发表机构
University of Bath; Louisiana State University（巴斯大学; 路易斯安那州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过高对比度周期度量图的同质化，利用双图耦合与临界高对比度机制，在连续谱中嵌入能量处创建并保持局部缺陷产生的束缚态。
AI 中文摘要
通过对高对比度周期度量图进行同质化，我们创建了连续介质，这些介质允许由局部缺陷产生的束缚态存在于连续谱中的嵌入能量处。这是通过将图的两个副本同时拟合到空间中，并通过连接边将它们耦合来实现的。通过傅里叶分析进行插值，在公共函数空间中表示相关算子，从而将图上的常微分方程同质化为空间中的偏微分方程。两个耦合图产生具有内部自由度的有效介质，允许分解为两个混合态的正交空间。临界高对比度在有效介质中保留微观共振，并允许一个混合态空间的谱带与另一个的谱隙重叠。这作为在有效介质连续谱中嵌入频率处产生束缚态的机制。由于缺陷区域上约化预解式的$O(\varepsilon)$算子范数估计，这些连续谱中的束缚态在$\varepsilon$尺度度量图上持续存在。
英文摘要
By homogenizing high-contrast periodic metric graphs, we create continuous media that admit bound states produced by local defects at energies embedded in the continuous spectrum. This is achieved by fitting two copies of a lattice graph simultaneously into space and coupling them by connecting edges. The homogenization of an ODE on a graph to a PDE in space is achieved by representing the associated operators in a common functional space through interpolation by Fourier analysis. The two coupled graphs result in an effective medium with internal degrees of freedom that allow a decomposition into two orthogonal spaces of hybrid states. Critical high contrast retains microscopic resonances in the effective medium and allows a spectral band of one hybrid state space to overlap a spectral gap of the other. This serves as the mechanism for creating bound states at frequencies embedded in the continuous spectrum of the effective medium. These bound states in the continuum persist for $\varepsilon$-scale metric graphs due to $O(\varepsilon)$ operator-norm estimates for reduced resolvents on the defect region.
