Application of braid statistics to particle dynamics

How, in a simple and forceful way, do we characterize the dynamics of systems with several moving components? The methods based on the theory of braids may provide the answer. Knot and braid theory is a subfield of mathematics known as topology. It involves classifying different ways of tracing curves in space. Knot theory originated more than a century ago and is today a very active area of mathematics. Recently, we have been able to use notions from braid theory to map the complicated trajectories of tiny magnetic beads confined between two plates and subjected to complex magnetic fields. The essentially two-dimensional motion of a bead can be represented as a curve in a three-dimensional space–time diagram, and so several beads in motion produce a set of braided curves. The topological description of these braids thus provides a simple and concise language for describing the dynamics of the system, as if the beads perform a complicated dance as they move about one another, and the braid encodes the choreography of this dance.