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Physical review. B, Condensed matter

Statistical potential in an ideal anyon gas

B. Kahng, K. Park

Published Apr 1, 1992• 3 citations
Publisher

Abstract

We calculate the e/Istatistical potentials between particles in an ideal anyon gas arising from the symmetry property of the wave functions. The statistical potential is known to be purely repulsive for fermions, and to be purely attractive for bosons. In contrast, the statistical potentials for anyons are found to behave differently; the statistical potential for quasibosons is not purely attractive, displaying a minimum at finite interparticle distance. That implies there exists a stable equilibrium interparticle distance between two quasibosons. The statistical potential for quasifermions behaves similarly to that for fermions. Our result supports that the probability amplitude of finding two anyons at the same space point is zero.

DOI
10.1103/physrevb.45.8158

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We prove upper and lower bounds on the ground-state energy of the ideal two-dimensional anyon gas. Our bounds are extensive in the particle number, as for fermions, and linear in the statistics parameter α\alpha α . The lower bounds extend to Lieb–Thirring inequalities for all anyons except bosons.