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Segregation and symmetry breaking of strongly coupled two-component Bose-Einstein condensates in a harmonic trap

We study ground states of two-component condensates in a harmonic trap. We prove that in the strongly coupled and weakly interacting regime, the two components segregate while a symmetry breaking occurs. More precisely, we show that when the intercomponent coupling strength is very large and both intracomponent coupling strengths are small, each component is close to the positive or the negative part of a second eigenfunction of the harmonic oscillator in $\R^2$. As a result, the supports of the components approach complementary half-spaces, and they are not radially symmetric.