**6. Steady-State**

The investigation of the time dependent transport of electrons through a photon cavity soon made it clear that for the continuous model the inherent time scales can lead to relaxation times far beyond what is accessible with simple integration of the GME [32,45,46,49,91]. The underlying cause for the diverse relaxation times is on one hand electron tunneling rates affected by the shape or geometry of the system and the condition of weak coupling. Different many-body states can have a high or low probability for electrons to be found in the contact areas of the central system. On the other hand are slow rates of FIR or terahetz active transitions, that are furthermore affected by the geometry of the wavefunctions of the corresponding final and initial states. In addition, the cavity decay, or coupling to the environment, affects relaxation times as we address below [98]. To avoid confusion it is important to remember that we calculate the eigenstates of the closed central system, the interacting electron and photon system, and the opening up of the system to the leads or the external photon reseroir is always a neccessary triggering mechanism for all transitions later in time, photon active or not.
