Statistical Interparticle Potential between Two Anyons

TL;DR

This paper investigates how the statistical interparticle potential between two anyons depends on their fractional statistical parameter, revealing regimes of repulsion and attraction influenced by quantum statistics.

Contribution

It provides a detailed analysis of the statistical potential for two anyons, highlighting how it varies with the fractional parameter and identifying conditions for repulsive or attractive interactions.

Findings

For α ≥ 1/2, the potential is always repulsive.

For 0 < α < 1/2, the potential is repulsive at short distances and attractive at long distances.

At α=0 (bosons), the potential can be attractive at all distances.

Abstract

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