Statistical Interparticle Potential between Two Anyons

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 $\alpha \ge \frac{1}{2}$ is always repulsive. For the system with $0<\alpha <\frac{1}{2}$, 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.

Latex 5 pages, correct typos and figure

References in corpus (3)

• Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics
• Haldane fractional statistics in the fractional quantum Hall effect
• Boson-Fermion Transmutation and the Statistics of Anyons

Cited by in corpus (5)

• Nonperturbative Thermodynamic Geometry of Anyon Gas
• Statistical correlations in an ideal gas of particles obeying fractional exclusion statistics
• Statistics of Anyon Gas and the Factorizable Property of Thermodynamic Quantities
• Quasimomentum distribution and expansion of an anyonic gas
• Statistical Interparticle Potential of an Ideal Gas of Non-Abelian Anyons