Conference - Multiscale problems in mathematical physics

Tuesday, June 15, 2021 - 17:00 to 17:55
Nicolas Rougerie
ENS Lyon
On quantum statistics transmutation via flux attachment
Abstract: 

We consider a model for two types (bath and tracers) of 2D quantum particles in a perpendicular (artificial) magnetic field. Interactions are short range and only inter-species, and we assume that the bath particles are fermions, all lying in the lowest Landau level of the magnetic field. Heuristic arguments then indicate that, if the tracers are strongly coupled to the bath, they effectively change their quantum statistics, from bosonic to fermionic or vice-versa. We rigorously compute the energy of a natural trial state, indeed exhibiting this phenomenon of statistics transmutation. The proof is based on (seemingly ?) new estimates for the characteristic polynomial of the Ginibre ensemble of random matrices.

Joint work with Douglas Lundholm and Gaultier Lambert

Partners

Irmar LMJL ENS Rennes LMBA LAREMA

Affiliation

ANR CNRS Rennes 1 Rennes 2 Nantes INSA Rennes INRIA ENSRennes UBO UBS Angers UBL