dorsal/arxiv
View SchemaA single-mode quantum transport in serial-structure geometric scatterers
| Authors | Pavel Exner, Milos Tater, David Vanek |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0103094 |
| URL | https://arxiv.org/abs/quant-ph/0103094 |
| DOI | 10.1063/1.1389287 |
| Journal | J. Math. Phys. 42 (2001), 4050-4078 |
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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"abstract": "We study transport in quantum systems consisting of a finite array of N\nidentical single-channel scatterers. A general expression of the S matrix in\nterms of the individual-element data obtained recently for potential scattering\nis rederived in this wider context. It shows in particular how the band\nspectrum of the infinite periodic system arises in the limit $N\\to\\infty$. We\nillustrate the result on two kinds of examples. The first are serial graphs\nobtained by chaining loops or T-junctions. A detailed discussion is presented\nfor a finite-periodic \"comb\"; we show how the resonance poles can be computed\nwithin the Krein formula approach. Another example concerns geometric\nscatterers where the individual element consists of a surface with a pair of\nleads; we show that apart of the resonances coming from the decoupled-surface\neigenvalues such scatterers exhibit the high-energy behavior typical for the\ndelta\u0027 interaction for the physically interesting couplings.",
"arxiv_id": "quant-ph/0103094",
"authors": [
"Pavel Exner",
"Milos Tater",
"David Vanek"
],
"categories": [
"quant-ph",
"cond-mat",
"math-ph",
"math.MP"
],
"doi": "10.1063/1.1389287",
"journal_ref": "J. Math. Phys. 42 (2001), 4050-4078",
"title": "A single-mode quantum transport in serial-structure geometric scatterers",
"url": "https://arxiv.org/abs/quant-ph/0103094"
},
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