Local density approximation for the almost-bosonic anyon gas

TL;DR

This paper investigates the energy properties of an almost-bosonic anyon gas using a local density approximation, establishing thermodynamic limits and deriving a Thomas-Fermi-like model for large statistics parameters.

Contribution

It proves the existence of the thermodynamic limit for the energy of the homogeneous anyon gas and develops an effective Thomas-Fermi model in the large statistics limit.

Findings

Thermodynamic limit exists and is domain shape independent.

Derived a Thomas-Fermi-like model for large effective statistics.

Established foundational results for almost-bosonic anyon gases.

Abstract

We study the minimizers of an energy functional with a self-consistent magnetic field, which describes a quantum gas of almost-bosonic anyons in the average-field approximation. For the homogeneous gas we prove the existence of the thermodynamic limit of the energy at fixed effective statistics parameter, and the independence of such a limit from the shape of the domain. This result is then used in a local density approximation to derive an effective Thomas--Fermi-like model for the trapped anyon gas in the limit of a large effective statistics parameter (i.e., "less-bosonic" anyons).