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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2002-39
December 2002

The Nelson Model with Less Than Two Photons


A. Galtbayar, A. Jensen and K. Yajima


We study the spectral and scattering theory of the Nelson model for an atom interacting with a photon field in the subspace with less than two photons. For the free electron-photon system, the spectral property of the reduced Hamiltonian in the center of mass coordinates and the large time dynamics are determined. If the electron is under the influence of the nucleus via spatially decaying potentials, we locate the essential spectrum, prove the absence of singular continuous spectrum and the existence of the ground state, and construct wawe operators giving the asymptotic dynamics.

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This paper has now been published in Ann. H. Poincaré 4 (2003), 239-273