Pré-Publication, Document De Travail 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.

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Dates et versions

hal-03106991 , version 1 (14-01-2021)
hal-03106991 , version 2 (05-02-2021)
hal-03106991 , version 3 (21-05-2021)
hal-03106991 , version 4 (05-07-2021)

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  • HAL Id : hal-03106991 , version 4

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Théotime Girardot, Nicolas Rougerie. SEMICLASSICAL LIMIT FOR ALMOST FERMIONIC ANYONS. 2021. ⟨hal-03106991v4⟩
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