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 literature. We obtain as a consequence, symmetry breaking of the minimisers for the harmonic potential.

DOI: 10.1051/cocv/2014040

Keywords: Bose-Einstein condensates, Γ-convergence, BV functions, isoperimetric problems

^{1}; Royo-Letelier, J.

^{2}

@article{COCV_2015__21_3_603_0, author = {Goldman, M. and Royo-Letelier, J.}, title = {Sharp interface limit for two components {Bose\ensuremath{-}Einstein} condensates}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {603--624}, publisher = {EDP-Sciences}, volume = {21}, number = {3}, year = {2015}, doi = {10.1051/cocv/2014040}, mrnumber = {3358623}, zbl = {1319.35206}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2014040/} }

TY - JOUR AU - Goldman, M. AU - Royo-Letelier, J. TI - Sharp interface limit for two components Bose−Einstein condensates JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 603 EP - 624 VL - 21 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2014040/ DO - 10.1051/cocv/2014040 LA - en ID - COCV_2015__21_3_603_0 ER -

%0 Journal Article %A Goldman, M. %A Royo-Letelier, J. %T Sharp interface limit for two components Bose−Einstein condensates %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 603-624 %V 21 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2014040/ %R 10.1051/cocv/2014040 %G en %F COCV_2015__21_3_603_0

Goldman, M.; Royo-Letelier, J. Sharp interface limit for two components Bose−Einstein condensates. ESAIM: Control, Optimisation and Calculus of Variations, Volume 21 (2015) no. 3, pp. 603-624. doi : 10.1051/cocv/2014040. http://archive.numdam.org/articles/10.1051/cocv/2014040/

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