Séance Séminaire

Séminaire ACSIOM

Phase separation in multicomponent Bose-Einstein condensates: uniform bounds and regularity properties

A k-component Bose-Einstein condensate is described, in the approximation of an ultracold dilute Bose gas, in terms of k wave functions which solve a system of coupled Gross-Pitaevskiĭ equations. It has been experimentally observed that the different wave functions may repel each other and arrange in segregated domains. This phenomenon is called phase separation. It takes place when the coupling terms of the system are multiplied by a large parameter (competition parameter). We study the phase separation in the approximation of real valued solitary waves, on a bounded domain of R^2, with zero boundary conditions. For a sequence of solutions with bounded energy we prove convergence to a segregated limit configuration, as the competition parameter tends to infinity, in the space of Hölder continuous functions. We also show that the limit configuration is Lipschitz continuous, which is the best possible regularity. The techniques applied are typical of free boundary problems: blow up technique and monotonicity formulae. Joint work with H. Tavares, S. Terracini and G. Verzini.