Parity violation, anyon scattering and the mean field approximation

TL;DR

This paper explores the scattering behavior of boson-based anyons with non-statistical interactions, highlighting the importance of phase shift periodicity, and assesses the validity of the mean-field approximation in such systems.

Contribution

It provides a detailed analysis of phase shift periodicity in anyon scattering and establishes criteria for the validity of the mean-field approximation, especially under weak statistical interactions.

Findings

Added phase shifts depend on the statistical parameter, even with fixed interactions.

The mean-field approximation is valid when the statistical interaction is weak.

Weaker interactions are required for boson-based than for fermion-based anyons.

Abstract

Some general features of the scattering of boson-based anyons with an added non-statistical interaction are discussed. Periodicity requirements of the phase shifts are derived, and used to illustrate the danger inherent in separating these phase shifts into the well-known pure Aharanov-Bohm phase shifts, and an additional set which arise due to the interaction. It is proven that the added phase shifts, although due to the non-statistical interaction, necessarily change as the statistical parameter is varied, keeping the interaction fixed. A hard-disk interaction provides a concrete illustration of these general ideas. In the latter part of the paper, scattering with an additional hard-disk interaction is studied in detail, with an eye towards providing a criterion for the validity of the mean-field approximation for anyons, which is the first step in virtually any treatment of this system. We find, consistent with previous work, that the approximation is justified if the statistical interaction is weak, and that it must be more weak for boson-based than for fermion-based anyons.