Mixing properties of the one-atom maser

We study the relaxation properties of the quantized electromagnetic field in a cavity under repeated interactions with single two-level atoms, so-called one-atom maser. We improve the ergodic results obtained in Bruneau and Pillet (J Stat Phys 134(5–6):1071–1095, 2009) and prove that, whenever the atoms are initially distributed according to the canonical ensemble at temperature $T>0$ , all the invariant states are mixing. Under some non-resonance condition this invariant state is known to be thermal equilibirum at some renormalized temperature $T^*$ and we prove that the mixing is then arbitrarily slow, in other words that there is no lower bound on the relaxation speed.