We study the problem of four and five anyons in a harmonic oscillator potential and make some exact statements regarding its energy spectra. We show that the spectra exhibit some mirror symmetric (reflection symmetric about the semionic statistics point θ=π/2) features analogous to the mirror symmetry in the two and three anyon spectra.

Modern Physics Letters BMay 10, 19960 citations

Energy spectra of three anyons in a harmonic well

W.Y Ruan, Tingwan Wu, R.Y Lie +1 more

Physics Letters AJun 1, 19961 citation

International Journal of Modern Physics B

THE EXACT ANYON SPECTRA AND FRACTIONAL STATISTICS

Chihong Chou

Published Jun 1, 1991• 3 citations

Publisher

Abstract

We seek the analytic eigenstates for an N-identical anyons in an external harmonic oscillator potential.

DOI: 10.1142/s0217979291001565

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Energy spectra of three anyons in a harmonic well

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Physics Letters AJun 1, 19961 citation

We study a many-body system consisting of

N

identical anyons in an external harmonic-oscillator potential. A partial set of exact solutions is obtained by using Jacobi coordinates. For completing the full investigation, we employ a perturbative method to compute those spectra, which have not been analytically obtained. Near the boson limit, we point out that the requirement of the boson being hard core is needed for performing the perturbative calculations, and the first-order

N

-anyon ground-state energies are explicitly presented by using a proper regulation procedure. Up to third perturbative order from the fermion limit, the three-anyon ground-state energy corrections are explicitly presented. Finally we compute the first-order three-anyon ground-state wave function near the fermion limit.