Transfer Matrix of Scatterers Connected in Parallel

Transport phenomena in parallel coupled scatterers are studied by transfer matrix formulism. We derive a simple recurrence relation for transfer matrix of one-dimensional two-terminal systems consisting of $N$ arbitrary scattering unit cells connected in parallel. For identical scattering sub-units we find that the effects of parallel connection on transport properties of the coupled system can be described by a similarity transformation on the single scatterer, with the similar matrix determined by the scattering matrix of the junction. While for distinct single scatterers, the similar matrices depend on both scattering properties of individual elements and structure of connection topologies.