Ground state patterns and phase transition of spin-1 Bose-Einstein condensates via \Gamma-convergence theory
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.
Keywords
Cite
@article{arxiv.1509.05182,
title = {Ground state patterns and phase transition of spin-1 Bose-Einstein condensates via \Gamma-convergence theory},
author = {I-Liang Chern and Chiu-Fen Chou and Tien-Tsan Shieh},
journal= {arXiv preprint arXiv:1509.05182},
year = {2015}
}