Anyon trajectories and the systematics of the three-anyon spectrum
arXiv:hep-th/9507034 · doi:10.1142/S0217751X96000584
Abstract
We develop the concept of trajectories in anyon spectra, i.e., the continuous dependence of energy levels on the kinetic angular momentum. It provides a more economical and unified description, since each trajectory contains an infinite number of points corresponding to the same statistics. For a system of non-interacting anyons in a harmonic potential, each trajectory consists of two infinite straight line segments, in general connected by a nonlinear piece. We give the systematics of the three-anyon trajectories. The trajectories in general cross each other at the bosonic/fermionic points. We use the (semi-empirical) rule that all such crossings are true crossings, i.e.\ the order of the trajectories with respect to energy is opposite to the left and to the right of a crossing.
arXiv comment15 pages LaTeX + 1 attached uuencoded gzipped file with 7 figures