Transport Channels in a Double Junction- coherent coupling changes the picture

Transport through a point contact is accurately modelled by assigning to the junction an ensemble of independent transport channels with possibly different transmissions. We here argue that for a series of two contacts, coherently coupled across an island, the transport channels are different from the ensembles that would describe each contact taken as stand-alone device. We further show that instead of two sets of channels with manifold cross-links over the island the double junction can be described by pairs of channels from both sides coherently coupled together, where each pair, however, has no coherent connection to the others. This finding will substantially simplify modelling transport by a Green's functions technique. Additional channels through only one junction may complete the picture. Finally we discuss how partial coherence across the island with an appropriate ansatz can be modelled in the same scheme.