Sharp interface limit for two components Bose−Einstein condensates∗
1 Max Planck Institute for Mathematics
in the Sciences, Inselstrasse
2 Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400 Klosterneuburg, Austria
We study a double Cahn−Hilliard type functional related to the Gross−Pitaevskii energy of two-components Bose−Einstein condensates. In the case of large but same order intercomponent and intracomponent coupling strengths, we prove Γ-convergence to a perimeter minimisation functional with an inhomogeneous surface tension. We study the asymptotic behavior of the surface tension as the ratio between the intercomponent and intracomponent coupling strengths becomes very small or very large and obtain good agreement with the physical literature. We obtain as a consequence, symmetry breaking of the minimisers for the harmonic potential.
Mathematics Subject Classification: 35Q40 / 35J50 / 49S05 / 49Q20
Key words: Bose-Einstein condensates / Γ-convergence / BV functions / isoperimetric problems
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