# Spectrum of Three Anyons in a Harmonic Potential and the Third Virial Coefficient

Sen, Diptiman (1992) Spectrum of Three Anyons in a Harmonic Potential and the Third Virial Coefficient. In: Physical Review Letters, 68 (20). pp. 2977-2980.

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## Abstract

We use supersymmetric quantum mechanics to show that the spectrum of three anyons in a harmonic potential exhibits an almost complete mirror symmetry about semions. Barring a subset of exactly solved states, all states come in pairs such that the energy of one state with the statistics parameter $\theta$ is equal to the energy of its partner state at $\pi-\theta$. Bosons, semions, and fermions have $\theta=0,\pi/2$, and $\pi$, respectively. From this, we show that the third virial coefficient of an ideal anyon gas is exactly mirror symmetric about semions.

Item Type: Journal Article Copyright of this article belongs to American Physical Society. Division of Physical & Mathematical Sciences > Centre for Theoretical Studies 18 Oct 2006 19 Sep 2010 04:31 http://eprints.iisc.ernet.in/id/eprint/8254