Semiclassical limit for almost fermionic anyons

• URL: http://arxiv.org/abs/2101.04457v4
• Date: Mon, 5 Jul 2021 12:33:32 GMT
• Title: Semiclassical limit for almost fermionic anyons
• Authors: Th\'eotime Girardot and Nicolas Rougerie
• Abstract summary: Quasi-particles obeying quantum statistics can be described as bosons and fermions with magnetic interactions. We prove that the ground state of a gas of anyons is described to leading order by a semi-classical, Vlasov-like, energy functional.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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