ASYMPTOTIC COMPLETENESS FOR THE SPIN-BOSON MODEL WITH A PARTICLE NUMBER CUTOFF

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Abstract
We study the spin-boson model with a particle number cutoff. The spin-boson model is a simplified model of an atom interacting with a quantized photon field. An important physical phenomenon that one would like to understand rigorously on this model is the phenomenon of radiative decay, where the atom asymptotically relaxes to its ground state by emitting photons. One of the possible approaches to radiative decay is through scattering theory. For the cutoff spin-boson hamiltonian, we prove the existence and asymptotic completeness of the channel wave operators, which have natural interpretation in terms of the radiative decay property.

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