  We calculate the stationary current through two double quantum dots which are
interacting via a common phonon environment. Numerical and analytical solutions
of a master equation in the stationary limit show that the current can be
increased as well as decreased due to a dissipation mediated interaction. This
effect is closely related to collective, spontaneous emission of phonons (Dicke
super- and subradiance effect), and the generation of a `cross-coherence' with
entanglement of charges in singlet or triplet states between the dots.
Furthermore, we discuss an inelastic `current switch' mechanism by which one
double dot controls the current of the other.
