Lowest Landau level functional and Bargmann spaces for Bose–Einstein condensates

A fast rotating Bose–Einstein condensate can be described by a complex valued wave function minimizing an energy restricted to the lowest Landau level or Fock–Bargmann space. Using some structures associated with this space, we study the distribution of zeroes of the minimizer and prove in particular that the number of zeroes is infinite. We relate their location to the combination of two problems: a confining problem producing an inverted parabola profile and the Abrikosov problem of minimizing an energy on a lattice, using Theta functions.