najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2024-15-2-155-159najo-29Research ArticleMATHEMATICSМАТЕМАТИКАMathematical model of weakly coupled spherical resonator chains under the influence of external magnetic fieldМатематическая модель слабосвязанных цепочек сферических резонаторов под действием внешнего магнитного поляМелиховаА. С.MelikhovaA. S.

Alina S. Melikhova – Center of Mathematics, ITMO University.

Kroverkskiy, 49, St. Petersburg, 197101

alina.s.melikhova@gmail.comhttps://orcid.org/0000-0001-7137-4067ПоповА. И.PopovA. I.

Anton I. Popov – Center of Mathematics, ITMO University.

Kroverkskiy, 49, St. Petersburg, 197101

popov239@gmail.comhttps://orcid.org/0000-0003-2115-2479БлиноваИ. В.BlinovaI. V.

Irina V. Blinova – Center of Mathematics, ITMO University.

Kroverkskiy, 49, St. Petersburg, 197101

irin-a@yandex.ruhttps://orcid.org/0000-0002-5251-5327ПоповИ. Ю.PopovI. Y.

Igor Y. Popov – Center of Mathematics, ITMO University.

Kroverkskiy, 49, St. Petersburg, 197101

popov1955@gmail.comITMO UniversityRussian Federation202431052025152155159Copyright © Melikhova A.S., Popov A.I., Blinova I.V., Popov I.Y., 20252025Мелихова А.С., Попов А.И., Блинова И.В., Попов И.Ю.Melikhova A.S., Popov A.I., Blinova I.V., 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/29

The Schrödinger operators with constant magnetic field in a bent chain and Y-type chain of coupled balls are considered. Coupling exists due to point-like openings at the touching points of neighbor spheres. The mathematical background of the model is the theory of self-adjoint extensions of symmetric operators. The spectral equations for the model operators in each case were derived and analyzed.

Рассмотрены операторы Шредингера с постоянным магнитным полем в изогнутой цепочке и цепочке связанных шаров Y-типа. Связь существует за счет точечных отверстий в точках соприкосновения соседних сфер. Математической основой модели является теория самосопряженных расширений симметричных операторов. Выведены и проанализированы спектральные уравнения для модельных операторов в каждом случае.

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