najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2020-11-6-619-627najo-358Research ArticleMATHEMATICSМАТЕМАТИКАResonance asymptotics for a pair quantum waveguides with common semitransparent perforated wallVorobievA. M.

Kronverkskiy, 49, St. Petersburg, 197101

lenden31@yandex.ruTrifanovaE. S.

Kronverkskiy, 49, St. Petersburg, 197101

etrifanova@gmail.comPopovI. Y.

Kronverkskiy, 49, St. Petersburg, 197101

popov1955@gmail.comITMO UniversityRussian Federation202029072025116619–627Copyright © Vorobiev A.M., Trifanova E.S., Popov I.Y., 20252025Vorobiev A.M., Trifanova E.S., Popov I.Y.Vorobiev A.M., Trifanova E.S., Popov I.Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/358

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.

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The authors declare that there are no conflicts of interest present.