# Local Density Approximation for Almost-Bosonic Anyons

## TL;DR

This paper investigates the energy behavior of almost-bosonic anyons in confined traps, establishing boundary-independent energy results and deriving a local density approximation akin to Thomas-Fermi models for trapped gases.

## Contribution

It provides the first rigorous analysis of the energy independence from boundary conditions for large statistics parameter anyons and introduces a local density approximation for trapped non-interacting anyons.

## Key findings

- Energy in large statistics parameter regime is boundary-independent.
- Derived a local density approximation for trapped anyons.
- Established a Thomas-Fermi-like model for the system.

## Abstract

We discuss the average-field approximation for a trapped gas of non-interacting anyons in the quasi-bosonic regime. In the homogeneous case, i.e., for a confinement to a bounded region, we prove that the energy in the regime of large statistics parameter, i.e., for "less-bosonic" anyons, is independent of boundary conditions and of the shape of the domain. When a non-trivial trapping potential is present, we derive a local density approximation in terms of a Thomas-Fermi-like model.