Solution of the Three--Anyon Problem

Abstract

We solve, by separation of variables, the problem of three anyons with a harmonic oscillator potential. The anyonic symmetry conditions from cyclic permutations are separable in our coordinates. The conditions from two-particle transpositions are not separable, but can be expressed as reflection symmetry conditions on the wave function and its normal derivative on the boundary of a circle. Thus the problem becomes one-dimensional. We solve this problem numerically by discretization. $N$-point discretization with very small $N$ is often a good first approximation, on the other hand convergence as $N\to \infty$ is sometimes very slow.

15 pages, LaTeX2.09

References in corpus (6)

• Equation of State of an Anyon Gas in a Strong Magnetic Field
• The Third Virial Coefficient of Free Anyons
• Three-Loop Calculation of the Anyonic Full Cluster Expansion
• Asymptotic analysis and spectrum of three anyons
• An improved calculation of the Third Virial Coefficient of a free anyon Gas
• Exact Multiplicities in the Three-Anyon Spectrum

Cited by in corpus (7)

• Statistics of fractionalized excitations through threshold spectroscopy
• The third virial coefficient of anyons revisited
• Quantum Mechanics of a Particle with Two Magnetic Impurities
• Anyons, Deformed Oscillator Algebras and Projectors
• The Lowest Landau Level Anyon Equation of State in the Anti-screening Regime
• On the Three-Anyon Harmonics
• THE MANY-ANYON PROBLEM