演講者：謝天長教授 (中原大學應用數學系)

標題：Ground-State Patterns and Phase Diagram of Spin-1 Bose--Einstein Condensates in Uniform Magnetic Field

時間：10月22日下午2點

地點：校本部第二綜合大樓8樓 B808 教室

摘要：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.