论文标题
通过线性耦合将驱逐潜力中的波浪场捕获
Trapping wave fields in an expulsive potential by means of linear coupling
论文作者
论文摘要
我们证明了两个线性耦合组件的一维（1D和2D）系统中的受封闭状态的存在，其中限制的谐波振荡器（HO）电位作用于一种组件，而驱除式反HO电位作用于另一个组件。系统CA以光学和BEC双核波导实现。在1D线性系统中，以基础状态（GS）和偶极模式（第一个激发态）的精确形式找到了Codimension-One溶液。通用溶液是通过变异近似产生的，并以数值形式找到。还可以为2D系统中的GS和涡流状态获得确切的编码溶液和通用数值（对于所有涡度的所有值，都可以找到确切的溶液）。就规范而言，被绑定状态的被困和抗捕获的组成部分都可能是主导的组成部分。局部模式可以将其归类为连续体中的约束状态，因为它们与Dellocalized的模式共存。 1D状态以及2D中的GS会受到较弱的影响，如果将自动吸引或令人反感的非线性添加到系统中，则保持稳定。自我吸引使涡流状态不稳定，而在自我抑制的作用下它们保持稳定。
We demonstrate the existence of confined states in one- and two-dimensional (1D and 2D) systems of two linearly-coupled components, with the confining harmonic-oscillator (HO) potential acting upon one component, and an expulsive anti-HO potential acting upon the other. The systems ca be implemented in optical and BEC dual-core waveguides. In the 1D linear system, codimension-one solutions are found in an exact form for the ground state (GS) and dipole mode (the first excited state). Generic solutions are produced by means of the variational approximation, and are found in a numerical form. Exact codimension-one solutions and generic numerical ones are also obtained for the GS and vortex states in the 2D system (the exact solutions are found for all values of the vorticity). Both the trapped and anti-trapped components of the bound states may be dominant ones, in terms of the norm. The localized modes may be categorized as bound states in continuum, as they coexist with delocalized ones. The 1D states, as well as the GS in 2D, are weakly affected and remain stable if the self-attractive or repulsive nonlinearity is added to the system. The self-attraction makes the vortex states unstable against splitting, while they remain stable under the action of the self-repulsion.
