Geodesic
A discrete “three-particle" Schrödinger operator in the Hubbard model
Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 2, pp. 228-243 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {A~discrete {\textquotedblleft}three-particle" {Schr\"odinger} operator in {the~Hubbard} model},
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Yu. Kh. Èshkabilov. A discrete “three-particle" Schrödinger 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/

[1] D. Mattis, Rev. Mod. Phys., 58 (1986), 361–379 ; E. Lieb, Phys. Rev. Lett., 62 (1989), 1201–1204 ; A. M. Tsvelick, P. B. Wiegman, Adv. Phys., 32 (1983), 453–713 | DOI | MR | DOI | MR | DOI

[2] B. V. Karpenko, V. V. Dyakin, G. A. Budrina, FMM, 61:4 (1986), 702–706

[3] Yu. A. Izyumov, Yu. N. Skryabin, Statisticheskaya mekhanika magnitno-uporyadochennykh sistem, Nauka, M., 1974 | MR

[4] L. D. Landau, E. M. Lifshits, Kvantovaya mekhanika. Nerelyativistskaya teoriya, Nauka, M., 1974 | MR

[5] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki. {\tm T. 1.} Funktsionalnyi analiz, Mir, M., 1977 | MR

[6] Yu. Kh. Eshkabilov, Dokl. AN RUz, 2006

[7] F. Trikomi, Integralnye uravneniya, IL, M., 1960

[8] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki. T. 4. Analiz operatorov, Mir, M., 1982 | MR

[9] M. Yu. Fedoryuk, Asimptotika: integraly i ryady, Nauka, M., 1987 | MR | Zbl