Discrete spectrum of an asymmetric pair of waveguides coupled through a~window
Sbornik. Mathematics, Tome 197 (2006) no. 4, pp. 475-504
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In this paper one analyses the discrete spectrum of an asymmetric pair of two-dimensional quantum waveguides with common boundary in which a window of finite size is made. The phenomenon of new eigenvalues arising at the boundary of the essential spectrum as the
length of the window passes over critical values is considered. For the newly arising eigenvalues one constructs asymptotic expansions with respect to the small parameter equal to the difference between the window length and the closest critical value. The behaviour of the spectrum under an unrestricted growth of the length of the window is also under investigation; asymptotic expansions for eigenvalues with respect to the large parameter, the length of the window, are constructed.
Bibliography: 22 titles.
@article{SM_2006_197_4_a0,
author = {D. I. Borisov},
title = {Discrete spectrum of an asymmetric pair of waveguides coupled through a~window},
journal = {Sbornik. Mathematics},
pages = {475--504},
publisher = {mathdoc},
volume = {197},
number = {4},
year = {2006},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2006_197_4_a0/}
}
D. I. Borisov. Discrete spectrum of an asymmetric pair of waveguides coupled through a~window. Sbornik. Mathematics, Tome 197 (2006) no. 4, pp. 475-504. http://geodesic.mathdoc.fr/item/SM_2006_197_4_a0/