Asymptotics of resonances for curved coupled waveguides

A system of two curved quantum waveguides laterally coupled through 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 induced by the window and for a bound state induced by the waveguide curvature are obtained using the method of matching of the asymptotic expansions of solutions of the boundary-value problem.