Physics – Mathematical Physics
Scientific paper
2003-12-04
Journal of Physics A. 2004. V. 37. No. 10. P. 3411-3428.
Physics
Mathematical Physics
Scientific paper
10.1088/0305-4470/37/10/007
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.
Borisov Denis
Exner Pavel
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