najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-963Research ArticleMATHEMATICSМАТЕМАТИКАEssential and discrete spectrum of a three-particle lattice Hamiltonian with non-local potentialsRasulovT. H.

Bukhara

rth@mail.ruRasulovaZ. D.

Bukhara

zdrasulova@mail.ruBukhara State UniversityUzbekistan20141508202553327342Copyright © Rasulov T.H., Rasulova Z.D., 20252025Rasulov T.H., Rasulova Z.D.Rasulov T.H., Rasulova Z.D.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/963

We consider a model operator (Hamiltonian) H associated with a system of three particles on a d-dimensional lattice that interact via non-local potentials. Here the kernel of non-local interaction operators has rank n with n ≥ 3. We obtain an analog of the Faddeev equation for the eigenfunctions of H and describe the spectrum of H. It is shown that the essential spectrum of H consists the union of at most n + 1 bounded closed intervals. We estimate the lower bound of the essential spectrum of H for the case d = 1.

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