Spectrum of three anyons in a harmonic potential and the third virial coefficient
Diptiman Sen
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 \ensuremath{\theta} is equal to the energy of its partner state at \ensuremath{\pi}-\ensuremath{\theta}. Bosons, semions, and fermions have \ensuremath{\theta}=0,\ensuremath{\pi}/2, and \ensuremath{\pi}, respectively. From this, we show that the third virial coefficient of an ideal anyon gas is exactly mirror symmetric about semions.
Physical Review Letters•May 18, 1992•31 citations