On the essential spectrum of a model operator associated with the system of three particles on a lattice. (Russian. English summary) Zbl 1449.81021
Summary: A model operator \(H\) associated with the system of three-identical particles on a lattice \(\mathbb{Z}^3\) is considered. The location of the essential spectrum of \(H\) is described by the spectrum of the corresponding Friedrichs model, that is, the two-particle and three-particle branches of the essential spectrum of \(H\) are singled out. It is proved that the essential spectrum of \(H\) consists of no more than three bounded closed intervals. An appearance of two-particle branches on the both sides of the three-particle branch is shown. Moreover, we obtain an analogue of the Faddeev equation and its symmetric version, for the eigenfunctions of \(H\).
MSC:
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 35P20 | Asymptotic distributions of eigenvalues in context of PDEs |
| 47N50 | Applications of operator theory in the physical sciences |
Keywords:
model operator; Friedrichs model; Hilbert-Schmidt class; Faddeev equation; essential spectrumReferences:
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