Dirichlet网络压缩引起的非平凡边缘耦合：弯曲波导的情况
Nontrivial edge coupling from a Dirichlet network squeezing: the case of a bent waveguide
摘要：
与诺依曼情形不同，狄利克雷网络的压缩极限在阈值区域中一般导致具有不连通边的量子图，例外可能来自阈值共振。在本文中，我们的主要观点是表明，修改局部的几何形状，我们可以实现在极限的非平凡的耦合之间的边缘，包括，特别是，类的$δ$型边界条件。我们在最简单的情况下，当弯曲的波导被压缩时，工作了一个说明这一要求。
英文摘要：
In distinction to the Neumann case the squeezing limit of a Dirichlet network leads in the threshold region generically to a quantum graph with disconnected edges, exceptions may come from threshold resonances. Our main point in this paper is to show that modifying locally the geometry we can achieve in the limit a nontrivial coupling between the edges including, in particular, the class of $δ$-type boundary conditions. We work out an illustration of this claim in the simplest case when a bent waveguide is squeezed.
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