Bound-state asymptotic estimates for window-coupled Dirichlet strips and layers

Details Bound-state asymptotic estimates for window-coupled Dirichlet strips and layers Bound-state asymptotic estimates for window-coupled Dirichlet strips and layers

1997-09-25

arxiv.org/abs/funct-an/9709003v1

J. Phys. A30 (1997), 7863-7878

Physics

Mathematical Physics

LaTeX source file (19 pages); the paper is due to appear in J.Phys.A: Math.Gen

Scientific paper

10.1088/0305-4470/30/22/023

We consider the discrete spectrum of the Dirichlet Laplacian on a manifold consisting of two adjacent parallel strips or planar layers coupled by a finite number N of windows in the common boundary. If the windows are small enough, there is just one isolated eigenvalue. We find upper and lower asymptotic bounds on the gap between the eigenvalue and the essential spectrum in the planar case, as well as for N=1 in three dimensions. Based on these results, we formulate a conjecture on the weak-coupling asymptotic behaviour of such bound states.

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