najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2019-10-4-415-419najo-515Research ArticlePHYSICSФИЗИКАOn formal asymptotic expansion of resonance for quantum waveguide with perforated semitransparent barrierVorobievA. M.

Kronverkskiy, 49, Staint Petersburg, 197101

lenden31@yandex.ruBagmutovA. S.

Kronverkskiy, 49, Staint Petersburg, 197101

bagmutov94@mail.ruPopovA. I.

Kronverkskiy, 49, Staint Petersburg, 197101

popov239@gmail.comITMO UniversityRussian Federation201905082025104415–419Copyright © Vorobiev A.M., Bagmutov A.S., Popov A.I., 20252025Vorobiev A.M., Bagmutov A.S., Popov A.I.Vorobiev A.M., Bagmutov A.S., Popov A.I.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/515

A quantum waveguide with a semitransparent barrier, placed across it, is considered. It is assumed that the barrier has a small window. This local perturbation of the waveguide causes the appearance of resonance states localized near the barrier with the window. The asymptotics (in small parameter – the window width) of the resonances (quasi-bound states) is obtained. The procedure of construction of full formal asymptotic expansion is described. The first two terms of the asymptotic expansion are obtained explicitly. These terms describe the shift of the resonance from the threshold and the life time of the corresponding resonance state.

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