On Rayleigh Scattering in Non-Relativistic Quantum Electrodynamics

Abstract

We consider a particle system coupled to the quantized electromagnetic or phonon field. Assuming that the coupling is small enough and that Fermi’s Golden Rule is satisfied, we prove asymptotic completeness for Rayleigh scattering on the states for which the expectation of either the photon/phonon number operator or an operator testing the photon/phonon infrared behaviour is uniformly bounded on corresponding dense sets. By extending a recent result of De Roeck and Kupiainen in a straightforward way, we show that the second of these conditions is satisfied for the spin-boson model.