Calculus of Variations and Geometric Measure Theory

M. Goldman - J. Royo-Letelier

Sharp interface limit for two components Bose-Einstein condensates

created by goldman on 08 Jan 2014
modified on 02 Sep 2014


Accepted Paper

Inserted: 8 jan 2014
Last Updated: 2 sep 2014

Year: 2014


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 $\Gamma$-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 litterature. We obtain as a consequence, symmetry breaking of the minimisers for the harmonic potential when this radio is sufficiently large.