Abstract: |
We develop an analytic theory for the ground state patterns and their phase transitions for spin-1 Bose-Einstein condensates on a bounded domain in the presence of a uniform magnetic field. Within the Thomas-Fermi approximation, these ground state patterns are composed of four basic states: magnetic state, nematic state, two-component state and three-component state, separated by interfaces. A complete phase diagram of the ground state patterns are found analytically with different quadratic Zeeman energy $q$ and total magnetization $M$ for both ferromagnetic and antiferromagnetic systems. Using the $\Gamma$-convergence technique, it is found that the semi-classical limits of these ground states minimize an energy functional which consists of interior interface energy plus a boundary contact energy.
As a consequence, the interface between two different basic states has constant mean curvature, and the contact angle between the interface and the boundary obeys Young`s relation. |
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