Ground-state patterns and phase diagram of spin-1 Bose-Einstein condensates in uniform magnetic field

We develop an analytic theory for the ground-state patterns and phase diagram of spin-1 Bose-Einstein condensates in a bounded domain in R-d in the presence of a uniform magnetic field. Our main results include: (1) obtaining a complete phase diagram with explicit analytic formulae of Thomas-Fermi solutions on the parameter q-M plane (q: quadratic Zeeman energy, M: total magnetization) for both ferromagnetic and antiferromagnetic systems, and (2) an entire characterization of ground-state patterns in the Thomas-Fermi regime and the semi-classical regime. In particular, a class of interesting ground states are mixed states. A mixed state consists of two constant states separated by an interface. This interface minimizes an effective energy, the sum of an interfacial energy and two boundary energies. As a result, the interface has constant mean curvature and the corresponding contact angle satisfies Young's relation as that in the classical wetting process. (C) 2018 Elsevier B.V. All rights reserved.