Abstract

The system leading to phase segregation in two-component Bose-Einstein condensates can be generalized to hyperfine spin states with a Rabi term coupling. This leads to domain wall solutions having a monotone structure for a non-cooperative system. We use the moving plane method to prove monotonicity and one-dimensionality of the phase transition solutions. This relies on totally new estimates for a type of system for which no Maximum Principle a priori holds. We also derive that one dimensional solutions are unique up to translations. When the Rabi coefficient is large, we prove that no non-constant solutions can exist.

中文翻译：

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耦合系统中畴壁的移动平面

摘要

在双组分玻色-爱因斯坦凝聚物中导致相分离的系统可以推广到具有 Rabi 项耦合的超精细自旋态。这导致非合作系统具有单调结构的畴壁解决方案。我们使用移动平面方法来证明相变解的单调性和一维性。这依赖于对一种没有先验最大值原则的系统类型的全新估计。我们还推导出一维解决方案在翻译之前是独一无二的。当 Rabi 系数很大时，我们证明不存在非常数解。