najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2022-13-3-245-249najo-235Research ArticleСтатьиSpectral gaps for star-like quantum graph and for two coupled ringsBlinovaI. V.irin-a@yandex.ruPopovA. I.popov239@gmail.comBosovaA. A.bossandbosss@yandex.ruITMO UniversityRussian Federation202206062025133245249Copyright © Blinova I.V., Popov A.I., Bosova A.A., 20252025Blinova I.V., Popov A.I., Bosova A.A.Blinova I.V., Popov A.I., Bosova A.A.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/235

The spectral problems for two types of quantum graphs are considered. We deal with star-like graph and a graph consisting of two rings connected through a segment. The spectral gap, i.e. the difference between the second and the rst eigenvalues of the free Schro¨ dinger operator, is studied. The dependence of the gap on the geometric parameters of the graph is investigated. Particularly, it is shown that the maximal gap is observed for the symmetric quantum graph.

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