具有一对远距离窗口的波导中束缚态的指数分裂
Exponential splitting of bound states in a waveguide with a pair of distant windows
摘要：
本文考虑具有Dirichlet边界的平面直条上的Laplacian算子，该直条上有两个等长的Neumann“窗”，窗的中心相距$2l$，并研究了离散谱的渐近性质为$l\to\infty$ .结果表明，在单窗口带的每个孤立本征值周围存在本征值对，它们的距离在极限$l\to\infty$内指数地消失。我们推导出一个渐近展开的情况下，一个单一的窗口引起的阈值共振的存在下，其他窗口变成一个单一的孤立的本征值。
英文摘要：
We consider Laplacian in a straight planar strip with Dirichlet boundary which has two Neumann ``windows'' of the same length the centers of which are $2l$ apart, and study the asymptotic behaviour of the discrete spectrum as $l\to\infty$. It is shown that there are pairs of eigenvalues around each isolated eigenvalue of a single-window strip and their distances vanish exponentially in the limit $l\to\infty$. We derive an asymptotic expansion also in the case where a single window gives rise to a threshold resonance which the presence of the other window turns into a single isolated eigenvalue.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
