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Douglas Lundholm

A Thomas-Fermi model for magnetically self-interacting bosons

Abstract: We consider a two-dimensional model for a confined quantum particle that interacts with itself purely magnetically, with a magnetic field proportional to the density and an interaction strength regulated by a single dimensionless parameter β. This model arises upon considering a gas of identical particles with statistics intermediate between bosons and fermions in a certain limit close to bosons, known as an-yons in the average-field approximation, with β = 0 corresponding to non-interacting bosons. In the "less bosonic" limit β → ∞ we derive an effective Thomas-Fermi-like description for the ground state. The talk is based on joint work with M. Correggi, R. Duboscq and N. Rougerie.