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Article Dans Une Revue Commun.Math.Phys. Année : 2021

Semiclassical Limit for Almost Fermionic Anyons

Résumé

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.

Dates et versions

hal-03129551 , version 1 (02-02-2021)

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Citer

Théotime Girardot, Nicolas Rougerie. Semiclassical Limit for Almost Fermionic Anyons. Commun.Math.Phys., 2021, 387 (1), pp.427-480. ⟨10.1007/s00220-021-04164-1⟩. ⟨hal-03129551⟩
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