Statistical Interparticle Potential between Two Anyons

Abstract

The density matrix of a two-anyon system is evaluated and used to investigate the &#34;statistical interparticle potential&#34; following the theory of Uhlenbeck. The main purpose is to see how the statistical potential will depend on the fractional statistical parameter $α$. The result shows that the statistical potential for a two-anyon system with $α\ge {1\over2}$ is always repulsive. For the system with $0<α< {1\over2}$, the potential is repulsive at short distances and becomes attractive at long distances. It remains only in the boson system ($α=0$) that the repulsive potential arising from the exclusion principle can disappear and lead to an attractive potential at all distances.