Asymptotics of an eigenvalue on the continuous spectrum of two quantum waveguides coupled through narrow windows

作者：Nazarov S A^*

来源：Mathematical Notes, 2013, 93(1-2): 266-281.

DOI：10.1134/S000143461301029X

• planar waveguide
• window-coupled quantum waveguides
• augmented scattering matrix
• Laplace operator
• Dirichlet boundary condition
• Neumann boundary condition
• Helmholtz equation
• Wood%26apos
• s anomalies

Conditions under which two planar identical waveguides coupled through narrow windows of width E %26gt; a parts per thousand(a) 1 have an eigenvalue on the continuous spectrum are obtained. It is established that the eigenvalue appears only for certain values of the distance between the windows: for each sufficiently small E %26gt; %26gt; 0, there exists a sequence of such distances; here N = 1, 2, 3, .... The result is obtained by the asymptotic analysis of an auxiliary object, namely, the augmented scattering matrix.

• 出版日期2013-1