# Phase Segregation for Binary Mixtures of Bose-Einstein Condensates

@article{Goldman2015PhaseSF, title={Phase Segregation for Binary Mixtures of Bose-Einstein Condensates}, author={Michael Goldman and Beno{\^i}t Merlet}, journal={SIAM J. Math. Anal.}, year={2015}, volume={49}, pages={1947-1981} }

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…

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## References

SHOWING 1-10 OF 46 REFERENCES

### Binary Bose-Einstein Condensate Mixtures in Weakly and Strongly Segregated Phases

- Physics
- 1998

We perform a mean-field study of the binary Bose-Einstein condensate mixtures as a function of the mutual repulsive interaction strength. In the phase segregated regime, we find that there are two…

### Interface tension of Bose-Einstein condensates

- Physics
- 2008

Motivated by recent observations of phase-segregated binary Bose-Einstein condensates, we propose a method to calculate the excess energy due to the interface tension of a trapped configuration. By…

### Sharp interface limit for two components Bose−Einstein condensates

- Physics
- 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…

### Tunable miscibility in a dual-species Bose-Einstein condensate.

- PhysicsPhysical review letters
- 2008

The observation of controllable phase separation in a dual-species Bose-Einstein condensate with 85Rb and 87Rb is reported on, which can clearly observe immiscible behavior via a dramatic spatial separation of the two species.

### Classification of the ground states and topological defects in a rotating two-component Bose-Einstein condensate

- Physics
- 2011

We classify the ground states and topological defects of a rotating two-component condensate when varying several parameters: the intracomponent coupling strengths, the intercomponent coupling…

### Thomas–Fermi Approximation for Coexisting Two Component Bose–Einstein Condensates and Nonexistence of Vortices for Small Rotation

- Physics
- 2015

We study minimizers of a Gross–Pitaevskii energy describing a two- component Bose–Einstein condensate confined in a radially symmetric harmonic trap and set into rotation. We consider the case of…

### VORTICES IN MULTICOMPONENT BOSE–EINSTEIN CONDENSATES

- Physics
- 2005

We review the topic of quantized vortices in multicomponent Bose–Einstein condensates of dilute atomic gases, with an emphasis on the two-component condensates. First, we review the fundamental…

### Interface layer of a two-component Bose-Einstein condensate

- Mathematics
- 2015

This paper deals with the study of the behaviour of the wave functions of a two-component Bose-Einstein condensate near the interface, in the case of strong segregation. This yields a system of two…

### Boundary of two mixed Bose-Einstein condensates

- Physics
- 2002

We study the boundary between two interpenetrating Bose-Einstein condensates interacting repulsively in the case of their spatial separation. We show that the analytical expressions for the…

### Remarks on the interface layer of a two-component Bose-Einstein condensate

- Mathematics
- 2015

We consider the heteroclinic connection problem for a class of Hamiltonian systems, containing a large competition parameter, which arise in the study of the behaviour of the wave functions of a…