Braid description of collective fluctuations in a few-body system

A few-body system of magnetic holes is studied both experimentally and numerically. Notions from braid theory are used to describe the motion in a very compact manner. The time history of n magnetic holes moving in a plane is represented by an n-strand braid, and the fluctuations of the signed crossing number is investigated. A wide range of dynamical behavior is observed. For certain parameter values the fluctuations are highly intermittent, and there is a hierarchical ordering of the dynamics in both space and time. In this case the motion is well modeled by a one-dimensional Lévy walk.