论文标题
具有排斥相互作用和线性耦合的两个组件系统中的对称破坏
Symmetry breaking in a two-component system with repulsive interactions and linear coupling
论文作者
论文摘要
我们将自发对称性破坏（SSB）的众所周知的理论处理扩展到两组分系统中，将线性耦合和自我吸引力的非线性结合到了线性耦合与排斥相互作用竞争的系统。首先，我们通过限制的谐波振荡器电位保持一维（1D和2D）地面（GS）解决方案（GS）解决方案（GS）溶液（GS）溶液和2D涡流状态。该系统可以在BEC和Optics中实现。通过托马斯 - 富尔米近似和基础耦合胶合pitaevskii方程的数值解，我们证明，当跨组件排斥力在GSS和涡流中发生SSB，在跨组件排斥更强时，在每个组件中都更强大。 SSB过渡被归类为超临界分叉，这会导致内部区域中具有破碎的对称性的状态，并在周围层中完整的对称性。与稳定的GSS和s = 1的涡流不同，S = 2的状态不稳定。我们还为系统中的1D间隙孤子传达了SSB，包括晶格电位。在这种情况下，SSB发生在相反的条件下，即，跨组件排斥必须比自我抑制弱，并且SSB由反对称的孤子子表现出来。
We extend the well-known theoretical treatment of the spontaneous symmetry breaking (SSB) in two-component systems, combining linear coupling and self-attractive nonlinearity, to a system in which the linear coupling competes with repulsive interactions. First, we address one- and two-dimensional (1D and 2D) ground-state (GS) solutions and 2D vortex states with topological charges S=1 and 2, maintained by a confining harmonic-oscillator potential. The system can be implemented in BEC and optics. By means of the Thomas-Fermi approximation and numerical solution of the underlying coupled Gross-Pitaevskii equations, we demonstrate that SSB takes place, in the GSs and vortices alike, when the cross-component repulsion is stronger that the self-repulsion in each component. The SSB transition is categorized as a supercritical bifurcation, which gives rise to states featuring broken symmetry in an inner area, and intact symmetry in a surrounding layer. Unlike stable GSs and vortices with S=1, the states with S=2 are unstable against splitting. We also address SSB for 1D gap solitons in the system including a lattice potential. In this case, SSB takes place under the opposite condition, i.e., the cross-component repulsion must be weaker than the self-repulsion, and SSB is exhibited by antisymmetric solitons.
