Sib. Èlektron. Mat. Izv., 2015, Volume 12, Pages 168–184
On the spectrum of a three-particle model operator on a lattice with non-local potentials
T. Kh. Rasulov, Z. D. Rasulova
Bukhara State University, Muhammad Igbol, 11, 705018 Bukhara, Uzbekistan
A model operator $H$ associated to a system of three particles on a $d$-dimensional lattice that interact via non-local potentials is considered. The channel operators are identified. An analogue of the Faddeev equation for the eigenfunctions of $H$ is constructed and the spectrum of $H$ is described. The location of the essential spectrum of $H$ is described by the spectrum of channel operators. It is shown that the essential spectrum of $H$ consists the union of at most $2n+1$ bounded closed intervals, where $n$ is the rank of the kernel of non-local interaction operators. The upper bound of the spectrum of $H$ is found. The lower bound of the essential spectrum of $H$ for the case $d=1$ is estimated.
model operator, discrete Schrödinger operator, non-local interaction operators, Hubbard model, channel operator, Hilbert–Schmidt class, Faddeev equation, essential and discrete spectrum.
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Received August 4, 2014, published March 14, 2015
T. Kh. Rasulov, Z. D. Rasulova, “On the spectrum of a three-particle model operator on a lattice with non-local potentials”, Sib. Èlektron. Mat. Izv., 12 (2015), 168–184
Citation in format AMSBIB
\by T.~Kh.~Rasulov, Z.~D.~Rasulova
\paper On the spectrum of a three-particle model operator on a lattice with non-local potentials
\jour Sib. \`Elektron. Mat. Izv.
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