Abstract:
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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