**Abstract: **Repeated interaction of a beam of two-level atoms with a one-mode photon cavity can produce a quite curious dynamics of the cavity state. For stationary beam of (randomly) excited atoms this state is not stationary and manifests a pumping by photons. For the case of a leaking cavity (Kossakowski-Lindblad dissipation) the corresponding open system yields a non-equilibrium steady state (NESS). This talk is a part of the France-Berkeley project in collaboration with Bruno Nachtergaele and Anna Vershynina (UC Davis).