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

Jean Francois Bony (1) , Jérémy Faupin (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 LMAM - Laboratoire de Mathématiques et Applications de Metz

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 I just above the ground state energy. Our results are uniform with respect to I. Their proofs are based on abstract Mourreʼs 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.

Mots clés: Non-relativistic QED; Resolvent estimates; Local energy decay; Mourre theory

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Jean Francois Bony, Jérémy Faupin. Resolvent smoothness and local decay at low energies for the standard model of non-relativistic QED. Journal of Functional Analysis, 2012, 262 (3), pp.850-888. ⟨10.1016/j.jfa.2011.10.006⟩. ⟨hal-00994365⟩