Title :

Phase segregation for binary mixtures of Bose-Einstein Condensates

Author(s) :

Goldman, Michael [Auteur]
Laboratoire Jacques-Louis Lions [LJLL]
Merlet, Benoît [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]

Journal title :

SIAM Journal on Mathematical Analysis

Pages :

1947–1981

Publisher :

Society for Industrial and Applied Mathematics

Publication date :

2017

ISSN :

0036-1410

English keyword(s) :

Bose-Einstein Condensates
Weighted Isoperimetric problems
Sharp interface limit
Gamma-convergence
Phase segregation

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Physique [physics]/Physique mathématique [math-ph]
Physique [physics]/Physique Quantique [quant-ph]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Théorie géométrique de la mesure et applications
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL