D. Borisov and P. Exner
Exponential splitting of bound states in 
a waveguide with a pair of distant windows
(102K, LaTeX2e, 1 ps-figure)

ABSTRACT.  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.