Semiclassical limit 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.
Cite
@article{arxiv.2101.04457,
title = {Semiclassical limit for almost fermionic anyons},
author = {Théotime Girardot and Nicolas Rougerie},
journal= {arXiv preprint arXiv:2101.04457},
year = {2021}
}