Resolvent smoothness and local decay at low energies for the standard model of non-relativistic QED

We consider an atom interacting with the quantized electromagnetic field in the standard model of non-relativistic QED. The nucleus is supposed to be fixed. We prove smoothness of the resolvent and local decay of the photon dynamics for quantum states in a spectral interval / just above the ground state energy. Our results are uniform with respect to I. Their proofs are based on abstract Mourre's theory, a Mourre inequality established by Frohlich. Griesemer and Sigal (see Frohlich et al. (2008) [14]), Hardy-type estimates in Fock space, and a low-energy dyadic decomposition. (C) 2011 Elsevier Inc. All rights reserved.