Douglas Lundholm: Anyons in the average field approximation

Abstract. Quantum systems confined to planar geometries may exhibit effective particles with unusual statistics, called anyons. These can be modeled as identical particles (bosons or fermions) in 2D with magnetic flux attached to them. In this talk I will discuss the validity of the average field approximation for anyons, in which the resulting magnetic field is replaced by that of the mean distribution of the particles. In a certain limit this turns out to be a correct description and the particles then behave like independent, identically distributed bosons interacting via a self-consistent magnetic field. The resulting non-linear energy functional is being studied in joint work with Michele Correggi, Romain Duboscq and Nicolas Rougerie.