Semiclassical limit for almost fermionic anyons

TL;DR

This paper investigates the semiclassical limit of almost fermionic anyons in two-dimensional space, demonstrating that their ground state can be approximated by a Vlasov-like energy functional, revealing their unique momentum distribution.

Contribution

It provides a rigorous validation of a mean-field approximation for almost fermionic anyons, connecting quantum statistics with a semi-classical energy description.

Findings

Ground state described by a semi-classical Vlasov-like functional

Momentum distribution exhibits anyonic behavior

Validation of mean-field approximation for almost fermionic anyons

Abstract

In two-dimensional space there are possibilities for quantum statistics continuously interpolating between the bosonic and the fermionic one. Quasi-particles obeying such statistics can be described as ordinary bosons and fermions with magnetic interactions. We study a limit situation where the statistics/magnetic interaction is seen as a "perturbation from the fermionic end". We vindicate a mean-field approximation, proving that the ground state of a gas of anyons is described to leading order by a semi-classical, Vlasov-like, energy functional. The ground state of the latter displays anyonic behavior in its momentum distribution. Our proof is based on coherent states, Husimi functions, the Diaconis-Freedman theorem and a quantitative version of a semi-classical Pauli pinciple.