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Nanosystems: Physics, Chemistry, Mathematics, 2014, Volume 5, Issue 3, Pages 327–342 (Mi nano862)  

Essential and discrete spectrum of a three-particle lattice Hamiltonian with non-local potentials

T. H. Rasulov, Z. D. Rasulova

Bukhara State University, Bukhara, Uzbekistan
Abstract: 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 $n\ge 3$. 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.
Keywords: three-particle lattice Hamiltonian, non-local interaction operators, Hubbard model, Faddeev equation, essential and discrete spectrum.
Received: 05.05.2014
Bibliographic databases:
Document Type: Article
PACS: 02.30.Tb
Language: English
Citation: T. H. Rasulov, Z. D. Rasulova, “Essential and discrete spectrum of a three-particle lattice Hamiltonian with non-local potentials”, Nanosystems: Physics, Chemistry, Mathematics, 5:3 (2014), 327–342
Citation in format AMSBIB
\Bibitem{RasRas14}
\by T.~H.~Rasulov, Z.~D.~Rasulova
\paper Essential and discrete spectrum of a three-particle lattice Hamiltonian with non-local potentials
\jour Nanosystems: Physics, Chemistry, Mathematics
\yr 2014
\vol 5
\issue 3
\pages 327--342
\mathnet{http://mi.mathnet.ru/nano862}
\elib{https://elibrary.ru/item.asp?id=21630408}
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