A~discrete ``three-particle" Schr\"odinger operator in the~Hubbard model
Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 2, pp. 228-243
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In the space $L_2(T^ \nu \times T^\nu)$, where $T^\nu$ is a $\nu$-dimensional
torus, we study the spectral properties of the "three-particle" discrete
Schrödinger operator $\widehat H=H_0+H_1+H_2$, where $H_0$ is the operator of
multiplication by a function and $H_1$ and $H_2$ are partial integral
operators. We prove several theorems concerning the essential spectrum of
$\widehat H$. We study the discrete and essential spectra of the Hamiltonians
$H^{\mathrm{t}}$ and $\mathbf{h}$
arising in the Hubbard model on the three-dimensional
lattice.
Keywords:
discrete Schrödinger operator, Hubbard model, discrete spectrum of a discrete operator, essential spectrum of a discrete operator.
@article{TMF_2006_149_2_a4,
author = {Yu. Kh. \`Eshkabilov},
title = {A~discrete ``three-particle" {Schr\"odinger} operator in {the~Hubbard} model},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {228--243},
publisher = {mathdoc},
volume = {149},
number = {2},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a4/}
}
TY - JOUR AU - Yu. Kh. Èshkabilov TI - A~discrete ``three-particle" Schr\"odinger operator in the~Hubbard model JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2006 SP - 228 EP - 243 VL - 149 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a4/ LA - ru ID - TMF_2006_149_2_a4 ER -
Yu. Kh. Èshkabilov. A~discrete ``three-particle" Schr\"odinger operator in the~Hubbard model. Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 2, pp. 228-243. http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a4/