Lindblad approximation and spin relaxation in quantum electrodynamics

This article is concerned with the time evolution of spin observables for generalized spin boson models. This applies in particular to a model of nuclear magnetic resonance, namely a 12-spin particle in a constant external magnetic field and in interaction with the quantized electromagnetic field (photons). We derive a Lindblad (or GKLS) type approximation of the spin dynamics initially in a photon vacuum state together with a precise control of the error coming from this approximation. The error term is bounded by g(2) where g is the coupling constant of the spin-photon interaction. The point here is the uniformity in time t > 0 of this error control.