Resonance phenomena in curved quantum waveguides coupled via windows

A system of two curved waveguides mutually coupled via a small window is considered by solving a boundary value problem with the Dirichlet conditions at the external boundaries and the Neumann conditions at an interface with the window. Asymptotic expansions (with respect to the window size) for a resonance related to the window and for a bound state related to the waveguide curvature are obtained using the method of matching of the asymptotic expansions of solutions of the boundary-value problem.