Quantum Hall physics in the 2D electron gas and in rotating Bose condensates

The quantum Hall effect, occurring in a two-dimensional electron gas exposed to a strong magnetic field at low temperatures, is one of the most studied systems in condensed matter physics over the past 20 years. One of the main reasons is that this system displays new and exotic quantum mechanical behaviour. In particular, it exhibits quasiparticle excitations which carry a fractional charge (e.g. 1/3 of the electron charge) and obey fractional statistics -- they are anyons. In recent years it has been re alized that the quantum Hall effect can also occur in another, seemingly very different, system -- rapidly rotating atomic Bose condensates. At present, there is a renewed general interest in fractional statistics, due to reports of the first ever dir ect experimental observation of anyon statistics, as well as a number of proposals to use anyons (in particular so-called non-abelian anyons) in the context of quantum computing. However, a number of important theoretical questions remain on the way to re ach this goal, e.g. concerning the robustness of these particles in realistic experimental settings. The main aim of this project is thus to address these questions and deepen the theoretical understanding of fractional statistics, especially non-abel ian anyons. The main methods to be used are field theory techniques and various trial wave functions.