Two component condensates: coexistence, segregation and vortex patterns
Two component condensates are described by two wave functions minimizing a Gross Pitaevskii type energy. Though the basic coupling is only through the modulus, it can produce effects on the vortex patterns. We will describe the main numerical features in the case of coexistence and segregation of the components, and also in the case of extra spin orbit or Rabi coupling. I will explain how some segregation cases can be analyzed through a Gamma limit leading to a phase separation problem of de Giorgi type, and how we hope to explain the appearance of vortex sheets. In the coexistence cases, we try to obtain an asymptotic expansion of the energy taking into account the various types of defects. The first term in the expansion is related to the Thomas Fermi limit of the profile and relies on singular perturbation techniques, while the next ones require a more precise analysis of the defects cores described by a vortex/spike problem.