Exponential splitting of bound states in a waveguide with a pair of distant windows
Exponential splitting of bound states in a waveguide with a pair of distant windows
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 …