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Investigation of the spectrum of a model operator in a Fock space. (English. Russian original) Zbl 1183.81066

Theor. Math. Phys. 161, No. 2, 1460-1470 (2009); translation from Teor. Mat. Fiz. 161, No. 2, 164-175 (2009).
Summary: We consider a model operator \(H\) corresponding to a quantum system with a nonconserved finite number of particles on a lattice. Based on an analysis of the spectrum of the channel operators, we describe the position of the essential spectrum of \(H\). We obtain a Faddeev-type equation for the eigenvectors of \(H\).
In an erratum [Theor. Math. Phys. 162, No. 2, 254 (2009); translation from Teor. Mat. Fiz. 162, No. 2, 304 (2009)] two misprints have been corrected.

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81V70 Many-body theory; quantum Hall effect
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References:

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