Anyon trajectories and the systematics of the three-anyon spectrum

Details Anyon trajectories and the systematics of the three-anyon spectrum Anyon trajectories and the systematics of the three-anyon spectrum

1995-07-06

arxiv.org/abs/hep-th/9507034v1

Int.J.Mod.Phys. A11 (1996) 1299-1314

Physics

High Energy Physics

High Energy Physics - Theory

15 pages LaTeX + 1 attached uuencoded gzipped file with 7 figures

Scientific paper

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.

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