S. Mashkevich et al., ANYON TRAJECTORIES AND THE SYSTEMATICS OF THE 3-ANYON SPECTRUM, International journal of modern physics A, 11(7), 1996, pp. 1299-1313
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.