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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 |
| Specialties: |
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| Approach: | Theoretical |
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 $\alpha$.
Author comments upon resubmission
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)