Dimensional Reduction of Two-Dimensional Anyons to a One-Dimensional Interacting Bose Gas

TL;DR

This paper conjectures and verifies that a 2D anyon system confined to a narrow channel reduces to a 1D interacting Bose gas, with the system becoming fermionic in the zero-width limit for all but bosons.

Contribution

It introduces a conjecture linking 2D anyons to 1D Bose gases and verifies it using first-order perturbation theory near bosons.

Findings

Reduction to 1D Bose gas in narrow channels

Fermionic behavior in zero-width limit for non-bosonic anyons

Verification of the conjecture in perturbation theory

Abstract

We conjecture that a two-dimensional anyon system reduces, when confined to a narrow channel, to a one-dimensional bose gas with a repulsive two-body $\delta$-function interaction. We verify this conjecture in first-order perturbation theory near bosons. If the channel width is reduced to zero, the one-dimensional system is fermionic for all anyons other than bosons.