, Volume 103, Issue 1, pp 398-411

Spectrum and scattering in a “spin-boson” model with not more than three photons

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Abstract

A model of radiative decay with a fixed atom and not more than three photons is studied. A spectral analysis of the Hamiltonian is made. This is done by means of scattering theory in a pair of spaces with a specially chosen embedding. The existence of wave operators and their asymptotic completeness are proved. The constructions are based on a detailed analysis of the resolvent of the Hamiltonian.

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 1, pp. 63–81, April, 1995.