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Some supersymmetric features in the spectrum of anyons in a harmonic potential

Sen, Diptiman (1992) Some supersymmetric features in the spectrum of anyons in a harmonic potential. In: Physical Review D, 46 (4). pp. 1846-1857.

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Abstract

The energy spectrum of two or more anyons in a harmonic oscillator potential exhibits some supersymmetric features. The supersymmetry operators map a theory with statistics parameter $\theta$ to one described by $\theta+\pi$. Thus fermions and bosons are mapped into each other, whereas semions remain invariant under a combined action of supersymmetry and parity. All the states of a given theory fall into families. The energy levels of states within the same family differ by multiples of the harmonic frequency. There is a bosonic SO(2,1) symmetry for any value of $\theta$. Finally, supersymmetry explains why most energy levels for three anyons have a mirror symmetry about semions. Consequently, the third virial coefficient is exactly mirror symmetric.

Item Type: Journal Article Copyright of this article belongs to American Physical Society. Division of Physical & Mathematical Sciences > Centre for Theoretical Studies 22 Aug 2006 19 Sep 2010 04:30 http://eprints.iisc.ernet.in/id/eprint/8083