Anyons — Fractional Statistics & Aharonov-Bohm

In 2+1 dimensions, particles can have fractional statistics: exchanging two anyons accumulates a phase e^{iθ} (bosons: θ=0, fermions: θ=π, anyons: 0<θ<π). Anyons arise as flux-charge composites via the Aharonov-Bohm effect: a charge q circling a flux tube Φ picks up phase 2πqΦ/Φ_0. A half-exchange gives phase θ/2. These excitations appear in the fractional quantum Hall effect (e.g. Laughlin ν=1/3: θ=π/3) and topological quantum computing.