An explicit realization of fractional statistics in one dimension

Abstract

An explicit realization of anyons is provided, using the three-body Calogero model. The fact that in the coupling domain, -¼<g<0, the angular spectrum can have a band structure, leads to the manifestation of the desired phase in the wave function, under the exchange of particles. Concurrently, the momentum corresponding to the angular variable is quantized, exactly akin to the relative angular momentum quantization in two dimensional anyonic system.