najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2023-14-2-151-157najo-121Research ArticleMATHEMATICSМАТЕМАТИКАExistence of the eigenvalues of a tensor sum of the Friedrichs models with rank 2 per turbationСуществование собственных значений тензорной суммы моделей Фридрихса с двумерными возмущениямиhttps://orcid.org/0000-0002-2868-4390ПасуловТ. Х.RasulovT. H.

Tulkin H. Rasulov

Bukhara

rth@mail.ruhttps://orcid.org/0000-0001-8924-0825БахроновБ. И.BahronovB. I.

BekzodI. Bahronov

Bukhara

b.bahronov@mail.ruBukhara State UniversityRussian Federation202303062025142151157Copyright © Rasulov T.H., Bahronov B.I., 20252025Пасулов Т.Х., Бахронов Б.И.Rasulov T.H., Bahronov B.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/121

In the paper we consider a tensor sum Hμ,λ,μ,λ  > 0 of two Friedrichs models hμ,λ with rank two perturbation. The Hamiltonian H is associated with a system of three quantum particles on one-dimensional lattice. We investigate the number and location of the eigenvalues of Hμ,λ. The existence of eigenvalues located respectively inside, in the gap, and below the bottom of the essential spectrum of Hμ,λ is proved.

В статье рассматривается тензорная сумма двух моделей Фридрихса  с возмущением второго ранга. Гамильтониану  соответствует система трех квантовых частиц на одномерной решетке. Исследуется количество и расположение собственных значений. Существование собственных значений, расположенных, соответственно, внутри, в зазоре и ниже дна существенного спектра доказано.

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