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Seminar
FIELD Math:Analysis
DATE February 18 (Thu), 2021
TIME 17:00-18:00
PLACE Online
SPEAKER Rougerie, Nicolas
HOST Lee, Jinyeop
INSTITUTE Universit? Grenoble Alpes and CNRS
TITLE Semiclassical limit for almost fermionic anyons
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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