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

We study transport in quantum systems consisting of a finite array of N ide ntical single-channel scatterers. A general expression of the S matrix in t erms of the individual-element data obtained recently for potential scatter ing is rederived in this wider context. It shows in particular how the band spectrum of the infinite periodic system arises in the limit N --> infinit y. 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 wit h a pair of leads; we show that apart from the resonances coming from the d ecoupled-surface eigenvalues, such scatterers exhibit the high-energy behav ior typical for the delta' interaction for the physically interesting coupl ings. (C) 2001 American Institute of Physics.