantum mechanics could have a significant speed advantage over a classical computer, with recent experimental prototypes suggesting this is indeed the case. We shall examine models of algorithms used in quantum computation with a view towards understanding better which quantum effects are most responsible for the observed speed-up in the computations. The final topic is systems in which non-linear effects are important. There are two properties of interest here: chaos (long-term unpredictability) and fractalness (self-similarity at different length scales). Such effects arise in many contexts, such as fluid flow, diffusion, chemical reactions, and biological processes. We shall examine a class of models of epidemic growth in a population, with attention paid to incorporating local interactions by analyzing such models on discrete networks. Due to the general nature, many of the tools of quantum theory, especially of systems near a critical point, will be of use.