ANYON TRAJECTORIES AND THE SYSTEMATICS OF THE 3-ANYON SPECTRUM

We develop the concept of trajectories in anyon spectra, i.e. the cont inuous dependence of energy levels on the kinetic angular momentum. It provides a more economical and unified description, since each trajec tory contains an infinite number of points corresponding to the same s tatistics. For a system of noninteracting anyons in a harmonic potenti al, each trajectory consists of two infinite straight line segments, i n general connected by a nonlinear piece. We give the systematics of t he three-anyon trajectories. The trajectories in general cross each ot her at the bosonic/fermionic points. We use the (semiempirical) rule t hat all such crossings are true crossings, i.e. the order of the traje ctories with respect to energy is opposite to the left and to the righ t of a crossing.