Geodesic
Branches of the essential spectrum of the lattice spin-boson model with at most two photons
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 2, pp. 293-310 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a lattice analogue of the $\mathcal A_m$ model of light radiation with a fixed atom and at most $m$ photons $(m=1,2)$. We describe the essential spectrum of the operator $\mathcal A_2$ in terms of the spectrum of the operator $\mathcal A_1$, i.e., we find the “two-particle” and “three-particle” branches of the essential spectrum of $\mathcal A_2$. We prove that the essential spectrum is a union of at most six intervals, and we study their positions. We derive an estimate for the lower bound of the “two-particle” and “three-particle” branches.
Keywords: spin-boson model, boson Fock space, block operator matrix, annihilation operator, creation operator, essential spectrum, discrete spectrum, Weyl criterion. 
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     title = {Branches of the~essential spectrum of the~lattice spin-boson model with at most two photons},
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T. H. Rasulov. Branches of the essential spectrum of the lattice spin-boson model with at most two photons. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 2, pp. 293-310. http://geodesic.mathdoc.fr/item/TMF_2016_186_2_a7/

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