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Young Seminar
Organizers: Douglas Lundholm (IHP) & Julien Sabin (Cergy)


Jimena Royo-Letelier (Paris-Dauphine/Versailles): "Optimal partition problems in Bose-Einstein condensates"
Wednesday 22 May 2013, 15:30 - 16:30
Salle 05


Abstract: This talk is about two-component Bose-Einstein condensate in a harmonic trap. When the two components repulse strongly, they segregate by having disjoint supports and break the radial symmetry of the system. Our aim is to describe these phenomena in the limits when the interaction between the particles of each component is very strong or very weak. We will show links between our model and optimal partition or phase transition problems. In a first time, I will address the case of weak particle interactions and show that the two components segregate, while their supports approaches complementary half spaces. Then, I will address the case of strong particle interactions. In this case, I will show that the Gross-Pitaevskii energy of a two component condensate can be rewritten as a weighted Cahn-Hilliard energy, and prove the Gamma-convergence to a perimeter minimization problem.