Transfer Matrix of Scatterers Connected in Parallel

TL;DR

This paper develops a transfer matrix approach to analyze transport in parallel-connected scatterers, deriving recurrence relations and describing how parallel connections influence overall transport properties.

Contribution

It introduces a recurrence relation for transfer matrices of parallel-connected scatterers and characterizes the effects of connection topology on transport.

Findings

Recurrence relation for transfer matrices of parallel scatterers

Parallel connection effects described by similarity transformation

Transport properties depend on scattering matrices and connection topology

Abstract

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.