Calculus of Variations and Geometric Measure Theory
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M. Goldman - B. Merlet

Phase segregation for binary mixtures of Bose-Einstein Condensates

created by goldman on 27 May 2015
modified on 30 Nov 2016


Submitted Paper

Inserted: 27 may 2015
Last Updated: 30 nov 2016

Year: 2015


We study the strong segregation limit for mixtures of Bose-Einstein condensates modelled by a Gross-Pitaievskii functional. Our first main result is that in presence of a trapping potential, for different intracomponent strengths, the Thomas-Fermi limit is sufficient to determine the shape of the minimizers. Our second main result is that for asymptotically equal intracomponent strengths, one needs to go to the next order. The relevant limit is a weighted isoperimetric problem. We then study the minimizers of this limit problem, proving radial symmetry or symmetry breaking for different values of the parameters. We finally show that in the absence of a confining potential, even for non-equal intracomponent strengths, one needs to study a related isoperimetric problem to gain information about the shape of the minimizers.

Keywords: Bose-Einstein Condensates, Weighted Isoperimetric problems, Sharp interface limit


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