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 $N\to \infty$. 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.

36 pages, a LaTeX source file with 2 TeX drawings, 3 ps and 3 jpeg figures attached

References in corpus (8)

• Kirchhoff's Rule for Quantum Wires
• Contact interactions on graph superlattices
• Weakly coupled states on branching graphs
• The Generalized Star Product and the Factorization of Scattering Matrices on Graphs
• Band spectra of rectangular graph superlattices
• Stability of driven systems with growing gaps, Quantum rings and Wannier ladders
• Resonance statistics in a microwave cavity with a thin antenna
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• Electron transport in a two-terminal Aharonov-Bohm ring with impurities
• Approximations by graphs and emergence of global structures
• Evolution with size in a locally periodic system: Scattering and deterministic maps
• Möbius transformations and electronic transport properties of large disorderless networks
• A quantum hybrid with a thin antenna at the vertex of a wedge
• Non-equilibrium current via geometric scatterers