This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Muminov, MukhiddinNeidhardt, HagenRasulov, Tulkin2016-03-242019-06-2820142198-5855https://doi.org/10.34657/2879https://oa.tib.eu/renate/handle/123456789/2914A lattice model of radiative decay (so-called spin-boson model) of a two level atom and at most two photons is considered. The location of the essential spectrum is described. For any coupling constant the finiteness of the number of eigenvalues below the bottom of its essential spectrum is proved. The results are obtained by considering a more general model H for which the lower bound of its essential spectrum is estimated. Conditions which guarantee the finiteness of the number of eigenvalues of H below the bottom of its essential spectrum are found. It is shown that the discrete spectrum might be infinite if the parameter functions are chosen in a special form.application/pdfeng510spin-boson Hamiltonianblock operator matrixbosonic Fock spaceannihilation and creation operatorsBirman-Schwinger principleessential spectrumpoint and discrete spectrumReport