Abstract

In this talk, I will introduce an analytic theory for the ground state patterns of spin-1 Bose-Einstein condensates (BECs) and their corresponding phase transition in an infinite trap potential on a bounded domain in the presence a uniform magnetic field. Configurations of the ground state in a system with different quadratic Zeeman energy and total magnetization is found within its Thomas-Fermi approximation. The sharp interface limit of the Spin-1 BEC model is derived through the Gamma convergence technique. A complete phase diagram for both ferromagnetic and antiferromagnetic systems is obtained in the semi-classical regime. It is shown that the interface between two different phases of a ground state has constant mean curvature, and its contact angle between the interface and the boundary obeys the Young's relation.