A single-mode quantum transport in serial-structure geometric scatterers

Abstract

We study transport in quantum systems consisting of a finite array of N identical single-channel scatterers. A general expression of the S matrix in terms of the individual-element data obtained recently for potential scattering is rederived in this wider context. It shows in particular how the band spectrum of the infinite periodic system arises in the limit N→∞. We illustrate the result on two kinds of examples. The first are serial graphs obtained by chaining loops or T-junctions. Another example concerns geometric scatterers where the individual element consists of a surface with a pair of leads; we show that apart from the resonances coming from the decoupled-surface eigenvalues, such scatterers exhibit the high-energy behavior typical for the δ′ interaction for the physically interesting couplings.