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Anyon trajectories and the systematics of the three-anyon spectrum

Stefan Mashkevich·Jan Myrheim·Kåre Olaussen·Ronald Rietman
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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.

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Stefan Mashkevich, Jan Myrheim, Kåre Olaussen, Ronald Rietman. 1995-07-06. Anyon trajectories and the systematics of the three-anyon spectrum. https://doi.org/10.1142/s0217751x96000584

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