This article is cited in 18 papers

Branches of the essential spectrum of the lattice spin-boson model with at most two photons

T. H. Rasulov

Faculty of Physics and Mathematics, Bukhara State University, Bukhara, Uzbekistan

Abstract: 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.

Received: 18.01.2015
Revised: 13.04.2015

DOI: 10.4213/tmf8854

 English version: Theoretical and Mathematical Physics, 2016, 186:2, 251–267

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