NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2014, 5 (3), P. 327-342
ESSENTIAL AND DISCRETE SPECTRUM OF A THREE-PARTICLE LATTICE HAMILTONIAN WITH NON-LOCAL POTENTIALS
T. H. Rasulov – Bukhara State University, Bukhara, Uzbekistan; firstname.lastname@example.org
Z. D. Rasulova – Bukhara State University, Bukhara, Uzbekistan; email@example.com
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.
Keywords: three-particle lattice Hamiltonian, non-local interaction operators, Hubbard model, Faddeev equation, essential and discrete spectrum.