{
  "annotation_id": "67d5e5cd-5b1a-4b5b-af9a-d39be250dfe5",
  "date_created": "2026-03-02T18:01:42.360000Z",
  "date_modified": "2026-03-02T18:01:42.360000Z",
  "file_hash": "0d9d3087a948ad92eef98a0b041a190df9572b58e9126127cb7c5105c7fd3f6d",
  "private": false,
  "record": {
    "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"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "88e5b3cb-bf9d-4ddf-87db-f92e3bc2e09e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}