Geodesic
Essential and discrete spectrum of a three-particle lattice Hamiltonian with non-local potentials
Nanosistemy: fizika, himiâ, matematika, Tome 5 (2014) no. 3, pp. 327-342.

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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. 
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     author = {T. H. Rasulov and Z. D. Rasulova},
     title = {Essential and discrete spectrum of a three-particle lattice {Hamiltonian} with non-local potentials},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {327--342},
     publisher = {mathdoc},
     volume = {5},
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     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2014_5_3_a0/}
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T. H. Rasulov; Z. D. Rasulova. Essential and discrete spectrum of a three-particle lattice Hamiltonian with non-local potentials. Nanosistemy: fizika, himiâ, matematika, Tome 5 (2014) no. 3, pp. 327-342. http://geodesic.mathdoc.fr/item/NANO_2014_5_3_a0/