Seminar Analysis and Mathematical Physics: Théotime Girardot (LPMMC)

Semiclassical limit for almost fermionic anyons

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. After introducing and stating this result I will give elements of proof based on coherent states,

Husimi functions, the Diaconis-Freedman theorem and a quantitative version of a semi-classical Pauli pinciple.

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