Giant vortex and the breakdown of pinning in a rotating Bose–Einstein condensate

This talk presents work in collaboration withA. Aftalion (Paris-6) and Lia Bronsard (McMaster). We consider the following variational problem arising from a two-dimensional model for rotating Bose–Einstein Condensates (BEC.) Let a = a(r) be a real-analytic radially symmetric function in the plane, with the property that A = {x ∈ R : a(|x|) > 0} is an annulus, and such that a vanishes linearly at each edge of the annulus A. Examples include a(r) = −b0 + b1r − b2r with appropriately chosen coefficients. Let Ω ∈ R, x = (x1, x2) ∈ R, x⊥ = (−x2, x1), and > 0. We study minimizers u ∈ H 0 (A;C) of the energy functional