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

by Nicolas Rougerie, Qiyun Yang

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Nicolas Rougerie
Submission information
Preprint Link: scipost_202303_00024v2  (pdf)
Date accepted: 2023-10-04
Date submitted: 2023-10-02 17:10
Submitted by: Rougerie, Nicolas
Submitted to: SciPost Physics Core
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
  • Condensed Matter Physics - Theory
  • Mathematical Physics
  • Quantum Physics
Approach: Theoretical


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 $\alpha$.

Author comments upon resubmission

Dear editor
We have modified the text in the direction of more mathematical details, for a slightly longer text in SciPost Physics Core.
Sorry that we did not find the time to deal with this until now.
with best regards
NR and QY

List of changes

The main changes are the statements of Lemma 2 and Lemma 3, with the associated discussion.
References have also been updated.

Published as SciPost Phys. Core 6, 079 (2023)

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