Essential and discrete spectrum of a three-particle lattice Hamiltonian with non-local potentials
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 ≥ 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
Supporting agencies: This work was supported by the IMU Einstein Foundation Program. T. H. Rasulov wishes to thank the Berlin Mathematical School and Weierstrass Institute for Applied Analysis and Stochastics for the invitation and hospitality.
About the Authors
T. H. Rasulov
Bukhara State University
Uzbekistan
Uzbekistan
Bukhara
Z. D. Rasulova
Bukhara State University
Uzbekistan
Uzbekistan
Bukhara
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Review
For citations:
Rasulov T.H., Rasulova Z.D. Essential and discrete spectrum of a three-particle lattice Hamiltonian with non-local potentials. Nanosystems: Physics, Chemistry, Mathematics. 2014;5(3):327-342.
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