 01101 Pavel Exner, Milos Tater, David Vanek
 A singlemode quantum transport in serialstructure
geometric scatterers
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Mar 15, 01

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Abstract. We study transport in quantum systems consisting of a
finite array of N identical singlechannel scatterers. A
general expression of the S matrix in terms of the
individualelement 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 $N\to\infty$. We illustrate the result on
two kinds of examples. The first are serial graphs obtained by
chaining loops or Tjunctions. A detailed discussion is presented
for a finiteperiodic "comb"; we show how the resonance poles
can be computed within the Krein formula approach. Another example
concerns geometric scatterers where the individual element
consists of a surface with a pair of leads; we show that apart of
the resonances coming from the decoupledsurface eigenvalues such
scatterers exhibit the highenergy behavior typical for the
delta' interaction for the physically interesting couplings.
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