SEMICLASSICAL LIMIT FOR ALMOST FERMIONIC ANYONS

Théotime Girardot (1) , Nicolas Rougerie (2)

1 LPM2C - Laboratoire de physique et modélisation des milieux condensés
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

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.

Mots clés: semi-classical; many-body; anyons; quantum gas; Pauli principle; limit

Domaines: Gaz Quantiques [cond-mat.quant-gas]; Physique mathématique [math-ph]

Théotime Girardot, Nicolas Rougerie. SEMICLASSICAL LIMIT FOR ALMOST FERMIONIC ANYONS. 2021. ⟨hal-03106991v2⟩