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

Pavel Exner·Milos Tater·David Vanek
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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 $N\to\infty$. We illustrate the result on two kinds of examples. The first are serial graphs obtained by chaining loops or T-junctions. A detailed discussion is presented for a finite-periodic "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 decoupled-surface eigenvalues such scatterers exhibit the high-energy behavior typical for the delta' interaction for the physically interesting couplings.

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Pavel Exner, Milos Tater, David Vanek. 2001-03-16. A single-mode quantum transport in serial-structure geometric scatterers. https://doi.org/10.1063/1.1389287

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