Resonance asymptotics for a pair quantum waveguides with common semitransparent perforated wall

A nanostructure model,which is represented as a pair of coupled two-dimensional quantum waveguides with common semitransparent wall, is considered. That wall has small window which induces a resonance state localized near the window. Semitransparency is the reason for the asymptotics difference in comparison with the non-transparent case. Using the matching of asymptotic expansions method, we obtain formulas for resonances and resonance states.