A. Galtbayar, A. Jensen, K. Yajima
The Nelson Model with Less Than Two Photons
(392K, pdf)

ABSTRACT.  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 
wave operators giving the asymptotic dynamics.