Anyons in a tight wave-guide and the Tonks-Girardeau gas

TL;DR

This paper studies a system of 2D anyons with general statistics, showing that under strong anisotropic trapping, their 1D behavior is governed by the Tonks-Girardeau model of impenetrable bosons, regardless of their statistics parameter.

Contribution

It demonstrates a dimensional reduction of 2D anyons to 1D, revealing that their leading-order physics aligns with the Tonks-Girardeau model regardless of the anyons' statistics.

Findings

1D physics is governed by the Tonks-Girardeau model.

The statistics parameter fects do not alter the leading-order 1D behavior.

Dimensional reduction links 2D anyons to well-understood 1D bosonic models.

Abstract

We consider a many-body system of 2D anyons, free quantum particles with general statistics parameter \alpha \in ]0,2[. In the magnetic gauge picture they are described as bosons attached to Aharonov-Bohm fluxes of intensity 2 \pi \alpha generating long-range magnetic forces. A dimensional reduction to 1D is obtained by imposing a strongly anisotropic trapping potential. This freezes the motion in the direction of strong trapping, leading to 1D physics along the weak direction. The latter is governed to leading order by the Tonks-Girardeau model of impenetrable bosons, independently of \alpha.