Vortex patterns and sheets in segregated two component Bose–Einstein condensates

Amandine Aftalion (1) , Etienne Sandier

1 CAMS - Centre d'Analyse et de Mathématique sociales

We study minimizers of a Gross-Pitaevskii energy describing a two-component Bose-Einstein condensate set into rotation. We consider the case of segregation of the components in the Thomas-Fermi regime, where a small parameter ε conveys a singular perturbation. We estimate the energy as a term due to a perimeter minimization and a term due to rotation. In particular, we prove a new estimate concerning the error of a Modica Mortola type energy away from the interface. For large rotations, we show that the interface between the components gets long, which is a first indication towards vortex sheets.

Mots clés: perimeter minimization; Gamma limit; segregation of species; vortex sheets

Domaines: Equations aux dérivées partielles [math.AP]

Amandine Aftalion, Etienne Sandier. Vortex patterns and sheets in segregated two component Bose–Einstein condensates. Calculus of Variations and Partial Differential Equations, 2020, 59 (19), ⟨10.1007/s00526-019-1637-6⟩. ⟨hal-03096201⟩