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A discrete “three-particle” Schrödinger operator in the Hubbard model. (English) Zbl 1177.82075
Theor. Math. Phys. 149, No. 2, 1497-1511 (2006); translation from Teor. Mat. Fiz. 149, No. 2, 228-243 (2006).
Summary: 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 $$\hat{H} = H_{0} + H_{1} + H_{2}$$, 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 $$\hat{H}$$. We study the discrete and essential spectra of the Hamiltonians $$H^{t}$$ and $$h$$ arising in the Hubbard model on the three-dimensional lattice.

##### MSC:
 82C10 Quantum dynamics and nonequilibrium statistical mechanics (general) 47B25 Linear symmetric and selfadjoint operators (unbounded)
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##### References:
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