96-29 P. Exner, S.A. Vugalter
Asymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window (34K, LaTeX) Feb 2, 96
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. Consider the Laplacian in a straight planar strip of width $\,d\,$, with the Neumann boundary condition at a segment of length $\,2a\,$ of one of the boundaries, and Dirichlet otherwise. For small enough $\,a\,$ this operator has a single eigenvalue $\,\epsilon(a)\,$; we show that there are positive $\,c_1,c_2\,$ such that $\,-c_1 a^4 \le \epsilon(a)- \left(\pi/ d\right)^2 \le -c_2 a^4\,$. An analogous conclusion holds for a pair of Dirichlet strips, of generally different widths, with a window of length $\,2a\,$ in the common boundary.

Files: 96-29.tex