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 nonrelativistic 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 I 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 Fröhlich, Griesemer and Sigal (see Fröhlich et al. (2008) [14]), Hardy-type estimates in Fock space, and a low-energy dyadic decomposition. © 2011 Elsevier Inc. All rights reserved