Abstract: We study the spectrum of the spin-boson Hamiltonian with two bosons for arbitrary coupling [Formula: see text] in the case when the dispersion relation is a bounded function. We derive an explicit description of the essential spectrum which consists of the so-called two- and three-particle branches that can be separated by a gap if the coupling is sufficiently large. It turns out, that depending on the location of the coupling constant and the energy level of the atom (w.r.t. certain constants dependi… Show more
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