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.