Quasimomentum distribution and expansion of an anyonic gas

TL;DR

This paper argues that the traditional momentum distribution is not suitable for anyonic systems in two dimensions and proposes using the asymptotic single-particle density after expansion as a better observable to characterize anyonic statistics.

Contribution

It introduces a new observable based on expansion dynamics to measure anyonic statistics, overcoming limitations of the momentum distribution.

Findings

Momentum distribution is not a proper observable for anyons.

Asymptotic single-particle density can serve as an alternative measurement.

Exact expansion dynamics examples support the proposal.

Abstract

We point out that the momentum distribution is not a proper observable for a system of anyons in two-dimensions. In view of anyons as Wilczek's composite charged flux-tubes, this is a consequence of the fact that the orthogonal components of the kinetic momentum operator do not commute at the position of a flux tube, and thus cannot be diagonalized in the same basis. As a substitute for the momentum distribution of an anyonic (spatially localized) state, we propose to use the asymptotic single-particle density after expansion of anyons in free space from the state. This definition is identical with the standard one when the statistical parameter approaches that for bosons or fermions. Exact examples of expansion dynamics, which underpin our proposal, and observables that can be used to measure anyonic statistics, are shown.